CONSTRUCTION TECHNIQUE AND STRENGTH OF CONNECTED  
REGOLITH BAG STRUCTURES 
 
 
Except where reference is made to the work of others, the work described in this thesis is 
my own or was done in collaboration with my advisory committee. This thesis does not 
include proprietary or classified information. 
 
 
Mandeep Singh 
 
 
 
Certificate of Approval: 
 
 
P.K. Raju David G Beale, Chair 
Thomas Walter Professor Professor 
Mechanical Engineering Mechanical Engineering 
 
 
 
 
 
Royall M. Broughton  Joe F. Pittman 
Professor Interim Dean 
Polymer and Fiber Engineering Graduate School
CONSTRUCTION TECHNIQUE AND STRENGTH OF CONNECTED  
REGOLITH BAG STRUCTURES 
 
Mandeep Singh 
 
 
 
A Thesis 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Master of Science 
 
 
Auburn, Alabama 
May 10, 2007 
 iii
CONSTRUCTION TECHNIQUE AND STRENGTH OF CONNECTED REGOLITH BAG 
STRUCTURES 
 
 
 
Mandeep Singh 
 
 
 
Permission is granted to Auburn University to make copies of this thesis at its  
discretion, upon the request of individuals or institutions and at their expense. 
The author reserves all publication rights. 
 
 
 
 
 Signature of Author 
 
 
 Date of Graduation 
 
 iv
VITA 
 
Mandeep Singh, son of Harbinder Pal Singh and Harvinder Kaur, was born on 
August 2, 1982 in Jamshedpur India. He graduated with a Bacherlor of Engineering 
degree in Mechanical Engineering in May 2004 from Madras University, India. He 
entered the graduate program at Auburn University in August 2004, where he worked 
under Dr. David Beale as a graduate research assistant in Mechanical Engineering 
department.   
 v
THESIS ABSTRACT 
CONSTRUCTION TECHNIQUE AND STRENGTH OF CONNECTED  
REGOLITH BAG STRUCTURES 
 
Mandeep Singh 
Master of Science, May 10, 2007 
(B.E, University of Madras, India, 2004) 
 
125 Typed Pages 
Directed by David G. Beale 
Masonry Arches have been used from a long time in construction of bridges, 
domes and other structures. They are constructed out of voussoirs and their stability is 
determined by drawing a funicular polygon representing force flow through the structure. 
If this line remains inside the structure then its stable, otherwise it forms hinges at the 
locations where the line comes outside of the structure, and collapses.  
The work presented in this thesis implements the use of funicular polygons in 
determining the stability of lunar structures prototypes made out of bags filled with 
regolith (lunar soil). These structures are made in the shape of a catenary arch using 
center connected and top connected bags. Various structures are developed at Auburn 
University and MSFC, to test their stability. Structures made out of top connected bags 
are found to be more stable, as demonstrated by construction of a simply hanging beam 
made out of top connected bags. During construction at Auburn University and 
 vi
MSFC, both the top and center connected bags are filled with vermiculite because of its 
light weight and also because of lack of regolith on Earth. 
These structures are constructed on frames which are removed after the structure 
is built completely. The structures are designed to be stable under their own load so the 
frames are not required once the construction is over. They are also designed such that 
the construction process can be carried out by taking minimum amount of material from 
Methods of filling the bags with regolith are also investigated and a screw conveyor 
system is found to be the most reliable. The stability of these structures is found by 
constructing funicular polygons, under given load conditions, in Solid Edge. This 
technique of determining the stability is found useful and reliable in construction of lunar 
structures that are based on masonry arches.  
 vii
ACKNOWLEDGMENTS 
 
I would like to thank Dr. Beale for his support and advice throughout my research 
at Auburn University. I would also like to thank Dr. Raju and Dr. Broughton for being on 
my graduate committee and for their contribution to my thesis. I would like to 
acknowledge my research mates Manoj Rajagopalan, David Branscomb, and staff of 
Polymer and Fiber Engineering Jeff Thompson, David Clark who helped me in various 
stages of my thesis. Finally, I would like to express my deepest gratitude to my parents, 
my sister and my friends whose love and encouragement has guided me through towards 
my goal.  
 viii
Style manual or journal used: Guide to Preparation and Submission of Theses and 
Dissertations 2005 
Computer software used: Microsoft
?
 Word
?
 2003, Microsoft
?
 Excel
?
 2003, 
Microsoft
?
 Visio
?
 2003, Solid Edge
?
, MSC
?
. Working Model 
 ix
TABLE OF CONTENTS 
LIST OF FIGURES xi 
LIST OF TABLES xiv 
CHAPTER ONE: INTRODUCTION................................................................................. 1 
1.1 Scope of thesis..........................................................................................................................1 
1.2 An overview of thesis.............................................................................................................2 
 
CHAPTER TWO: BACKGROUND.................................................................................. 3 
2.1  Scientific Importance of Moon............................................................................................3 
2.2  Development Phases...............................................................................................................5 
2.3  Challenges in Designing a Lunar Base..............................................................................6 
2.4  Requirements of a Lunar Base.............................................................................................8 
2.5  Oxygen Production................................................................................................................10 
2.6  Site Selection ..........................................................................................................................10 
2.7  Construction Materials.........................................................................................................13 
2.7.1  Regolith..........................................................................................................................13 
2.7.2  Cast Basalt and Glass.................................................................................................13 
2.7.3  Ceramics ........................................................................................................................14 
2.7.4  Cement ...........................................................................................................................14 
2.7.5  Metals .............................................................................................................................14 
2.8  Design of Masonry Arches .................................................................................................14 
2.9  Stability of Arch.....................................................................................................................16 
2.10  Design of Voussoir Arches .................................................................................................19 
2.10.1  Shape of the Arch........................................................................................................20 
2.10.2  Thickness of Masonry Arch.....................................................................................21 
2.10.3  Horizontal Thrust ........................................................................................................22 
2.11  Research Objective................................................................................................................28 
 
CHAPTER THREE: LUNAR STRUCTURES................................................................ 30 
3.1  Cable Structures .....................................................................................................................31 
3.1.1  Small Span System.....................................................................................................31 
3.1.2  Medium Span Structure.............................................................................................33 
3.1.3  Long Span Systems ....................................................................................................33
 x
3.2  Mobile Lunar Bases ..............................................................................................................34 
3.3  Inflatable Structures..............................................................................................................35 
 
CHAPTER FOUR: EXPERIMENTAL SETUP............................................................... 38 
4.1  Types of Bags .........................................................................................................................38 
4.1.1.  Center Connected Bags .............................................................................................38 
4.2.2.  Top Connected Bags ..................................................................................................39 
4.2  Stitching Techniques and Materials used for Bags......................................................41 
4.3  Techniques used for Filling Bags......................................................................................42 
4.3.1.  Vermiculite and its Properties .................................................................................42 
4.3.2  Manual Filling of Bags..............................................................................................44 
4.3.3  Filling of bags using Sand Blower.........................................................................45 
4.3.4  Leaf Blower ..................................................................................................................47 
4.3.5  Screw Conveyor System...........................................................................................49 
4.4  Frames.......................................................................................................................................51 
4.4.1  Frame for 8 Bag Structure ........................................................................................51 
4.4.2  Frame for 16 Bag Center Connected Structure ..................................................53 
4.4.3  Frame for 60 Bag Top Connected Structure .......................................................55 
 
CHAPTER FIVE: ANALYTICAL TEST OF STABILITY ............................................ 58 
5.1  Exploratory study to build a Working Model brick element from Springs and 
Dampers.................................................................................................................................................59 
5.2  Excel Spread Sheet................................................................................................................69 
5.3  Stability of 8 Bag Structure ................................................................................................71 
5.4  Stability of 16 Bags Structure ............................................................................................75 
5.5  Stability of 46 and 60 Bags Structure ..............................................................................80 
5.6  Stability of 60 Bags Structures ..........................................................................................82 
5.6.1  Erecting the Structure ................................................................................................89 
 
CHAPTER SIX: CONCLUSIONS AND SUMMARY ................................................... 98 
6.1  Thesis Summary.....................................................................................................................98 
6.2  Future Research and development....................................................................................99 
REFERENCES ............................................................................................................... 101 
APPENDIX A...?.??????????????????????????..104 
APPENDIX B...?.??????????????????????????..108 
APPENDIX C...?.??????????????????????????..110 
 
 xi
LIST OF FIGURES 
Figure 1  Proposed Lunar Sites on Moon.......................................................................... 12 
Figure 2 Parts of Masonry Arch........................................................................................ 15 
Figure 3 Line of thrust lying inside the arch..................................................................... 18 
Figure 4 a. Formation of hinges b. Line of thrust acting through the arch ....................... 19 
Figure 5 Catenary.............................................................................................................. 20 
Figure 6 Catenary arch with loads acting on it ................................................................. 22 
Figure 7 Catenary arch with dimension (in) ..................................................................... 24 
Figure 8 Force Diagram for the catenary.......................................................................... 25 
Figure 9 First line drawn parallel to the line connecting h and W4.................................. 26 
Figure 10 Second line drawn from the first intersection point to W3 .............................. 27 
Figure 11 The completed funicular polygon lying inside the arch ................................... 28 
Figure 12 Small Span System........................................................................................... 32 
Figure 13 Medium Span System....................................................................................... 33 
Figure 14 Long Span Systems .......................................................................................... 34 
Figure 15 Habitat made out of three modules................................................................... 35 
Figure 16 Inflatable Structures.......................................................................................... 36 
Figure 17 Cal Earth Structure Concepts ........................................................................... 37 
Figure 18 Center Connected Bags .................................................................................... 39 
Figure 19 Top Connected Bags......................................................................................... 40 
Figure 20 Structure made out of Top Connected Bags..................................................... 40 
Figure 21 Stitch................................................................................................................. 41 
Figure 22 Center Connected Bags Filled with Vermiculite.............................................. 44 
Figure 23 Sand Blower ..................................................................................................... 45 
Figure 24 Schematic of Sand Blower used....................................................................... 46 
Figure 25 Leaf Blower...................................................................................................... 48
 
 xii
Figure 26 Screw Conveyor System- Image shows a motor attached to helical screw 
running inside the tube. The container is filled with vermiculite. When vermiculite 
pours into the screw it is carried through the pipe and into the bags........................ 50 
Figure 27 Frame for 8 Bag structure with dimensions (in)............................................... 52 
Figure 28 Structure without frame.................................................................................... 53 
Figure 29 Frame for 16 Bag structure............................................................................... 54 
Figure 30 Structure without the frame.............................................................................. 55 
Figure 31 Frame for 60 Bag Structure .............................................................................. 56 
Figure 32 46 bag structure resting on its frame ................................................................ 57 
Figure 33 First Working Model Brick Element developed using springs, dampers and 
rigid bodies................................................................................................................ 60 
Figure 34 A closer look at the model developed .............................................................. 60 
Figure 35 A set of 2 brick elements fixed together to act as a beam ................................ 61 
Figure 36 The Model falling down under the load of gravity........................................... 61 
Figure 37 Next model developed with rigid elements on top........................................... 62 
Figure 38 Model failing under the load of gravity............................................................ 62 
Figure 39 Graph showing the y-position of the model ..................................................... 63 
Figure 40 Next model developed with rigid bodies on both the outside and inside. The 
outer bodies are used to model bag and inner bodies are used to model sand.......... 64 
Figure 41 The model vibrates under the load of gravity................................................... 64 
Figure 42 Graph showing the oscillatory motion of the model ........................................ 64 
Figure 43 Model with balls to simulate sand packed inside bags..................................... 65 
Figure 44 Model failing under the load of gravity............................................................ 66 
Figure 45 Graph showing the y-position of the model ..................................................... 66 
Figure 46 Arch Constructed using springs and rigid bodies............................................. 68 
Figure 47 Arch stable when simulated in Working Model............................................... 69 
Figure 48 Arch with various loads acting on it................................................................. 70 
Figure 49 Center Connected Bags with no Load.............................................................. 72 
Figure 50 Funicular Polygon for 8 bag structure with 150 lbs weight on it ..................... 73 
Figure 51 8 bag structure forming M-shape when loaded ................................................ 74
 xiii
 
Figure 52 Funicular polygon of loaded 8 bag structure.................................................... 74 
Figure 53 Buckle on each pocket, fixed using rivets........................................................ 77 
Figure 54 Bags stacked on each other............................................................................... 78 
Figure 55 16 bag structure standing without frame .......................................................... 79 
Figure 56 Funicular polygon developed for the 16 bag structure..................................... 80 
Figure 57 Funicular Polygon for 46 bag structure............................................................ 82 
Figure 58 Top Connected bags acting as cantilever ......................................................... 83 
Figure 59 CAD image of top connected cantilever beam................................................. 84 
Figure 60 Front View with Dimensions (ft) ..................................................................... 85 
Figure 61 Funicular polygon for 60 bag structure ............................................................ 86 
Figure 62 Another possible configuration for 60 bag structure........................................ 87 
Figure 63 60 Bag structure with dimensions (ft) .............................................................. 88 
Figure 64 Funicular Polygon ............................................................................................ 89 
Figure 65 CAD Model Template to Guide Erecting......................................................... 90 
Figure 66 Air-Filled 46 Bag Structure, 5 pipes guiding bag filling.................................. 92 
Figure 67 Big Filling Process ........................................................................................... 93 
Figure 68 Rectangular Packed Bags ................................................................................. 93 
Figure 69 Front View........................................................................................................ 94 
Figure 70 Rear View......................................................................................................... 95 
Figure 71 Closer views of structure.................................................................................. 96 
 xiv
LIST OF TABLES 
Table 1 Vermiculite Chemical Composition .................................................................... 42 
Table 2 Excel Spread Sheet .............................................................................................. 69 
Table 3 Co-ordinates of points shown in Figure 64.......................................................... 90 
 1
CHAPTER ONE 
INTRODUCTION 
Masonry arches have been used from a long time to construct bridges, building, 
domes etc. Over the years various shapes of masonry arches have been developed ranging 
from circular, elliptical to catenary etc. They are a classic example of form following 
function and have been used primarily because of their ability to carry vertical loads as 
longitudinal load to the abutments of the arch. These longitudinal loads act as vertical and 
horizontal reactions forces on the abutment, giving the arch its stability. This thesis 
presents a way of adapting this technique to the development of a lunar structure made 
out of multi pocket bags filled with regolith. The main objective of this is to be able to 
construct a lunar structure in the shape of catenary arch with minimum amount of raw 
materials carried from Earth.  
 
1.1 Scope of thesis 
The development of a catenary arch to be made on the moon, using techniques 
used in construction of masonry arches involves the development of an analysis 
technique that can reliably predict the stability of such a structure. In this report the 
technique of finding stability using funicular polygons has been primarily used. Various 
real structures were made manually in Auburn University and NASA-Marshall Space 
Flight Center (MSFC) using bags filled with vermiculite. The construction of these 
 2
structures involved construction of frames to support the structure while construction, 
filling of bags with vermiculite (sand was not used primarily because of its high weight) 
and testing their stability. The construction of frames has been discussed in this report 
along with the various techniques used to fill the bags with vermiculite. These structures 
were also drawn in Solid Edge and their stability was tested using funicular polygons. 
The results obtained using funicular polygons can easily be compared to the stability of 
structures built using bags, as long as the bags behave similar to rigid voussoirs.  
 
1.2 An overview of thesis 
The thesis provides a look into the construction of structure to be built on the 
moon, which can be used to store equipments, machines and can also be used as a habitat. 
In this regard, chapter 2 presents a brief literature review of various papers published 
over the year discussing techniques of lunar base construction and also other important 
parameters involved like site selection, challenges faced, requirements etc. Chapter 3 
discusses some lunar structures that have been proposed by various authors. Chapter 4 
discusses the experimental setup required for construction of the lunar structure proposed 
in this thesis. The stitching of bags used for construction, techniques used to fill the bags, 
construction of frames has been discussed in detail. In Chapter 5, the analytical technique 
developed using funicular polygons is discussed. A small section is devoted to initial 
exploratory studies carried to test if Working Model could be used to determine the 
stability of the structure being developed.  
 3
CHAPTER TWO 
BACKGROUND 
The construction of lunar structures for storing goods, equipments and even for 
use as a human habitat has been of primary interest, from the time man landed on moon.  
The design of a lunar structure is based on factors like environment, gravity, materials 
used, safety, rigidity etc. The design of a lunar structure is important for numerous 
reasons. For any kind of scientific research on the surface of moon, a lunar structure will 
be required to store equipments. This structure will also protect the equipments from 
lunar environment. For human habitation the lunar structure will also need to provide 
adequate protection from harmful radiations. Designing of such structures involves 
structural analysis and design. This section reviews only arch structures as determined by 
using funicular polygon. Detailed description of the funicular polygon technique is 
discussed in this chapter.  The first part of this chapter will deal with the scientific 
importance of moon. Then a brief overview of various environmental factors and 
construction techniques of a lunar structure will be discussed.  
 
2.1 Scientific Importance of Moon 
 The Moon is a suitable platform to carry out observations about the universe, 
explore even further into space and help us in understanding it even better. The Moon can 
 4
also act as a source of natural energy and minerals. Setting up of a lunar base has been 
discussed ever since the first Apollo mission to the moon. After decades of space 
exploration, setting up of a lunar base is the obvious next step to help us in exploring it 
even further. Research in site selection and construction of a lunar base is required. The 
international space stations like Mir are an important step in this direction. Setting up of a 
lunar base will involve use of regolith and other materials found on moon, therefore 
reducing the need to carry heavy payloads from Earth. This can be a significant 
advantage over developing of space station, for which the raw material required needs to 
be carried from earth. 
 Development of a lunar base will also give us experience and help us in building 
base on Mars [2]. With recent discoveries that life forms might have existed on Mars, our 
interest in sending manned missions to Mars has increased, even though there are lots of 
challenges associated with it. For one, Mars is around 100 times farther from Earth, than 
the moon even in its nearest approach [2]. With current technology available, manned 
missions to Mars will take years to complete. Hence setting up a lunar base would help us 
in understanding various effects of extended stay in space on human bodies and help us 
in preparing more efficient and reliable manned missions to Mars. As mentioned before 
setting up of a lunar base will also help us in exploring space further. There are various 
questions that need to be answered and it is believed that this can be done only by setting 
up a base on moon [1]. Some of the important issues that need to be answered are [1]: 
? Relationship of earth and moon. 
? Origin of moon.  
? Presence of water on moon.  
 5
? Mineral composition in regolith and the potential of moon being used as a 
resource hub 
 
2.2 Development Phases 
 Development of a lunar base has been categorized into three important steps [2]- 
? Pioneering phase 
? Consolidation phase 
? Settlement phase 
 
Pioneering phase 
 During this phase, the basic aim will be to travel to moon with simple equipments 
like telescopes, dune buggies, cameras etc. Site selection and understanding of how 
various factors will affect the lunar base will be the important steps associated in this 
phase. The dune buggies can be used to explore areas in close proximity while the 
telescopes and cameras can be used to set up a small observatory.  
 
Consolidation Phase 
 This phase will involve bringing of life support system, power system, lunar 
transport system to the moon. These equipments will help in construction of bigger and 
better observatories.  
 
 
 
 6
Settlement Phase  
 This phase will be characterized by growth in population on the lunar base, 
efficient observatories running on power obtained from natural resources available on 
moon.  
 
2.3 Challenges in Designing a Lunar Base 
 The design of a lunar base does not end with understanding of the phases 
involved. The conditions found on moon are very different from those found on earth and 
hence challenges faced by various environmental factors need to be taken into account 
and addressed before designing of the base. Some of the factors are [7]: 
? Temperature 
? Atmosphere 
? Radiation 
? Meteorite Impacts 
 
Temperature 
 Temperatures on moon can vary drastically between the night and day cycle in 
moon. During day the temperatures can soar to 380K [7] and during the night they can 
drop down to 100K [7]. This variation in temperature can cause adverse affect on humans 
and even on material properties. It was observed that 50 to 100 cm of regolith placed on 
top of the regolith can reduce the temperature variations observed inside the base. This 
can be attributed to its low thermal conductivity. Surface of the moon also undergoes 
large temperature variations during the night and day cycle. Because of this metal 
 7
structures constructed on the surface can undergo severe thermal stressed because of 
expansion and contraction. This can considerably reduce the life cycle of a structure.  
 
Atmosphere 
 The moon?s s atmosphere is considerably different from earth. Moon has very few 
gases present in atmosphere and quantity of oxygen present is too low to sustain life 
without other aids. The thin atmosphere also makes moon more susceptible to harmful 
solar winds, meteorites etc. The thin atmosphere can also prove beneficial as it can allow 
for experiments to be carried out in vacuum if required.  
 
Radiation 
 Due to the lack of atmosphere on Moon, harmful radiations coming from sun and 
other parts of the solar system do not get absorbed and reach the moon?s surface. These 
radiations are harmful for human body and can cause considerable damage. Solar Winds 
and Solar Flare are some major sources of radiation on moon. Even in protective 
clothing, astronauts face a risk from these radiations. Accurate and efficient techniques to 
predict these events need to be developed. Lunar bases should also be protected from 
these harmful radiations. It has been found that 400 gm/cm
2 
of regolith will be needed to 
prevent over exposure of humans to these ultra violet radiations [10]. Other materials like 
lead, water, copper, hydrogen have also been found to act as barriers to radiations. [10].  
 
 
 
 8
Meteorite Impacts 
 Meteorite impacts on Moon are more frequent and a bigger problem than on 
Earth. This is due to the lack of atmosphere on Moon. As a result, meterorite impacts can 
cause craters in metal structures. Even micrometeorites can cause considerable damage to 
the structure over a period of time Meteorites weighing more then 1 gram can cause 
considerable damage to a structure.  
 
2.4 Requirements of a Lunar Base 
 After discussing the challenges it can be seen that any lunar base designed should 
be able to meet some design requirements in order to support life system inside. Some of 
the issues that a lunar base should be able to address are as follows- 
? Gravity 
? Vacuum 
? Shielding 
? Internal Air Pressurization 
 
Gravity 
 Gravity experienced on moon is around a 1/6 of that experienced on Earth. 
Therefore during designing of the lunar structure, mass should be taken as important 
design variable rather then weight [5].  
 
 
 
 9
Vacuum 
 The lack of atmosphere creates construction and maintenance issues that need to 
be taken care of. Many materials can be unstable in such an environment. The use of 
hydraulics will be limited because of leakge of oil, vapors etc [5]. Vacuum implies that 
the only source of heat transport would be radiation [7]. This would affect the design of 
thermal systems. Vacuum will also increase the friction between moving parts because of 
the lack of an air layer between them. [5].  
 
Shielding 
 A lunar base should be able to shield itself against radiations, meteorites etc. as 
discussed before, regolith can be used as an effective shielding device. This layer of 
regolith should be able to provide adequate protection from radiation exposure. The 
amount of radiation exposure should not exceed 5 rem (radiation equivalent man). The 
extra weight of regolith can be used to balance off the forces due to internal air 
pressurization.  
 
Internal Air Pressurization 
 To support life system, oxygen supply and pressure must be maintained inside the 
structure for human habitation. A human body needs air pressure to balance the internal 
blood pressure. Internal air pressure of 15 psi is considered safe for life support [5]. The 
structure should also be designed to be fail safe against leakages.  
 
 
 10
2.5 Oxygen Production 
 Since oxygen is the most important requirement for life support considerable 
research has been done to determine methods of producing oxygen on moon. Regolith is 
a good source of oxygen as it contains almost 50% of oxygen by weight [13]. Ilmenite 
(FeTiO
3
) is present in lunar soil and this can be used to extract oxygen using the 
following chemical process [14]- 
 
2
23
222
2223
2
1
2
1
OCCO
COTiOFeCFeTiO
OHOH
OHTiOFeHFeTiO
+?
++?+
+?
++?+
 
Equation 1 
   
 Various techniques for carrying out this process, known as Ilmenite Reduction 
[12] have been researched on. Mishra et al. discuss a technique of producing oxygen from 
regolith using molten salt technology [11]. Design concept of a lunar rover able to carry 
out the chemical process on Moon?s surface has also been developed [12].  
 
2.6 Site Selection  
 Site selection is an important step towards the construction of a lunar base. The 
site should be selected on the basis of following factors [1][13] 
? Science 
? Resources 
 11
? Operational Considerations. 
? Lighting 
? Landscape 
? Terrain 
 
Science 
 A lunar base will be used to carry out various scientific experiments. The soil 
around the base must be able to support the weight of the telescopes. Settling can occur 
under the support of a telescope and this can lead to malfunctioning [5]. Moon has two 
different types of terrain [1]- mare and highland. Both represent two different periods of 
lunar history and hence are equally important in understanding the moon?s evolution. 
 
Resources 
 As mentioned before, a lunar base will depend on regolith for shielding purposes 
and for production of oxygen. The site chosen must have enough amount of Ilmenite for 
oxygen production. The site must also be able to provide adequate sunlight during day 
time. A site selected close to the poles of the moon will be hidden from sun for long 
durations and hence will not prove to be an ideal site location.  
 
Operational Considerations 
 The development of a lunar base will also be followed by development of 
emergency systems that can act immediately during a human crisis. A command module 
has been proposed [1]. This module will orbit around the moon and will help in 
 12
evacuating humans back to earth during emergency. The site selected should be easily 
approachable by this module for quick evacuation. Landing site safety and mobility 
around the site will also effect site selection.  
 
Lightning, Landscape, Terrain 
 As discussed before, adequate lighting is required for human survival and for 
carrying out various experiments. The terrain around the site should not act as a barrier 
for sunlight but at the same time a site selected around a mountain or crater can help in 
shielding the site from meteorites. The landscape again should be smooth for ease of 
construction purposes. 
 As can be seen, site selection poses quite a unique challenge because of the 
contradictory nature of some site selection requirements. A site meeting all these 
requirements will be difficult to find. Various sites have been proposed and each has 
different scientific importance. Figure 1 below shows some sites selected as suitable 
based on the requirements [13].  
 
Figure 1 Proposed Lunar Sites on Moon 
 
 13
2.7 Construction Materials 
 Various indigenous materials have been proposed for the construction of lunar 
base [8]. Use of indigenous materials reduces the need to carry heavy pay load from earth 
to the moon. This also reduces the cost of construction. Some of the materials proposed 
are as follows. 
? Regolith 
? Cast basalt and glass 
? Ceramics 
? Cement 
? Metals 
 
2.7.1 Regolith 
 Regolith is found in abundant quantities on moon and hence can be used easily 
without having to process it. Lunar Base can also be made by digging in the regolith and 
creating bunkers to stay in. they can also be used to make structures out of bags filled 
with regolith. The bags will need to be brought from earth along with a feeding system. 
These bags can also act as good shielding materials because as discussed before, regolith 
can help in keeping out harmful radiations very effectively.  
 
2.7.2 Cast Basalt and Glass 
 These can be produced easily on moon?s surface using cooling molten basalt 
process [8]. They can be used as structural materials for construction of buildings and 
pavements.  
 14
 
2.7.3 Ceramics 
 Ceramics can again be easily produced on moon using lunar soil. Ceramics can be 
used to make structural materials like bricks, blocks. They also have good thermal 
insulation and are resistant high temperatures making them ideal to be used on moon.  
 
2.7.4 Cement 
 Cement can be produced from lunar soil and glass by means of sintering and 
crushing processes. Water required can also be obtained by reducing lunar oxides with 
hydrogen [8]. Cement can be used as for making heat insulators, shields, roads, 
foundations 
 
2.7.5 Metals 
 Metals can be extracted from lunar soil using various chemical processes. The 
equipments required for this kind of operation will need to be carried from earth. Metals 
can be used for construction of railroads, structural support members, bridges.  
 
2.8 Design of Masonry Arches 
 Masonry arches have been used for about 5000 years [15] and are one of the 
oldest structural elements in use. The fundamentals of masonry arch are used to design 
the lunar base and hence a description of masonry arches plays an important role in this 
thesis.  
 15
 A masonry arch is a structure of masonry covering an opening and carrying load 
as longitudinal thrust. Voussoir arch is a type of masonry arch where the arch is 
composed of independent blocks of masonry [16]. Such an arch is robust because of the 
fact that it utilizes the strong compressive property of its masonry in transmitting stresses 
through its geometry [15] 
 An arch is composed of following parts as shown in Figure 2 below.  
 
Figure 2 Parts of Masonry Arch.  
 
Intrados 
It is the intersection of the soffit with a vertical plane perpendicular to the axis of the 
arch. Soffit is defined as a material which covers the underside of a building or structure 
such as an arch, beam, balcony etc.  
 
Extrados 
It is the intersection of the outer surface with a vertical plane perpendicular to the axis of 
the arch.  
 
 16
Crown 
It is the highest point on the arch.  
 
Rise 
It is defined as the perpendicular distance from the highest point of the intrados to the 
ground.  
 
Keystone 
It is the voussoir at the crown of the arch. It is used to give the arch stability.  
 
2.9 Stability of Arch 
 It has been found that masonry arches fail due to instability rather than a lack of 
material strength [17]. This is because of the fact that stresses in masonry arches are 
much lesser than the crushing capacity of stone. Therefore to determine the stability of a 
masonry arch, equilibrium approach using geometrical rules can be utilized. Few basic 
assumptions are used while using this technique [17]- 
1. Stone has no tensile strength: This assumption is based on the fact that the stones 
might have tensile strength but the joints will not and tensile force cannot be 
transmitted from one portion of the structure to other.  
2. The compressive strength of stone is effectively infinite.  
3. Sliding failure between bricks cannot occur 
 
 17
The graphical method utilizes the concept of line of thrust or funicular polygon. 
This is the path which represents the resultants of compressive forces through the stone 
structure. This line is a resultant of two forces [16]:  
? weight of the arch 
? Horizontal thrust 
 Horizontal thrust depends on the weight of the voussoirs and the flatness of the 
arch. The more flat the arch is, higher the horizontal thrust is [17]. The weight of 
voussoirs acting on each other creates a line of thrust. For an arch to be stable, this line of 
thrust should lie within the thickness of the arch [17]. If the line of thrust lies outside the 
arch, then the joint will tend to open up on the opposite side and area of contact between 
voussoirs will be reduced. This technique of determining the stability of an arch based on 
the line of thrust is essentially a geometric technique. Figure 3 shows the line of thrust 
(LT) acting inside an arch as a result of the horizontal thrust (HT) and weight (W).  
 18
 
 
Figure 3 Line of thrust lying inside the arch 
 The failure of an arch is caused due to the formation of hinges. Whenever the line 
of thrust goes outside the arch, a hinge is formed [17]. The number of hinges required for 
collapse can be calculated. If a structure has three hinges then it becomes a statically 
determinate structure. If there are four hinges, the structure acts as a mechanism and the 
arch fails [17].  
 If the structure is stable under given external loads, various positions of the thrust 
lines are possible. If a thrust line is found to be lying inside an arch for a given set of 
external loads, then it can be assumed safely that the structure is safe. This line of thrust 
need not be the actual line of thrust. For the same structure, with same external loads, a 
HT
LT
W
 19
line of thrust can be found to be lying outside the arch, but this cannot make the structure 
unstable.  
 It was also found out that an arch will turn itself into a statically determinate 
structure if there are any imperfections present in the structure [17]. This can be seen in 
the figure below.  
 
  
Figure 4 a. Formation of hinges b. Line of thrust acting through the arch 
 As can be seen in Figure 4a the shape of the arch is fixed by the shape of the 
voussoirs, and if the shape implied by the geometry of abutments is different then the 
arch will accommodate itself to those abutments and will form hinges in doing so. In the 
figure above, the arch forms a statically determinate structure because of presence of 
three hinges.  
 
2.10 Design of Voussoir Arches 
 As discussed in previous section if a line of thrust can be found that stays inside 
the arch, then it can be assumed to be stable for that set of load. This line of thrust can be 
 20
found using graphical methods. Following are some of the parameters needed for this 
graphical method 
 
2.10.1 Shape of the Arch 
 Masonry arches are designed in the shape of a catenary. A catenary is defined as 
the shape formed by a chain suspended between two fixed ends and hanging under the 
force of gravity. It is shaped in the form of a parabola. Figure 5 shows a simple catenary.  
 
Figure 5 Catenary 
 
Catenary is better defined using the following equation [18] -  
 
)cosh()(
)(
a
t
aty
ttx
=
=
      
Equation 2 
 
 21
 a determines the shape of the catenary. As a changes, the catenary opens up or 
closes. The arch length of the catenary also is important and is defined using the 
following equation [18]:  
 )sinh()(
a
t
ats =  
Equation 3 
 s is the arch length of the catenary and it is important in finding the surface area 
while designing the arch.  
 
2.10.2 Thickness of Masonry Arch 
 The line of thrust should always lie inside the thickness of the arch (h) and hence 
it plays an important part in designing of the arch. Various equations have been suggested 
to calculate the thickness of the arch based on span (S) and/or the rise (f) [15]- 
 
Sh
f
s
h
fh
Sh
40000
2
18282
220
36650
=
++=
=
=
 
Equation 4 
 
 Spalding [16] and Taha [15] talk about these equations in detail. The effectiveness 
of each equation depends on the safety factor required for a particular arch. Any of the 
equations can be used to design an arch and then the line of thrust can be developed for 
that configuration. The most suitable design will be one in which the line of thrust lies 
well within factor of safety.  
 22
2.10.3 Horizontal Thrust 
 It has been discussed before that a masonry arch tends to settle down according to 
the geometry of the abutments and forms a three pinned arch. This three pinned arch is a 
statically determinate structure. For the construction of funicular polygon, the following 
parameters are involved 
a. The amount of horizontal thrust 
b. External forces acting on the structure 
c. Weight of the voussoirs 
d. Span of the arch 
e. Height of the arch 
 Parameters like external force, weight, span and height of the arch are known. The 
value of horizontal thrust needs to be determined. In case of the three pinned arch, half of 
the arch can be taken with forces acting on it as shown in the figure below.  
  
Figure 6 Catenary arch with loads acting on it 
 23
H= Horizontal thrust acting on the arch that needs to be calculated 
R= Reaction force acting due to the weight of the voussoirs and external force acting on 
the arch 
W1, W2, W3, W4= External Forces acting on the arch 
 Using momentum about point O, the reaction forces and horizontal thrust can be 
calculated. In this report Solid Edge has been used extensively to design the arches and 
construct a funicular polygon. This is done by using the horizontal thrust values obtained 
after analyzing the structure and the load acting on the structure. Other important factors 
that need to be known are the span of the arch, the height of the arch and the point of 
application of the loads.  
 To demonstrate the method of constructing a funicular polygon using Solid Edge 
an example is used which is shown in Figure 7. The vertical lines represent the point of 
application of the load acting on the arch. Since the arch is symmetric about its center, it 
is enough if funicular polygon is constructed for just one side of the arch. It can be 
mirrored using Solid Edge to fit the other half of the curve.  
 24
 
Figure 7 Catenary arch with dimension (in) 
 W1, W2, W3 and W4 are the loads acting on the structure and (x1, y1), (x2, y2) 
etc are the co-ordinates of the point of application of loads. The horizontal thrust is found 
to be h. Now before constructing the funicular polygon, a force diagram is constructed as 
shown in Figure 8. h is the horizontal line and the loads W1, W2 etc are drawn 
perpendicular to h. Then a line is drawn starting from h to each of the loads as shown in 
Figure 8.  
 25
 
Figure 8 Force Diagram for the catenary 
 Using the force diagram, the funicular polygon can be constructed in the catenary 
arch shown in Figure 7. To start of, a line parallel to the line connecting W4 to h is drawn 
in the catenary starting from within the base of the arch on the right side. This line is 
drawn till it intersects the line drawn through the first line of force which is W4 in this 
case. This is shown in Figure 7 
 26
 
Figure 9 First line drawn parallel to the line connecting h and W4 
 It can be seen that the first line is drawn from somewhere in between the 
thickness of the arch. As has been discussed before, that if any funicular line is found to 
be inside the thickness of the arch, then the arch can be said to be stable. Hence it is 
enough if we can draw a funicular line that lies within the arch in Solid Edge to show that 
an arch is stable. If no such line is found, then the arch is unstable. Using trial and error 
process, it can be seen if any funicular line will lie within the thickness of the arch. In this 
example, the first line is drawn from somewhere in between. For the next step, another 
line, parallel to line joining h and W3, is drawn from the point where the first line 
intersects the line of force W4. This line extends till it intersects the line of force running 
through W3. This is shown in Figure 10. 
 27
 
Figure 10 Second line drawn from the first intersection point to W3 
 Proceeding in a similar fashion, parallel lines can be drawn to lines connecting 
W1 and W2 to h. In this manner a funicular polygon is obtained which lies inside the arch 
in this case. Figure 11 shows the completed funicular polygon constructed for this 
example, which shows that this configuration is stable.  
 28
 
Figure 11 The completed funicular polygon lying inside the arch 
 This way a funicular polygon can be constructed for any catenary shape structure 
if the loads acting on it and its dimensions are provided.  
 
2.11 Research Objective 
 The design of a lunar base involves various steps. In this case the lunar base is 
being designed in the shape of a catenary arch consisting of regolith bags acting as 
voussoirs. Just like in masonry arch, the funicular polygon principle is used to determine 
the stability of the lunar base. This thesis attempts to see how well this principle 
translates to a structure made of regolith bags. A structure made of regolith bag is 
different from one made using masonry because regolith has lower compressive strength 
than compared to masonry, and this must be taken into account while designing the 
 29
structure. Also the bags tend to slip on each other while in masonry arch, slippage is 
almost negligible. Another difference is that the bags are connected to each other, either 
as top connected or center connected, while in masonry arch, the voussoirs are not 
connected to each other with a fabric link.  
 Another objective of this thesis is to test various shapes of structures made out of 
different types of bag to determine the best possible structure. To help in this objective, 
spread sheets and simulation package like MSC. Working Model is explored to determine 
the stability.  
 Various techniques for filling of bags with regolith are also discussed. Each 
process has its own advantages and disadvantages and the best technique is also 
proposed. A brief overview of the material used for the bags and the stitching technique 
is also discussed.  
 In this chapter the research that has been done previously on development of 
structures on the moon has been discussed. The various phases of development of a lunar 
structure have been discussed along with the challenges involved in development of a 
lunar base. Site selection is an important step in developing a lunar base and the process 
involved in selecting a good site has also been discussed. The later part of the chapter 
discusses masonry arches and their stability. This is useful in understanding how the 
masonry arch technique can be used to design a lunar base which is one of the research 
objective of this study.  
 30
CHAPTER THREE 
LUNAR STRUCTURES 
 Numerous lunar structures have been proposed and in this chapter we?ll look at a 
few of them. In the previous chapter we have discussed some of the essential 
requirements and constraints faced by a lunar structure. Various structural concepts have 
been proposed to satisfy these requirements [19], some of which are concrete structures, 
metal structures, pneumatic structures, hybrid structures. Various research tools and 
decision making science have been proposed to determine the efficiency of a structural 
concept [19]. Some of the tools used for this purpose are Operation Research and 
Decision Science [20]. A numeric scoring system to evaluate a structure has also been 
proposed [21]. This scoring system evaluates eight structural concepts, which are [21]- 
? Inflatable 
? Framed/Rigidized Foam  
? Polygonal Framed 
? Hexagonal Framed 
? Square Module 
? Spherical Hybrid 
? Semi cylindrical Hybrid
? Rigid Tower 
 31
These techniques can be used to determine the viability of a concept which is an 
important step leading up to the construction of structure.  
The eight types of structures listed above are basic design concepts and any type 
of structure developed will fall under them. Some of the structures developed are 
discussed in the following sections.  
 
3.1 Cable Structures 
 Cable structures similar to cable bridges have been used extensively on earth 
because they have the advantage of carrying loads efficiently through axial tension [23]. 
Some of the properties that make a cable structure a viable option are [23] 
? They are easily transportable and easy to erect 
? They carry loads efficiently using tensile stresses.  
? They can be prefabricated on earth and carried to the moon.  
Three different types of cable structures have been developed for the moon. They are- 
Small Span Systems, Medium Span Systems, and Long Span Systems. These structures 
have been developed for two modes, one in which internal pressure is maintained and one 
in which internal pressure cannot be maintained because of leakage in the structure. 
These structures are therefore designed to keep the structural integrity intact in both the 
modes [23].  
 
3.1.1 Small Span System 
 A cable reinforced fabric structure was developed. For the first mode during 
which internal pressure is to be maintained, the fabric will be active in supporting the 
 32
structure. For the other mode, a three hinged arch is proposed. Figure 12 displays the 
structure developed [23]  
 
Figure 12 Small Span System 
                                                                                                                                                                  
The use of various indigenous materials available on moon has been discussed in 
the construction of these lunar bases [22].  
 As can be seen from the figure the structure is circular in shape. This limits the 
span of the structure because with larger span, the structure will become higher and more 
unstable [23].  
 
 
 33
3.1.2 Medium Span Structure 
 In medium span structures pretensioned cables are used to extend the structure 
beyond the dimensions of a small span structure [24]. Configurations like convex, 
concave, convex-concave were discussed, but the convex-concave configuration was 
chosen to be more suitable for lunar structures [23]. Figure 13 shows such a structure 
developed [23].  
  
Figure 13 Medium Span System 
 The figure shows that the roof is made out of a concave-convex cable system. The 
advantages of this system are that it is much lighter because of extensive use of cables. 
Also it is much easier to construct [23].  
3.1.3 Long Span Systems 
 Tension cable systems are again used for designing of larger lunar bases. Floor 
supports are used to resist the compressive forces [23]. This system will offer lots of 
 34
usable space and it has been designed to function reliably in both modes. Figure 14 shows 
a long span structure in more detail [23].  
 
Figure 14 Long Span Systems 
3.2 Mobile Lunar Bases 
 Various mobile lunar bases have been discussed [25][26]. These lunar bases can 
be constructed by assembling two or more of mobile modules together. While moving to 
a different location, each module can relocate to the new location easily using robotic 
legs or wheels. One such structure discussed in [26], uses three modules docked together 
to form a 4 person shelter for 45 days. This structure can dissemble and relocate to a new 
site of interest easily. Each module consists of crew quarters, power systems and other 
life support systems. Each module is equipped with 6 legs powered by electric motors, 
giving the module three degrees of freedom. These legs also act as structural supports 
when the modules dock with each other and form a habitat. Figure 15 shows the proposed 
habitat [26] made out of three modules and assembled in the form of a T. this 
configuration allows more modules to be added to the habitat.  
 35
 
Figure 15 Habitat made out of three modules 
 Each module has been designed to provide the required radiation shielding to its 
occupants. These modules are also designed to protect the occupants from meteorite 
impacts [26].  
 
3.3 Inflatable Structures 
  Inflatable structures in form have also been proposed [19] as permanent lunar 
base concepts. This concept is made up of inflatable, pressurized tensile structures. 
Regolith is used to provide radiation shielding. Air needed for inflating the structure can 
be carried from Earth in form of high pressure gas or cryogenic liquid [27]. Cryogenic 
Air is a more viable option because of its higher density. While relocation of the base, air 
can either be discharged to the moon or it can be stored for future use. Storing it and 
using air again, will reduce the costs involved with bringing air from earth. For removing 
air from the structure, water must be first removed from it. This can be done using a 
HVAC system. After that a cryo pump can be used to store the air in cryogenic containers 
[27]. An example of an inflatable structure is shown in Figure 16 below [19].  
 36
 
Figure 16 Inflatable Structures 
  
In this chapter we have seen three different types of structures- Cable Structures, 
Mobile Structures and Inflatable Structures. This thesis aims at developing a structure 
made of regolith bags, stacked on each other. Such a structure has been in development 
[28] and is used as an emergency shelter and for other purposes. These structures are 
made of bags filled with sand and piled on each other, are connected using barbed wire. 
These structures are cheap in construction and provide adequate protection on Earth. 
Figure 17 shows some of the structures developed by the Cal Earth Forum [28].  
 37
 
Figure 17 Cal Earth Structure Concepts 
  
 The structures proposed in this thesis are similar in principle to the structures 
shown above. Different geometric configurations were evaluated and as discussed in 
previous chapters, the strength of each configuration was also evaluated.  
  
 38
CHAPTER FOUR 
EXPERIMENTAL SETUP 
In this chapter we?ll discuss about the various construction steps involved in 
erecting the structures. They can be categorized into following steps:  
? Design and construction of frame needed to support the structure 
? Filling of the bags with vermiculite 
? Mounting of the bags on the frame and adjusting them as per the dimensions 
developed from the CAD model 
? Removal of the frame 
Each construction steps has various steps involved in it and they?ll be discussed 
with respect to each structure. Various different techniques were also used to fill the bags. 
Advantage and disadvantage of each technique will also be discussed.  
 
4.1 Types of Bags 
 The following types of bags were used in design and construction of the lunar 
structure-  
4.1.1. Center Connected Bags  
 These bags are connected by a stitch running through their center as shown in 
Figure 18. The materials used for the bag and the stitching technique will be discussed in 
 39
a later section. These bags assume circular cross section on filling completely with 
vermiculite and look like stacks of balls placed on each other. The final shape these bags 
assume depend on the amount of vermiculite filled in each bag. If the bags are tightly 
packed then they assume circular shape as shown in Figure 18. If they are not completely 
filled the vermiculite inside the bags remains loose. The amount of vermiculite required 
inside each bag depends on the structure size and dimensions and will discussed in more 
detail in the later sections. 
  
Figure 18 Center Connected Bags 
 
4.2.2. Top Connected Bags  
 These bags are connected by fabric running on top as shown in Figure 19. Each 
bag forms a ?tooth? in this structure. On filling the bags with vermiculite, the shape they 
assume is based on the amount of vermiculite poured into them. If the bags are tightly 
packed, they start assuming a round shape, very similar to the shape of bags shown in 
Figure 18. But since the bags are top connected, the fabric on top stretches and the 
distance between the bags on top becomes less than the distance at the center of the bags. 
This is not desirable as it makes the structure difficult to construct. On the other hand, a 
partially filled bag can be made into a shape of a rectangle and this way it becomes easier 
 40
to the pile the bags on each other.  A structure made out of a top connected bags is shown 
in Figure 20 
 
 
Figure 19 Top Connected Bags 
 
 
Figure 20 Structure made out of Top Connected Bags 
 
 
 41
4.2 Stitching Techniques and Materials used for Bags 
 Nylon was used in the construction of the bags of both type discussed above. For 
the top connected bags, different portions of fabric were cut out for and then stitched 
together. The bottom part of the bag is first constructed and then the top is stitched onto 
it. Two stitches were used for the construction of the bags. The top stitch was made up of 
double bonded polyester and the bottom stitch was made out of Kevlar. Figure 21 shows 
an image of the stitch. Zippers were used on one side of the bag, to keep an end 
accessible for pouring vermiculite into the bags. The zippers can withstand temperatures 
in the range -73
0
C to +260
0
C. They act as a sealing membrane and can withstand pressure 
of up to 700psi.  
 
Figure 21 Stitch 
 For the center connected bags again nylon was used. These bags were constructed 
by stitching together two pieces of fabric. One end was closed and the other end was left 
open for pouring vermiculite. After filling the bags the open end is taped shut. This is not 
an optimum technique as the taped end can open up very easily and cause leakage of 
vermiculite.  
 
 
 42
4.3 Techniques used for Filling Bags 
Filling the bags with vermiculite was a very time consuming process. Different 
techniques were used with little or no success before deciding on the best way to fill 
bags. Before discussing the techniques used for filling bags, the properties of vermiculite 
will be discussed.  
4.3.1. Vermiculite and its Properties 
 Vermiculite was used instead of sand or regolith primarily because of its light 
weight in this project. Vermiculite has been extensively used in various industries for 
around 80 years [29]. The chemical formula for vermiculite is 
(MgFe,Al)
3
(Al,Si)
4
O
10
(OH)
2
.4H
2
O [30] and it is primarily composed of the following 
minerals [29] 
Table 1 Vermiculite Chemical Composition 
ELEMENT PERCENT BY WEIGHT 
SIO2 38-46 
AL2O3 10-16 
MGO 16-35 
CAO 1-5 
K2O 1-6 
FE2O3 6-13 
TIO2 1-3 
H2O 8-16 
OTHER 0.2-1.2 
 43
 Vermiculite is found primarily in Australia, Brazil, China, South Africa [29] [30]. 
It is a non toxic material which expands on the application of heat in a process called 
exfoliation [30]. After this process vermiculite becomes lightweight, non-combustible 
and a good insulator [29]. Hence it has found use in a variety of applications like [29] 
[30] 
? Fire protection  
? Fertilizer 
? Pesticide 
? Acoustic Finishes 
? Absorbent packing 
? Used in swimming pools to provide smooth pool base 
? Furnace insulation 
4.3.1.1 Safety Aspects of Vermiculite  
 Vermiculite has been proved safe to work with and poses no serious health risks 
on exposure [29]. The only serious health risk is when there are traces of asbestos present 
in vermiculite. The presence of asbestos can be found out through the Material Safety 
Data Sheets provided by the manufacturer. These sheets will inform the user about the 
material composition of vermiculite and will also provide information about any 
hazardous materials present in vermiculite and their safe handing and disposal [29].  
 Inhalation of vermiculite can cause minor coughing, sneezing [29]. This can be 
prevented by using dust respirators. Safety glasses should also be used to prevent minor 
eye irritations because of vermiculite.  
 44
4.3.2 Manual Filling of Bags 
 Initially, considering the small size of the bags used, manual filling the bags was 
the cheapest and fastest way available. In this process, the bags were filled with 
vermiculite using a funnel attached to a hole in the bag. The vermiculite was then poured 
into this funnel using a scoop. The bags were held upright at 90
O
 during this process. This 
technique works very well for center connected bags, because the round shape required 
for such a structure is achieved easily, because vermiculite settles down due to gravity 
given the erect positions of the bag. For a top connected bag this technique does not work 
very well as the bags attain a round shape instead of the desired rectangular shape. Figure 
22 shows the bags erect and taped shut after filling them with vermiculite.  
 
Figure 22 Center Connected Bags Filled with Vermiculite 
Advantages 
? Easy and cheap technique for filling small bags 
? Minimum equipment is required 
 45
Disadvantages 
? Not suitable for filling large bags 
? Not suitable for filling Top Connected bags 
? It is a tiring process and requires minimum of 2-3 persons 
 
4.3.3 Filling of bags using Sand Blower 
 
Figure 23 Sand Blower 
Sand blower was used to fill the bags with vermiculite. Figure 23 shows an image 
of the sand blower used. The sand blower used was a pneumatic type. It was connected to 
air supply and it was then filled with vermiculite. A schematic of the sand blower is 
shown in Figure 24 
 
 46
 
Figure 24 Schematic of Sand Blower used 
  
As can be seen from the figure above the top of the cylinder is connected to an air 
supply. The cylinder is filled with vermiculite. The cylinder has a hole at the bottom 
through which the vermiculite can flow. When the air supply is switched on, air flows 
through as indicated by the directions shown in the figure. The vermiculite flows through 
the hole in the cylinder and into the valve. Here it mixes with air blowing through and 
comes out through a pipe as shown above. This end is inserted into the bag to fill them 
up.  
 
 47
Advantages 
? It?s a fast technique of filling the bags 
? This technique only requires a couple of people to fill the bags. Ideally one 
should be enough 
? The equipment setup is pretty cheap and easy to construct.  
 
Disadvantages 
? The vermiculite that comes out is usually at a very high speed mixed with air. 
Hence when the outlet pipe is inserted into the bag, the vermiculite stirs up the 
contents of the bags inside. This causes lot of vermiculite to escape out of the 
bag. This is not ideal for filling the bags fast 
? A lot of air also is accompanied with vermiculite. This is not desired as it 
blows out the vermiculite present inside the bag, through the hole on top.  
? This technique causes vermiculite to blow out into the face of the operator and 
hence it has some health concerns.  
This technique was not used extensively as the amount of the vermiculite leaking 
through the bag during filling, was more then the amount of vermiculite going inside the 
bags. 
4.3.4 Leaf Blower 
 A leaf blower was also used to try and fill the bags. This leaf blower is designed 
to suck up leaves from its inlet hole using a fan and then blow them out into a bag 
attached to its other end. The inlet hole was instead attached to the bottom of a cylinder 
filled with vermiculite using pipes and fixtures. On switching it on, the fan was able to 
 48
blow out vermiculite through the outlet and into the bags. This technique is very similar 
to the one where a sand blower was used. Figure 25 shows a leaf blower used for filling 
the bags.  
 
Figure 25 Leaf Blower 
Advantages 
? This is also a fast technique of filling the bags 
? The leaf blower is easily available and cheap 
? A maximum of 2 people are required for this technique 
Disadvantages 
? This technique is very similar to sand blower technique and hence, even here a 
lot of vermiculite is blown out of the bag 
? While operating the leaf blower, electric shocks were experienced. This was 
supposed to be caused by static charges transmitting through vermiculite. 
 49
Hence proper safety measures need to be taken while operating the leaf 
blower.  
? There is a risk of the motor, operating the blower, burning out due to the 
friction created between vermiculite and the fan attached to the motor.  
This technique was not very successful in the filling the bags because of reasons 
discussed above. Because of the shock experienced, a leaf blower powered by a gasoline 
engine was also tried. But it was not very successful because it was blowing out 
vermiculite at a high velocity and also it was seen that, the fan blowing the vermiculite 
out was getting stuck because of the weight of vermiculite acting on it. Another 
configuration was tried in which the leaf blower was attached upside down, to the bottom 
of a tank filled with vermiculite. This configuration is very similar to the one shown in 
Figure 26, but instead of the auger, a leaf blower was fixed. This was done to make the 
filling process easy but similar disadvantages as discussed before were encountered.   
 
4.3.5 Screw Conveyor System 
 A screw conveyor system was purchased from Hapman industries. Also known as 
Auger this system consists of a helicoid screw conveyor attached to a motor. The 
helicoids screws rotate, powered by the motor. When vermiculite is poured into the screw 
system it is carried through and into the bags. The screw is enclosed in a pipe and this 
pipe is inserted into the open ends of the bag. Vermiculite is filled in a container and this 
container is placed on top of the screw conveyor system. When the vermiculite drops on 
the helicoid screw, its gets carried forward due to rotation of the screws. The pipe used 
here was around 12 ft long. The pipe can be inserted till up to 1 ft inside the bag. The 
 50
bags are placed horizontally on the ground, and vermiculite is brought in by the screw 
system. Filling bags this way is easier but it was time consuming. The screws system 
could not be used for long durations at a time because the pipe heated up due to the 
friction between vermiculite and helicoid screw. 
 
Figure 26 Screw Conveyor System- Image shows a motor attached to helical screw running inside the 
tube. The container is filled with vermiculite. When vermiculite pours into the screw it is carried 
through the pipe and into the bags.  
Advantages 
? A relatively easy system of filling the bags 
? Less number of people required to fill the bags 
 51
Disadvantages 
? The equipment required is complex and expensive.  
? Its takes a while to assemble the system  
? Not easily transportable like leaf blower or sand blower 
? The pipe heats up because of the friction and hence the system has to be stopped 
frequently. 
4.4 Frames  
 Frames were used as temporary centering to mount the bags on. The advantage of 
using a frame is that it makes the construction of the structure easy. Also it gives 
temporary support to the structure during construction. Frames are also helpful in giving 
the desired shape to the structure.  
 Different frames were developed for different bag structures. The frames were 
made out of aluminum or wood. Both were used primarily to reduce the weight of the 
frames.  
4.4.1 Frame for 8 Bag Structure 
 This frame was made out of aluminum plates bend in the shape of a desired 
catenary arch. Figure 27 shows an image of CAD model of the frame designed for 
construction of this structure, whereas Figure 22 shows the frame made out of aluminum 
with bags on top if it. The shape of the three catenary supports on the frame was defined 
by the arch length, which is given by Equation 3. The arch length is important because 
the whole bag should be able to rest on the frame. Using Solid Edge, the shape was 
designed such that the total arch length of the catenary was equal to or more than the 
length of the bags. These bags were filled manually and then mounted on the structure. 
 52
The frame was then removed and structure was able to stand on its own as shown in 
Figure 28.  
 
Figure 27 Frame for 8 Bag structure with dimensions (in) 
 
 53
 
Figure 28 Structure without frame 
 
4.4.2 Frame for 16 Bag Center Connected Structure 
 The 16 bag structure was made out of center connected bags. The frame designed 
was again made out of aluminum plates bend into the shape of desired catenary. The 
shape of this frame is very similar to the one shown in Figure 27, the only changes being 
in the dimensions. Figure 29 below shows the frame made for 16 bag structure 
 54
 
Figure 29 Frame for 16 Bag structure 
  
 The bags were filled manually and were then mounted on the frame as shown in 
the figure above. After all the bags were mounted, the frame was removed. The Figure 30 
below shows the structure standing under its own weight without the support of the 
frame.  
 55
 
Figure 30 Structure without the frame 
 
 During construction of this structure it was observed that mounting the bags on 
the frame was a tedious process because of the weight of the bags. A better way of 
approaching this would be to use a pulley lever system to lift the bag from the middle and 
place it on the frame and then adjust the bags so that they confirm to the arch?s shape.  
 
4.4.3 Frame for 60 Bag Top Connected Structure 
 The frame for this structure was made out of wood. The frame was made in such a 
way so that it could be used to mount different structures of different sizes. Wood was 
primarily used to reduce the weight of the structure and its costs. The bags used were 
around 30 feet long and the structure made out of the bags was around 10 feet high. 
Hence the frame designed for supporting this structure had to be big and strong enough to 
 56
hold the structure. This frame consisted of 2 parts. Each part was designed to support one 
half the structure. Each part consisted of 4 vertical posts arranged in the corners of a 
square. The Figure 31 below shows the structure in more details 
 
Figure 31 Frame for 60 Bag Structure 
 Wooden plates were then fixed to two opposite sides of the frame. Rods were run 
through these plates. Each rod was used as a support for mounting the structure on. The 
design of this frame was such that it could support a structure made out of either 46 bags 
or 60 bags.  Another structure was made out of bags that were 1/3
rd
 the size of bags 
shown in Figure 31. This structure was designed to support this structure also. A CAD 
image showing how a structure resting on its frame would like is shown in Figure 32 
 57
 
Figure 32 46 bag structure resting on its frame  
 58
CHAPTER FIVE 
ANALYTICAL TEST OF STABILITY 
 
 The stability of the structures made was tested by analytical method and computer 
simulations. In this chapter, both these techniques will be discussed. Working Model, 
MSC. Marc was used primarily for computer simulation of the arch and some of the 
models developed are discussed in this chapter.  
Funicular polygons, which have been discussed in previous chapter, were used to 
test the stability of the arches under different load and boundary conditions. Funicular 
polygon is the line of thrust acting through the arch. If the line of thrust goes outside the 
arch then the structure is unstable. The line of thrust can be found by using the following 
parameters 
? Forces acting on the structure 
? Span of the structure 
? Height of the structure 
 For constructing the force polygon, the horizontal thrust needs to be found and 
this can be found using force equations and moment equations of the loads acting on the 
structure. Once the horizontal thrust has been found, the force polygon can be constructed 
and then the funicular polygon can be constructed.  
 
 59
5.1 Exploratory study to build a Working Model brick element from Springs and 
Dampers 
MSC. Working Model was used in the initial stage to try and model a structure 
made out of various element or body types available in Working Model. Working Model 
is essentially a 2D simulation software, which can be used to model various physical 
problems. It also allows the user to change various properties associated with the 
elements available. Therefore, by using Working Model, the aim was to see how a 
structure made out of sand bags would behave under different load conditions. In this 
section we will discuss various models developed.  
In Working Model, there are no element types available to model sand or regolith. 
Hence each bag was assumed as compressible. Springs and rigid bodies were used 
instead to model the bag. Figure 33 shows a single bag. The four corners of the bag are 
made out of rigid bodies. They are attached with springs to each other. A body is 
suspended in the middle of the bag and 4 springs are attached diagonally to the 4 corners 
as shown in the figure. The body suspended in the middle is used so that a mass can act in 
the center of the body. In Working Model, springs cannot be given any mass, hence in 
order that a mass acts in the middle of the bag, a small rigid body was placed and 
suspended with strings. Without a mass acting the center, it was difficult to approximate 
the model as bag.  
 
 60
 
Figure 33 First Working Model Brick Element developed using springs, dampers and rigid bodies 
Figure 33 shows that the model is made up of 4 rigid bodies on the corner, 
attached to each other with springs. 4 more rigid bodies were placed inside to model soil. 
Hence the 4 rigid bodies on top connected with springs can be called the ?fabric? of this 
model or the bag. The rigid bodies were given L- shape as can be seen in an enlarged 
image in Figure 34. L-shape was given so that, while running the simulation under load 
of gravity, the inner rigid bodies could rest on the outer rigid bodies. This was an 
approximation of soil settling inside the bags. The 2 outer rigid bodies on the left were 
fixed to the ground. Hence the model constructed was that of a cantilever beam.  
 
 
Figure 34 A closer look at the model developed 
 61
 
There were a total of 3 bags made in this model glued to each other as shown in 
Figure 35. The properties of the springs and rigid bodies present in this system were 
chosen at random to start of with and then varied to test how the model works.  
 
 
Figure 35 A set of 2 brick elements fixed together to act as a beam  
 
It was seen that under the force of gravity, the model starting failing as the free 
end of the structure became unstable. As can be seen in Figure 36, the free end of the 
model has bent down due to the force of gravity. The properties associated with springs 
and rigid bodies were varied, but the end result was the same. The failure of this model 
can be associated to some of weakness present in Working Model. Springs in Working 
Model have no contact properties and hence a rigid body can pass through a spring in 
Working Model. This limits the use of springs as fabric, because they won?t be able to 
hold any rigid body inside them.  
 
 
Figure 36 The Model falling down under the load of gravity  
 
 62
 Since springs have no contact properties, another model was developed where 2 
more rigid bodies were attached as shown in Figure 37. Springs were still attached to the 
model because they helped in modeling the stretching of fabric under load. The 2 rigid 
bodies on the top and bottom acted as a barrier since they had contact properties.  
 
Figure 37 Next model developed with rigid elements on top.  
  
 On simulating this model it was observed that it became highly unstable. As 
shown in Figure 38, the free end of the model starts falling down. The 2 rigid bodies 
attached to the model also are unstable. The properties of springs and rigid bodies were 
modified and similar results were obtained.  
 
Figure 38 Model failing under the load of gravity 
 63
  
 Figure 39 shows a graph plotted for the displacement of the right most body in the 
y axis. Since the slope of the graph keeps on increasing it can be seen that the model is 
unstable. Figure 38 shows that the L-shaped rigid bodies on the inside also act unstable 
and start to hinge on the outer L-shaped body. To prevent this from occurring another 
model was developed where the L-shaped bodies on the inside were replaced with balls.  
 
Figure 39 Graph showing the y-position of the model 
 
 Figure 40 shows a model with more rigid bodies attached to it. The L-shaped 
bodies on the inside were replaced with balls to prevent them from hinging around the 
outer L-shape bodies. Also 6 rigid bodies were added to the top and bottom part of the 
model as can be seen in Figure 40. These bodies act as the fabric in a sand bag.  
 64
 
Figure 40 Next model developed with rigid bodies on both the outside and inside. The outer bodies 
are used to model bag and inner bodies are used to model sand 
 On simulating this model, stability was observed as shown in Figure 41 and the 
graph in Figure 42 shows that the system oscillates.  
 
Figure 41 The model vibrates under the load of gravity.  
 
Figure 42 Graph showing the oscillatory motion of the model  
 65
 The previous model was a success as it did not fall down under the load of gravity 
and instead remained stable. Next another model was created based on the previous 
model, but the springs inside were replaced by circles of equal dimensions and properties. 
This was done to model the sand particles inside the bag and to see how well Working 
Model was able to simulate multiple bodies. Figure 43 shows the model developed. 
Another difference from the previous model is that the springs connecting the rigid 
bodies on the inside of the model were replaced by rigid bodies on all 4 corners. 2 rigid 
bodies were placed on each side and connected to each other using a sliding joint. This 
was done so that all the 4 sides could elongate or compress under load.  
 
Figure 43 Model with balls to simulate sand packed inside bags 
  
 On running the simulation it was observed that the model failed under the load of 
gravity. Also, due to the presence of numerous bodies, the simulation took a huge amount 
of time. Figure 45 shows a graph for the displacement of top right L-shaped rigid body?s 
displacement along the y-axis. As can be seen, the body along with other bodies in the 
system keeps falling and hence this model is a failure.  
 66
 
Figure 44 Model failing under the load of gravity 
  
  
Figure 45 Graph showing the y-position of the model  
 
 All the above models were developed to see how a bag filled with sand would act 
under the load of gravity if hung like a cantilever beam. This was done to get some 
insight into how well Working Model would be able to simulate a sand bag and what 
kind of approximations can be made. It was observed that Working Model has limited 
use in simulating such a model because of the following reasons 
 67
1. Only rigid bodies can be simulated in Working Model. To simulate compression 
of a body, springs can be used but springs have no contact properties, hence it 
becomes difficult to model the contact between 2 deformable bodies. 
2. It was seen that Working Model has limitations when it comes to modeling the 
friction between 2 or more bodies. A very high friction value between 2 bodies 
should be able to prevent them from sliding on each other under suitable load 
conditions. But in Working Model sliding could not be prevented even after 
giving very high value of friction of coefficient. This limits the way the model is 
developed as in case of masonry arch it is assumed that voussoirs don?t slide on 
each other.  
A simple model of a masonry arch was developed in Working Model, where each 
bag was approximated as 4 rigid bodies in corner of the bag attached to each other using 
springs. Figure 46 shows the model created to simulate a masonry arch. The 2 ends of the 
structure are fixed to the ground. As can be seen, bags are joined to each other using a 
common spring. This is done because in a masonry arch it assumed that the voussoirs 
don?t slide on each other.  
 
 
 68
 
Figure 46 Arch Constructed using springs and rigid bodies 
 
 The properties of the springs were chosen at random first to see how the model 
simulates. On simulating under the load of gravity it was observed that the system 
oscillates and settles around the position shown in Figure 47. The advantage of this 
model is that the bags are compressible because of the presence of springs. This 
approximates the regolith structure very closely. The disadvantage of this model is that it 
fails when more bags are used instead of 6 used in this case.  
   
 69
 
Figure 47 Arch stable when simulated in Working Model 
 
5.2 Excel Spread Sheet for Funicular Polygon 
 To calculate the horizontal thrust, as discussed before, reaction forces on the 
structure, span of the structure and height of the structure are needed. An excel 
spreadsheet was developed to calculate the horizontal thrust. A sample excel spread sheet 
is shown in table below.  
Table 2 Excel Spread Sheet 
 W
1 
W
2 
W
3 
W
4 
W
5 
x
i
(in m) 0.157988 0.118542 0.078994 0.039522 0
y
i
(in m) 0.112522 0.184404 0.22479 0.24323 0.245618
W
i
(in N) 140 107 85 75 0
?W
i 
140 247 332 407 407
W
i
x
i 
22.11832 12.68397 6.71449 2.96418 0
?W
i
x
i 
22.11832 34.80229 41.51678 44.48096 44.48096
 70
       
H 113.5244         
  
This spread sheet can be better explained with the help of Figure 48 shown below  
 
Figure 48 Arch with various loads acting on it 
 
 71
 In this image only half an arch is shown as it is assumed the arch is symmetrical 
along the axis, both in shape and in force distribution. W
1
, W
2
, W
3
, W
4
 and W
5
 are the 
forces acting on the structure. The first row ?x
i
? is the distance along the x axis from the 
point of action of force to the middle of the arch denoted by line ad. The second row ?y
i
? 
is the vertical distance from the point of application of force, which is along the y axis, to 
the bottom of the arch denoted by point ?b?. The third row ?W
i
? is the force acting at 
each point in Newton. The fourth row ??W
i
? is the cumulative value of the forces. Similarly 
the fifth column is the product of the force and distance along the x axis. The next row ??W
i
x
i
? is 
the cumulative sum of the previous row. These variables are required to calculate the 
horizontal thrust. The horizontal thrust is calculated using the following equation 
y
xWxW
H
iii
)()1*( ???
=  
Equation 5 
 Here ?x1? is half the span of the arch or the distance between points ?a? and ?b? 
along the x axis and ?y? is the vertical distance between points ?a? and ?b?. This 
equation is found from statics by calculating the momentum of the structure about the 
point ?a?.  The force equations satisfying the equilibrium position can also be found. 
These 2 equations when solved give the solution for H. The equations and the solution 
can be found in the Appendix.  
5.3 Stability of 8 Bag Structure  
 The construction of the 8 bag structure has been discussed in previous chapters. 
The 8 bag structure was filled with vermiculite using manual technique and mounted on a 
frame as shown in Figure 27. After mounting the frame was removed and the structure 
was able to stand under its own weight as shown in Figure 49. External loads in the form 
 72
of sand bags were also applied to the structure to test its stability. Funicular polygons 
were developed for the structure with load and no load.  
The structure was mounted on the frame and the frame was then removed. The 
bags were tightly stacked up against the frame and they were stacked in such a way that 
both the ends of the bag rest on ground. The frame was then removed and it was observed 
that the structure was able to stand on its own without any support from the frame. An 
image of the structure made is shown below.  
 
Figure 49 Center Connected Bags with no Load 
 
 Length of base= 18 in 
 Height = 16 in  
 The image shows that the bag is able to stand on its own. Extra weight was also 
added to this structure to test its stability. Sand bags weighing 150 lbs were added on top 
of the structure and it was observed that the bag was still able to support itself. A little 
compressive flattening at the contact between bags was observed, but the amount of 
 73
flattening depended upon the amount of vermiculite filled inside the bags and the load on 
the bag. The bags were tightly packed in this case. Because of this the compression of 
bags was not very high. Slipping was not observed between the bags and this was in 
agreement with the masonry arch theory as discussed in chapter 2. The presence of 
stitches between the bags gives an extra degree of stability to the structure. The funicular 
polygon was drawn for this configuration of the arch with 150 lbs weight acting on it and 
is shown in Figure 50. It was seen that the line of thrust stays inside the structure and 
hence confirming the results obtained from this experiment.  
  
Figure 50 Funicular Polygon for 8 bag structure with 150 lbs weight on it 
 
 Another configuration was tested, where the length of the base was reduced and 
hence the height was increased. On adding weight to the structure it was seen that the 
 74
bags settle down into an ?M? shape configuration by forming hinges as shown in Figure 
51. This structure was also observed to be stable, as it was still able to support itself with 
external weight acting on it, in ?M? shape. An image of this new configuration is shown 
below.  
  
Figure 51 8 bag structure forming M-shape when loaded 
 Funicular polygon drawn for this configuration is shown below 
  
Figure 52 Funicular polygon of loaded 8 bag structure 
 75
 It can be seen from the funicular polygon that the line of thrust goes outside the 
structure making it unstable, but in this case, the bags remain stable. This can be 
compared to a masonry arch, where the arch would fail if the funicular polygon goes 
outside the structure. The masonry arch fails because hinges are formed and they make 
the structure unstable. The voussoirs in the arch are not connected to each other and 
hence when hinges form, they open up at the location of the hinge. But with the structure 
made out of 8 pocket bag, even though the funicular polygon shows the structure is 
unstable, the structure does not fail and instead goes into an m-configuration. The m-
shape shows the location of potential hinges in the structure. The location of the hinges is 
at the top of structure where the bags go into m shape. Since these bags are center 
connected, the hinge is not able to separate the bag and therefore the structure does not 
fail. It was noticed that addition of extra weight lead to the collapse of the structure. this 
shows that the m-shape configuration can be assumed to be a stable shape but the factor 
of safety reduces here considerably.  
5.4 Stability of 16 Bags Structure  
 The structure constructed out of 8 bags was very small compared to the final 
structure desired. Due to the small size and less number of bags it performed favorably 
and in line with results obtained from funicular polygon analysis. For the next step, a 
bigger structure was desired. For this 16 center connected bags were stitched. The 
dimension of each bag is as follows 
Length = 3 ft 
Width= 6 in 
 76
 The bags were filled using manual technique discussed in chapter four. Each bag 
took a lot of time to be filled and 2 person were needed, one to hold the bag and the other 
to pour the vermiculite in. These bags were considerably larger than the small 8 bags and 
also heavier. Because filling the bags was performed manually, the bags were not able to 
be packed tight initially. This was done to help in reducing the weight of the structure. 
After all the 16 bags were filled, the structure was mounted on a frame discussed in 
chapter 4. The weight of the bags was considerable and hence 3-4 set of hands were 
required to lift the bags from the floor and mount them on the frame. For mounting 
purposes a lever pulley system was considered, which could lift the bags from the middle 
and mount them on the frame, but was not implemented. Another approach was the use 
of a belt running through the middle of the bags to lift them up. As shown in Figure 53, a 
buckle was riveted to the middle of each bag. The idea was to run a belt through all these 
buckles and then to pull the belt from 2 ends in such a manner that the bags would rise up 
from the middle. The belts had to be pulled from under the bag such the when pulled the 
force exerted would act towards the center of the bag. The idea was to bring the ends of 
the bag together using the belt, which would then make the other pocket stack on each 
other because the belt ran through buckles placed in the middle of each pocket. This 
technique can be better visualized as bending a bar from its middle by exerting force on 
its ends, acting towards the center. When the ends of the bar are fixed such that they can 
only move in one plane, the force exerted would cause the middle of the bar to rise and 
bend. But this technique did not work out because of the weight of each pocket. A huge 
amount of force needed to be applied to lift the bag and also, the bags were not stacking 
on each other as easily as thought of.  
 77
 
Figure 53 Buckle on each pocket, fixed using rivets.  
 
 For manually mounting the bags on the frame, the bags were first lifted and 
mounted on the frame. Then starting from one side, each bag was compressed against the 
table. In this manner, the bags were packed tightly against each other increasing the area 
of contact between them as shown in Figure 54. This was done to all the bags. At the 
ends, sand bags were placed to prevent the structure from slipping on the table.  
 78
 
Figure 54 Bags stacked on each other.  
 79
 After mounting the bags in the first trial it was noticed that the bags at the top of 
the structure needed to be packed more tightly with vermiculite as they were not 
compressing against each other and making the structure unstable. Hence the bags were 
pulled down and the top 5 bags were packed tightly (to around 3/4
th
 of its volume). After 
this the bags were mounted on the frame again. This structure looked a little more stable 
than the previous one. But after the frame was removed, the structure stood for a while 
and then collapsed within few minutes. Figure 55 shows the structure standing on its own 
without the help of a frame.  
 
 
Figure 55 16 bag structure standing without frame  
 The funicular polygon in Figure 56 developed for this structure also shows similar 
results. As can be seen, the funicular polygon goes out on top of the structure and hence it 
fails. During the construction process difficulties were faced in stacking the bags on each 
 80
other. This made it difficult to keep the bags in desired position against the frame while 
stacking them up. On the top where the bags were tightly packed, the desired catenary 
shape was not assumed as can be seen in Figure 55. This is because the bags were packed 
tightly. This made the bags less compressible because of which they couldn?t be stacked 
on each other at top. This showed that the bags on top needed free volume to compress 
against each other.  
 
Figure 56 Funicular polygon developed for the 16 bag structure 
 Working with this center connected bag showed the in stability of a structure 
made out of such bags. Hence top connected bags were used for next set of experiments.  
5.5 Stability of 46 and 60 Bags Structure 
 A 60 bag structure was discussed in previous chapter. The 60 bag structure was 
not easy to be handled by hands. So a smaller structure made out of bags which were 
1/3
rd
 the size of the actual bags. This helped in reducing the weight of the bags after they 
were filled with vermiculite. To make the construction of the structure even easier, only 
46 bags were used instead of 60. As discussed before this structure is made out of 3 bags 
 81
of different sizes. There are 10 bags of each size in one half of the structure. So starting 
from the top, 23 bags were taken on each side. The remaining bags were stacked up 
against the sides of the structure and they helped the ends in sticking to the ground.  
 For filling the bags, first manual technique was used. It didn?t work out because 
of the large number of bags present.  Next leaf blower and sand blower were used to fill 
the bags but were soon dismissed because of the problems discussed in chapter four. 
Finally the screw conveyor was used to fill the bags. This technique took a long time to 
fill each bag and also the conveyor system would become very hot due to friction as 
discussed in previous chapters. Because of this manual technique was again used to fill 
the bags up.  
 To form a catenary arch after the bags were filled; a drum was placed under the 
middle of the bags that is around the 23
rd
 and 24
th
 bag. This drum was placed on a jack 
which could be raised or lowered. When the jack was raised, the bags would rise from the 
middle and form a catenary arch shape. But a problem was encountered because the jack 
could not be raised higher enough. Also the bags were tightly packed. Because of this, 
each bag assumed a round shape instead of the rectangular shape desired. This caused the 
bags to roll on each other and the ends of the structure assumed a circular shape. Because 
of lack of time and manpower, this structure could not be developed further. But 
funicular polygons were developed for this structure and were found to be stable. Figure 
57 shows a funicular polygon developed for a 46 bag structure with no external forces 
acting on it.  
 
  
 82
 
Figure 57 Funicular Polygon for 46 bag structure.  
   
5.6 Stability of 60 Bags Structures 
 The construction of the 60 bags top connected structure was carried out in MSFC. 
This was the final structure to be developed. A top connected bag was used after it was 
observed in previous experiments that a structure made out of center connected bags 
would be more unstable. To test the stability of a top connected bag, a small 6 bag piece 
of fabric was made in Auburn University and tightly packed with vermiculite. One end of 
this bag was then fixed and the other end was left free as in a cantilever beam. It was 
observed that the bags were able to support their own weight and did not collapse under 
the load of gravity. Figure 58 shows the cantilever beam made out of top connected bags.  
 83
 
Figure 58 Top Connected bags acting as cantilever 
 On closer look it was seen that the fabric on top of the structure goes into tension 
and the bags start compressing onto each other. If the same structure was made out of a 
center connected bag, then gravity would make the beam fail, because there would be no 
tension on top of the bags to hold them upright. Also in center connected bags, each 
pocket tends to roll on each other under the load of gravity. On the other hand, rolling of 
packets on each other is prevented by the top layer of fabric in top connected bags.  
Figure 59 shows a CAD image of the structure discussed above. As can be seen, the 
rolling of pockets on each other is not possible because of the top layer of fabric and also 
because of the shape of the bags. The structure shown in Figure 59 looks different from 
that shown in Figure 58. This is because while performing the experiment, the bags 
assumed a slight circular shape and didn?t remain in a perfect rectangular shape as 
desired. This was primarily due to the settling of vermiculite due to gravity. The walls of 
each pocket, being made of fabric, would stretch a little bit and form a circular shape. 
Since each pocket has a fixed distance between them, the circular shape of the pockets 
 84
increases the distance and causes the fabric on top to go into tension. And since the 
pockets push against each other, they start compressing.  
 
Figure 59 CAD image of top connected cantilever beam 
 The tension on the top layer and compression between the bags keeps the 
structure from failing. This cantilever beam experiment shows the stability that can be 
achieved by using top connected bags, because of the ability of the top layer to resist 
tensile loads.  
 The 60 bags constructed for this structure consisted of 3 bags of different 
dimensions, each type being 20 in number. So each half of the structure consisted of 10 
bags of each kind. The dimensions of each set of bags is as follows 
? 20 pockets at the bottom measuring 6? x 2? in cross-section. 
? 20 pockets above the bottom pockets, measuring 6? by 1.5? in cross-section. 
? 20 pockets that form the crest of the arch, measuring 6? by 1? in cross-section. 
 Before constructing the structure analysis was performed on a series of 60 bag 
structures each with different dimensions. It was observed that taller configurations 
Top layer 
goes into 
tension on 
loading 
Bags assume slight 
circular shape and start 
compressing 
 85
would be more stable, and would be able to support more weight. The first structure that 
was analyzed is shown in Figure 60.  
 
Figure 60 Front View with Dimensions (ft) 
 Funicular polygon was developed for this structure with no external load acting 
on it. Figure 61 shows the funicular polygon, and it can be seen that the bag will form 
hinges between the 15
th
 and 16
th
 bag. Assuming that the bags are symmetric, the hinge 
would form on the other side of the structure too. These hinges will tend to open towards 
the outside of the bags. But because of the presence of a layer of fabric on top, the 
formation of these hinges will be prevented. Hence this configuration might be stable.  
   
 86
 
Figure 61 Funicular polygon for 60 bag structure 
 Another funicular polygon was made for this structure, under the same load, by 
starting the construction of the polygon from middle of the structure instead of the ends 
of the structure as in the previous case. The funicular polygon developed for this case is 
shown in Figure 62 
 87
 
Figure 62 Another possible configuration for 60 bag structure.  
 This shows that hinges will form around the 20
th
 and 21
st
 bag. Since these hinges 
will open towards the inside of the structure where there is no fabric present, this 
structure might fail. Since both the funicular polygons developed for this model go out of 
the structure, it can be assumed that the structure will be unstable. Therefore this structure 
was not developed further.  
 Another model was developed where, the height of the structure was increased 
and the width was reduced. This configuration is shown in Figure 63.  
 88
 
Figure 63 60 Bag structure with dimensions (ft) 
 The funicular polygon developed for this configuration lies inside the arch and 
hence shows that this configuration can be stable. The funicular polygon is shown in 
Figure 64.  
 89
 
Figure 64 Funicular Polygon 
 This shows that the arch becomes more stable on increasing the height of the 
structure. Since the length of the bags remains the same, increasing the height causes the 
ends to come closer as can be seen clearly by comparing Figure 64 and Figure 62. 
Because of this the distance between bags on each side decreases. And as we go towards 
the top bags, the reduced distance causes the bags to get more tightly packed against each 
other. More tightly bags on top makes it difficult for the bags to start failing from the top 
and this gives the taller structure more stability.  
 
5.6.1 Erecting the Structure 
 Only 46 of the 60 bags were used when building at MSFC.  This was done 
because the remaining 14 bags could be used a strong foundation to hold the structure 
and also, with 46 bags the structure was more manageable.  Figure 65 shows a stable 
 90
structure, designed to be stable. Only 3 large bags were present as bottom bags.  A 
wooden frame in Figure 66 was constructed and the structure was erected on this frame. 
Pipes were placed at 5 points on the frame in the shape of an approximate catenary. The 
positions of these points were determined from Figure 65, which shows the catenary 
shape build in Solid Edge. This shape corresponds to the actual catenary being 
constructed out of 60 bags. Table 3 shows the x and y co-ordinates of the points shown in 
Figure 65.  
 
Figure 65 CAD Model Template to Guide Erecting 
Table 3 Co-ordinates of points shown in Figure 65 
POINT X Y 
A 0 0 
1 1.45 18 
2 2.151 23.746 
 91
3 2.985 29.475 
4 3.9 35.18 
5 5.1 40.857 
6 6.4 46.49 
7 7.9 52.08 
8 9.6 57.61 
9 11.59 63.06 
10 13.806 68.411 
11 16.31 73.63 
12 19.129 78.687 
13 22.29 83.536 
14 25.817 88.127 
15 29.724 92.399 
16 33.56 95.88 
17 38.66 99.73 
18 43.65 102.65 
19 48.913 105.087 
20 54.39 106.955 
21 60 108.287 
 
 Assuming that the structure is symmetric, the position of the pipes is given by the 
following x, y co-ordinate values- 
Actual Pipe Locations: Lower Level Pipes: x=14.5?, y=70? 
 92
                                            2
nd
 Level Pipes: x=25.7?, y=88? 
          Top Pipe: x=60, y=108? 
 
 
Figure 66.  Air-Filled 46 Bag Structure, 5 pipes guiding bag filling. 
 
After airfilling the bags, filling of bags with vermiculite proceeded from bottom 
bags up.  Bags were filled using a Hapman Flexible Screw Conveyor System. The white 
pipe contains a helicoid screw (without a center core tube), rotated by a motor that feeds 
and forces vermiculite into the bags.  The white pipe was inserted into the bag to within 1 
foot of the bag end, and the motor turned on to rotate the screw.  As vermiculite flowed 
out, the tube was slowly and incrementally pulled from the bag.  This operation was 
labor-intensive, required human assistance to distribute the vermiculite as it came out of 
the tube into the bag (Figure 67).   
 93
 
Figure 67: Big Filling Process 
 
Lower bags were filled and formed to a near rectangular shape as shown in Figure 
67, while trying to provide bag angle as the structure grew which can be seen by the 
angle obtained by the black zippers.   
 
 
Figure 68.  Rectangular Packed Bags 
 
 94
Filling of the top 20 bags required a different technique.   Unfilled bags which 
hang down from the top fabric cannot be filled with a rectangular shape. This is because 
due to gravity and the looseness of the bag the vermiculite will settle at the bottom of the 
bag making it round in shape. Therefore the top 20 bags must be filled to capacity with 
vermiculite, which causes them to round. The top three bags couldn?t be filled because 
with the topmost bags were nearly touching each other. This left no place for the top 
three bags. The maximum amount of material that could be placed in a bag was restricted 
by the Helicoid Screw System, which was limited to a relatively low compaction 
pressures because of the stiffness and strength limitations of the relatively flexible and 
shaftless helicoid.  Low compaction pressure contributed to the top three bags not filling 
at pressures below desired.   The final erected prototype is shown in Figure 69 (front 
view) and Figure 70(rear view).   In these figures the pipes have been removed and the 
structure is able to stand on its own.  It was noticed that the structure settled around 2? 
once the top 3 pipe supports were removed.   
 
Figure 69.  Front View 
 95
   
 
Figure 70.  Rear View.   
Upon review of the standing structure and the process of erecting, the following 
observations were made- 
1. The left side of the structure in Figure 69 (right side in Figure 70) is the ?good 
side?.  It was built and maintained a catenary shape very near design 
specifications, except for the topmost bags.   
2. The right side of the structure in Figure 69 (left side in Figure 70) is the ?bad 
side?.  Here several flaws were observed that were a result of bags not filled to 
capacity 
3. Figure 71a shows that several bags on the bad side with a flattened profile that 
lost the catenary-shape curvature.  Bags slipped downward despite attempts to 
erect the structure with a catenary shape; bags slippage was visible and occurred 
over a several second interval.   Slippage is attributed to a shortage of vermiculite 
due to incomplete packing, which did not occur on the good side; the vermiculite 
 96
grains may slide (shear) with respect to each other inside the bags.   This situation 
is correctable (but difficult given that zippers are only on one end) by hand 
loading more vermiculite through an open zipper and forcing material into the bag 
with a plunger.  A simpler fix would have been to have used an auger-type system 
which deposits vermiculite under higher pressure than the helicoid. 
 
 
Figure 71 Closer views of structure 
Figure 71b shows a tightly filled bag; it bulges and exhibits a hardness which can 
be felt by applying finger pressure.  Tightly filled bags are necessary to create bags with 
sufficient vermiculite strength.  Part of the internal bag pressure is a result of loading 
from the bags above. 
 97
4.  Figure 71c shows another characteristic of a well-built structure with tight bags.  
Here it is difficult to insert a finger between the bags, implying that the bags are 
tightly packed with respect to each other.  Compressive and shearing loads are 
transmitted without failure across the fabric boundary, from bag-to-bag. 
5.  Figure 71d show a characteristic of inadequately packed bags.  Here it is easy to 
insert a finger between the bags ? this may imply the beginnings of hinge 
formation.  The bags themselves are loosely packed - by applying finger pressure 
the bags easily indented.  The dark patch in the figure represents glue that was 
placed in-between the bags as an experiment.  The glue did not appear to affect 
the structure.  If the glue had affected the structure, the glued fabric would have 
been in tension, and this was not the case. 
 This shows that a catenary arch can be constructed from regolith top connected 
bags by using proper techniques and analysis. The funicular polygon proved to be reliable 
in estimating the stability of the structure.  
 98
CHAPTER SIX 
CONCLUSIONS AND SUMMARY 
This thesis presents the process involved in construction of a lunar garage made 
out of multi pocket bag filled with regolith. The theory and principle behind Masonry 
Arches was adopted to be used in the design and construction of lunar base.  Various 
techniques were developed and tested at Auburn University and MSFC to develop a 
better understanding of the various issues involved in constructing such a lunar base. 
Analytical methods of finding structures stability were also developed. This chapter 
presents a brief summary of various methods discussed previously in this thesis.  
6.1 Thesis Summary 
 For the testing and construction of lunar base, two types of bags were developed. 
One was center connected bags and the other was top connected bags. As the name 
suggests, the center connected bags were made by stitching together pockets through 
their center whereas in a top connected bag, pockets were stitched onto a layer of fabric. 
This fabric ran through the top and all the pockets hung freely on the bottom.  
 The first structure was developed out of 8 pocket center connected bags. These 
bags were filled with vermiculite and mounted on a frame. The structure made, was 
found to be stable. The analytical solution developed using funicular polygons also 
showed the structure as stable. The next structure developed was made out of 16 pocket 
center connected bags. Filling of bags manually with vermiculite was a tedious and 
 99
tiresome process. The structure constructed was not very stable and the funicular polygon 
developed for this structure showed similar results. The next structure constructed was 
made out of 5 pocket top connected bag. The bags were filled manually and a cantilever 
beam was constructed using this bag. The cantilever beam was constructed to show the 
extra stability and bending strength top connected bags would provide over center 
connected bags. The stability of the cantilever beam proved this. This showed that 
structures made out of top connected bags would offer more stability. So the next 
structure was developed using top connected bags. A 60 pocket bag was used to develop 
this structure. Because of the large number of pockets present, manual filling of pockets 
with vermiculite was ruled out. Other methods like using a sand blower, a leaf blower etc 
were tested but were found unsuitable. Finally a screw conveyor system was purchased 
and used for filling the bags. This method, though more efficient then other methods, was 
still very labor intensive and involved the manual spreading of the vermiculite inside the 
bags. For this structure, it was decided that only 46 bags would be used. This reduced the 
time needed to fill the bags, and also the remaining bags were used as foundation support 
for the structure. The funicular polygons developed for this structure showed a stable 
configuration and this was confirmed after erecting the structure, as it could stand on its 
own under the load of gravity.  
6.2 Future Research and development 
 Finite element analysis of the structure can provide more accurate results for test 
of stability of a lunar structure. Hence future work can involve the development of finite 
element models of the structure that could be tested by applying appropriate load 
conditions and boundaries. There are various difficulties in developing such a model, as a 
 100
model developed using soild elements and membrane elements can prove to be very 
complex. An approximate model, needs to be developed  
 A lot of techniques were used to fill the bags with vermiculite, and the screw 
conveyor system was found to be the most suitable. Better techniques can be developed 
as even the screw conveyor system had its shortcomings. If a lunar structure is to be 
made on the moon, a proper and more reliable technique of filling the bags with regolith 
needs to be developed. The collection and storage of regolith on the moon is another area 
of research. Also, the ability of the structure to shield harmful radiations on the moon?s 
surface need to be looked into and is an area of active research. Another area of research 
is the development of support frames that are needed during the construction of the lunar 
structure. Frames that could be easily assembled on the moon?s surface and which can be 
adapted easily to fit various structures need to be developed.  
 101
REFERENCES 
[1] L.A. Taylor, Dong-Hwa S Taylor, ?Considerations for return to the moon and 
lunar base site selection workshops?, Journal of Aerospace Engineering, April, 
pp. 68-79, 1997 
[2] H.J. Smith, A.A. Gurshtein, W. Mendell, ?International Manned Lunar Base: 
Beginning the 21
st
 Century in space?, Science and Global Security, vol. 2, pp. 
209-233, 1991 
[3] H.H. Schmitt, ?Business approach to lunar base activation.? , Space Technology 
and Applications Int., vol. 654, pp. 1061-1066, 2003 
[4] H. Benaroya, ?An overview of lunar base structures: past and future?, AIAA Space 
Architecture Symposium, Houston, Texas, Oct. 10-11, 2002 
[5] H. Benaroya, L. Bernold, K.M Chua, ?Engineering, Design and Construction of 
Lunar Bases?, Journal of Aerospace Engineering, vol. 15, no. 2, pp. 33-45, 2002 
[6] J. L. Klosky, S. Sture, Hon-Yim Ko, F. Barnes, ?Geotechnical Behaviour Of JSC-
1 Lunar Soil Simulant?, Journal of Aerospace Engineering, vol. 13, no. 4, pp. 
133-138, 2000 
[7] G.B. Ganapathi, J. Ferrall, P.K. Seshan, ?Lunar Base Habitat Designs: 
Characterizing the Environment, and Selecting Habitat Designs for Future Trade 
offs?, Jet Propulsion Laboratory, May 1993.
 102
[8] S. Matsumoto, T. Yoshida, H. Kanamori, K. Takagi, ?Construction Engineering 
Approach for Lunar Base Development?, Journal of Aerospace Engineering, vol. 
11, no. 4, pp.129-137, 1998  
[9] P. Eckart, ?Lunar Base Parametric Model?, Journal of Aerospace Engineering, 
vol. 10, no. 2, pp.80-90, 1997 
[10] J.H. Adams, R. Silberberg, C.H, Tsao, J.R. Letaw, ?Radiation Transport of 
Cosmic Ray Nuclei in Lunar Material and Radiation doses?, Lunar Bases and 
Space Activities of the 21
st
 Century, pp. 663, 1985 
[11] B. Mishra, M. Duke, D.L. Olson, J. Roubidoux, J. McDermott, D. Tordonato, 
?Low Temperature Molten Salt Electrolysis For Oxygen Production from Lunar 
Soil?, Space Resources Roundtable VII: LEAG Conference on Lunar Exploration, 
pp. 66, 2005 
[12] McCoy Bonnie, ?Lunar Oxygen Production Detailed Design Review?.  
[13] The Artemis Project- http://www.asi.org/ 
[14] Lunar Oxygen Production Plant: Specification Sheet- 
http://www.tsgc.utexas.edu/tadp/1995/spects/o2.html 
[15] M.M R. Taha, ?Design of Masonry Arches,? ENCI 595.05 
[16] F. P. Spalding, ?Masonry Structures?, New York, John Wiley & Sons, Inc. 1921 
[17] J. Heyman, ?The Masonry Arch?, New York, Halsted Press, 1982  
[18] Wolfram Mathworld- http://mathworld.wolfram.com/Catenary.html 
[19] Task Committee on Lunar Base, ?Overview of Existing Lunar Base Structural 
Concepts?, Journal of Aerospace Engineering, vol. 5, no.2, pp.159-174, 1992 
 103
[20] H. Benaroya, M. Ettouney, ?Framework for Evaluation of Lunar Base Structural 
Concepts?, Journal of Aerospace Engineering, vol. 5, no.2, pp. 187-198, 1992 
[21] R.M. Drake, P.J. Richter, ?Concept Evaluation Methodology for Extraterrestrial 
Habitats?, Journal of Aerospace Engineering, vol. 5, no. 3, pp. 282-296, 1992 
[22] L.S Bell, M. G. Fahey, T.K. Wise, P. C. Spana, ?Indigenous Resource Utilization 
in Design of Advanced Lunar Facility?. Journal of Aerospace Engineering, vol. 5, 
no. 2, 1992. 
[23] M. Ettouney, H. Benaroya, N. Agassi, ?Cable Structures and Lunar 
Environment?, Journal of Aerospace Engineering, vol. 5, no. 3, 1992.  
[24] F.K, Schleyer, ?Analysis of Cables, Cable Nets and Cable Structures?, 
Cambridge,The MIT Press  
[25] D. V. Smitherman, Jr. , V. Dayal, D.J. Dunn, II, ?Architecture for a Mobile Lunar 
Base Using Lunar Materials?, Space Technology and Applications International 
Forum, vol. 813, pp. 1022-1029, 2006 
[26] D. Smitherman, M.Rais-Rohani, D. Dunn, D. Perkinson, ?Hybrid Robotic Habitat 
for Lunar Exploration?, Space Technology and Applications International Forum, 
vol. 746, pp. 1078-1087, 2005 
[27] J.M Hines, C.E Miller, R.M. Drake, ?Mechanical Equipment Requirements for 
Inflatable Lunar Structures?, Journal of Aerospace Engineering, vol. 5, no. 2,  
1992 
[28] Cal Earth Forum, http://www.calearth.org/  
[29] The Vermiculite Association, http://www.vermiculite.org/ 
[30] Vermiculite, http://en.wikipedia.org/wiki/Vermiculite 
 104
APPENDIX A 
Excel Spread Sheets developed for 8 bag structure for different load conditions 
x(in m) 0.26129 0.186614 0.111938 0.037262 0
y(in m) 0.210439 0.317322 0.37084 0.393141 0.397942
W(in N) 140 107 85 75 0
?W 140 247 332 407 407
Wx 36.58057 19.96768 9.514713 2.794635 0
?Wx 36.58057 56.54825 66.06296 68.8576 68.8576
       
H 170.5789  
       
x(in m) 0.26129 0.186614 0.111938 0.037262 0
y(in m) 0.210439 0.317322 0.37084 0.393141 0.397942
W(in N) 140 107 85 150 0
?W 140 247 332 482 482
Wx 36.58057 19.96768 9.514713 5.58927 0
?Wx 36.58057 56.54825 66.06296 71.65223 71.65223
       
H 226.8756  
       
x(in m) 0.26129 0.186614 0.111938 0.037262 0
y(in m) 0.210439 0.317322 0.37084 0.393141 0.397942
W(in N) 140 214 85 150 0
?W 140 354 439 589 589
Wx 36.58057 39.93535 9.514713 5.58927 0
?Wx 36.58057 76.51593 86.03064 91.61991 91.61991
       
H 267.0339  
       
x(in m) 0.26129 0.186614 0.111938 0.037262 0
y(in m) 0.210439 0.317322 0.37084 0.393141 0.397942
W(in N) 400 107 85 150 0
?W 400 507 592 742 742
Wx 104.5159 19.96768 9.514713 5.58927 0
?Wx 104.5159 124.4836 133.9983 139.5876 139.5876
       
H 275.666         
 
 105
Excel Spread Sheet for 16 bag structure  
big sang bags-no load-16 bags supported       
mass of each bag= 100*5*5*pi*27*(0.0254)^3      
3.475          
Weight  
34.09          
  
x(in m) 0.653 0.566 0.4785 0.3912 0.3039 0.217 0.129 0.0422 0
y(in m) 0.2627 0.375 0.4258 0.4469 1.334     
W(in 
N) 40 40 40 40 40 40 40 40 0
?W 40 80 120 160 200 240 280 320 320
Wx 26.119 22.63 19.138 15.647 12.157 8.667 5.178 1.6876 0
?Wx 26.119 48.75 67.886 83.533 95.691 104.4 109.5 111.22 111.22
           
H 94.19                 
Excel Spread Sheet for 60 bag top connected structure  
File Name= catenary_Teeth_bag_nasa_presentation_funipoly.par
30 ft long structure, with 60 bags. 1 ft long and 5 ft deep bags. E7.079
Weight
69.4
Total Weight of 60 4200
Weigh of 30 bags= 140
x(in m 1.14 1.057 0.975 0.894 0.813 0.732 0.65 0.569 0.488 0.406 0.325 0.24 0.1626 0.081 0
y(in m 0.26 0.375 0.426 0.447 1.334 4.445
W(in N 140 140 140 140 140 140 140 140 140 140 140 140 140 140 140
?W 140 280 420 560 700 840 980 1120 1260 1400 1540 1680 1820 1960 2100
W x 159 147.9 136.6 125.2 113.8 102.4 91.03 79.65 68.28 56.9 45.52 34.1 22.758 11.38 0
?W x 159 307.2 443.8 569 682.8 785.2 876.2 955.9 1024 1081 1127 1161 1183.4 1195 1195
H 307
File Name= catenary_Teeth_bag_nasa_presentation_funipoly_thickbase.par
30 ft long structure, with 60 bags and wide base. 30 vertical forces assumed. 
x(in m 0.94 0.889 0.838 0.787 0.737 0.686 0.635 0.584 0.501 0.417 0.334 0.25 0.1669 0.083 0
y(in m 0.26 0.375 0.426 0.447 1.334 4.445
W(in N 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140
?W 280 550 810 1060 1300 1530 1750 1960 2160 2350 2530 2700 2860 3010 3150
W x 263 240 217.9 196.9 176.8 157.7 139.7 122.7 100.1 79.29 60.09 42.6 26.705 12.52 0
?W x 263 503.2 721.1 918 1095 1252 1392 1515 1615 1694 1754 1797 1823.6 1836 1836
H 451
 
 106
Excel Spread Sheet for 60 bag top connected structure 
30 ft long structure, with 60 bags. Base widened to 10ft and ht reduced to 14 ft
file name=  catenary_Teeth_bag_funipoly_longbase_reducedht.par
x(in m) 1.404 1.307 1.21 1.114 1.017 0.92 0.823 0.726 0.629 0.533 0.436 0.339 0.242 0.145 0.048
y(in m) 0.263 0.375 0.426 0.447 1.334 3.622
W(in N 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140
?W 280 550 810 1060 1300 1530 1750 1960 2160 2350 2530 2700 2860 3010 3150
W x 393.1 352.9 314.7 278.4 244 211.6 181.1 152.5 125.9 101.2 78.44 57.62 38.74 21.8 6.788
?W x 393.1 746.1 1061 1339 1583 1795 1976 2128 2254 2355 2434 2492 2530 2552 2559
H 596.9
30 ft long structure, with 60 bags. Base widened to 10ft and ht redenisty of regolith on moon= 500kg/m3
file name=  catenary_Teeth_bag_funipoly_longbase_reducedht_wrego.par
weight on each bag( from left)
rego w 299.6 263.2 238.1 218.9 205.8 190.5 179.7 172.5 162.6 155.8 149.9 144.8 138.3 137 67.25
x(in m) 1.404 1.307 1.21 1.114 1.017 0.92 0.823 0.726 0.629 0.533 0.436 0.339 0.242 0.145 0.048
y(in m) 0.263 0.375 0.426 0.447 1.334 3.622
W(in N 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140
W with 579.6 533.2 498.1 468.9 445.8 420.5 399.7 382.5 362.6 345.8 329.9 314.8 298.3 287 207.3
?W 579.6 1113 1611 2080 2525 2946 3346 3728 4091 4437 4766 5081 5380 5666 5874
W x 813.8 697 602.9 522.1 453.2 386.8 329 277.8 228.2 184.2 143.8 106.7 72.23 41.7 10.05
?W x 813.8 1511 2114 2636 3089 3476 3805 4083 4311 4495 4639 4745 4818 4859 4869
H 1086
30 ft long structure, with 60 bags. 1 ft long and 5 ft deep bags. Ea7.079 6ft rego added on top
Weight
69.45
Total Weight of 60 ba 4200
Weigh of 30 bags= 42 140
weight on each bag because of rego(from left)
rego w 385.4 329.7 291.2 255.7 226.5 206 185.6 172.4 159.9 152 144.6 140.3 136.6 134.8 134.5
x(in m) 1.138 1.057 0.975 0.894 0.813 0.732 0.65 0.569 0.488 0.406 0.325 0.244 0.163 0.081 0
y(in m) 0.263 0.375 0.426 0.447 1.334 4.445
W(in N 140 140 140 140 140 140 140 140 140 140 140 140 140 140 140
W with 525.4 469.7 431.2 395.7 366.5 346 325.6 312.4 299.9 292 284.6 280.3 276.6 274.8 274.5
?W 525.4 995.1 1426 1822 2189 2535 2860 3173 3472 3765 4049 4329 4606 4881 5155
W x 597.8 496.3 420.6 353.8 297.9 253.1 211.7 177.8 146.3 118.7 92.52 68.34 44.97 22.33 0
?W x 597.8 1094 1515 1869 2166 2420 2631 2809 2955 3074 3167 3235 3280 3302 3302
H 671.1
 
 
 
 
 
 107
Excel Spread Sheet for 46 bag top connected structure under different load conditions 
File name= catenary_Teeth_bag_10ftbase_8ftht_fpoly.par
weight of 18 in bag= 95.49
weight of 12 in bag= 63.66
x(in m) 1.438 1.4 1.347 1.276 1.181 1.111 0.918 0.743 0.506 0.177 0
y(in m) 2.43
W(in N) 192 192 192 192 192 128 128 128 128 128 0
?W 192 384 576 768 960 1088 1216 1344 1472 1600 1600
W x 276.2 268.8 258.7 245 226.7 142.2 117.5 95.15 64.8 22.61 0
?W x 276.2 545 803.6 1049 1275 1418 1535 1630 1695 1718 1718
H 390.8
 
weight of 18 in bag= 95.49
weight of 12 in bag= 63.66
x(in m) 1.259 1.049 0.839 0.629 0.42 0.21 0
y(in m) 2.293
W(in N) 316.7 316.7 316.7 212.2 212.2 212.2 0
?W 316.7 633.3 950 1162 1374 1587 1587
W x 398.6 332.2 265.7 133.5 89.03 44.53 0
?W x 398.6 730.7 996.5 1130 1219 1264 1264
H 477.9
 
weight of 18 in bag= 95.49
weight of 12 in bag= 63.66
x(in m) 1.229 1.025 0.82 0.615 0.41 0.205 0
y(in m) 2.881
W(in N) 316.7 316.7 316.7 212.2 212.2 212.2 0
?W 316.7 633.3 950 1162 1374 1587 1587
W x 389.3 324.4 259.6 130.4 86.95 43.48 0
?W x 389.3 713.8 973.3 1104 1191 1234 1234
H 410.8
 
 108
APPENDIX B 
Derivation of Equation 5  
 
where,  
 H= Horizontal thrust acting on the arch 
 R= Reaction force due to the vertical loads acting on the arch
 109
 x= half the span of the arch 
 W
1
, W
2
, W
3
, W
4, 
W
5
 = Vertical loads acting on the arch 
 x
1, 
x
2, 
x
3, 
x
4, 
x
5
= x
1 
is the distance on x-axis between W
1 
and the line ?ad?. Other 
distances are defined similarly 
 y= The vertical distance between point ?a? and point ?b? 
Calculating the moment about point ?a? gives 
0*******(
5544332211
=?+++++ XRyHxWxWxWxWxW  
Now from force equilibrium we get 
RWWWWW =++++ )(
54321
 
Solving these 2 equations we get 
 
This can be written as  
y
xWXW
H
i
iiii
)*(*)(
5
1
5
1
??
==
?
= , which gives us Equation 5
y
xWxWxWxWxWXWWWWW
H
)*****(*)(
554433221154321
++++?++++
=
 110
APPENDIX C 
Model of some structures developed for 60 pocket top connected bags 
 
 
 
 111
Figure showing the position of each bag on the 46 bag structure developed at MSFC