MBR Space Settlement Challenge Project

Multiphysics Simulations of the Behaviors of

Martian Concrete under in-situ Conditions

Prepared by

Yifei Ma

School of Civil and Construction EngineeringOregon State University

101 Kearney Hall, Corvallis, OR 97331

December 2018

Abstract

The idea of building habitat on Mars has developed from the phase of fantasy intothe phase of implementation in the 21st century. Martian concrete (also known as sulfurconcrete or Lunar concrete), produced by mixing hot sulfur and aggregate, is consideredsuperior as a construction material. Although this material has only recently been consid-ered as an extraterrestrial construction material, it has been extensively used and studiedthroughout human history. Various experimental studies have shown that Martian con-crete exhibits appealing characteristics such as high strength and durability, excellentresistance to acid and salt exposure, and low water permeability. However, test resultsobtained under terrestrial environmental conditions are not directly adaptable to Martianconditions, where stresses induced by diurnal temperature variation may lead to seriousstructural problems. These extreme Martian environmental conditions cannot be easilyreproduced on the Earth to experimentally assess the workability of Martian concrete un-der in-situ conditions. However, considering the relatively straightforward mechanismsbehind the thermal-mechanical processes, the performance of Martian concrete can becomputationally modeled by implementing multiphysics simulations. With such a nu-merical tool, the performance of Martian concrete under various conditions and designparameters can be predicted to inform structural designs.

In the present work, we propose a three-dimensional discrete element method modelto simulate the behaviors of Martian regolith concrete under extraterrestrial conditions.This DEM-based multiphysics simulation model will, for the first time, enable assessmentof the performance of Martian concrete under in-situ conditions. Implementation of thisresearch will provide structural engineers with a predictive and proactive tool to estimatethe response of Martian concrete under various conditions and design parameters, en-hancing confidence in the safety and efficiency of the design, and will inform decisions tomodify sulfur ratio or improve the mix design. Most importantly, by providing structuralengineers with a quantitative, science-based understanding of the performance of Martianconcrete under extreme conditions, the decision-making process during both design andmaintenance will be more seamless and defensible. The issues pertaining to this topic,such as effect of temperature, are discussed. The most significant project outcomes willbe: (i) a promising multiphysics model that structural engineers can use to evaluate theperformance of Martian concrete under various in-situ conditions or extreme loads, e.g.fire or blast; (ii) a reasonable initial set of input parameters for habitat structural de-sign based on the performance of Martian concrete predicted by the DEM models; and(iii) a guideline for the improvement of Martian concrete in terms of sulfur content anddurability.

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1 Introduction

Previous work [12, 19, 20] has shown experimentally and numerically that the perfor-mance of Martian concrete is equivalent to or better than that of Portland cement con-crete. However, all the test results were obtained in a terrestrial environment, i.e., roomtemperature and barometric pressure. Knowing that the workability of Martian concreteis a strong function of environmental conditions, the results cannot be directly appliedto predict its in-situ behavior. The discrete element method (DEM) has become an in-dispensable numerical tool to model complex rock behaviors. It has a unique advantagethat relatively few parameters, which can be obtained from a simple suit of physical testson a small amount of sample, are required to simulate bulk behaviors. Extensive physicalprocesses relevant to the proposed work have been simulated using DEM, including par-ticle breakage [13], rock fracture [5], heat transfer [25], and microstructure evolution [24].However, DEM has received only limited use for modeling coupled thermal-mechanicalprocesses, typical in-situ working condition of Martian concrete. Therefore, DEM is thenatural choice for simulating the processes of interest due to the complex coupled physicsand the discontinuous, heterogeneous nature of Martian concrete.

1.1 Material Property

Martian concrete is produced by hot-mixing sulfur and aggregate [1]. The mechanicalbehavior is therefore closely related to the sulfur content. Experimental study [11, 16, 20]with sulfur content ranging from 25% to 70% shows that the average compressive strengthof the material varies from 6 MPa to 34 MPa with an optimum percentage at about 35%.Meanwhile, the compressive to tensile strength ratio is rather a constant at σc/σt ∼ 10.The variation of the compressive strength with percentage of sulfur is summarized in Fig.1. The average density is found to be 2200 kg/m3, which is close to portland cementconcrete. A separate study of sulfur concrete made of Martian soil simulant (JSC Mars-1A) shows similar strength properties but the optimum sulfur content is about 50% [20].The discrepancy primarily stems from the different aggregate size distributions. Thecompressive stress-strain curve reported in [20] shows a typical pattern for quasi-brittlematerial with a peak strain εp w 1%.

1.2 Environmental Condition

Knowing that environmental conditions can significantly change the strength and behav-iors of sulfur bonding[7], it is essential to characterize Martian climate conditions andaddress the impacts. Mars has been studied since early 1960s using telescopes or Earth-orbiting instruments. With the help of Mariner and Viking Programs launched by theNational Aeronautics and Space Administration (NASA) [21, 22], Martian atmosphere

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20 30 40 50 60 700

5

10

15

20

25

30

35

0

10

20

30

40

50

Figure 1: Experimental results of the compressive and tensile strength of Martian concrete[16].

and climate conditions measured in close range or directly from the surface become avail-able since 1965. Because of the greater distance from the sun and the existence of a thinatmosphere on Mars, the average highest temperature is lower and the lowest tempera-ture is higher than that on the moon. It has been reported that the average temperatureon Mars ranges from -153 ◦C at the poles to about 20 ◦C at the equator with a commonvalue of -63 ◦C [23]. The atmosphere pressure is about 0.6% atm. According to thetemperature-pressure phase diagram of sulfur, see Fig. 2, sulfur remains in solid phaseunder Martian conditions. However, due to the lack of atmosphere and relatively shortdistance to the sun, average temperature and pressure on the moon are much lower thanon Mars. Therefore, sulfur on the moon is in the vapor phase, which rises sulfur sublima-tion concerns when using sulfur concrete under Lunar conditions [7]. Nevertheless, thethin atmosphere on Mars is sufficient to keep sulfur stay in solid phase under workingconditions.

Mariner 9 probe first confirmed that planet-wide dust storm occurs on Mars for about1/3 of martian year [17, 27]. Data obtained by Viking spacecraft and Opportunity roverfrom the surface shows that the average wind speed is 61 km/h with gusts up to 94 km/h[18]. Because of the low density of the Martian atmosphere, wind speed of 65-79 km/his needed to lift dust from the surface. However, no actual transport of material wasobserved at Viking spacecraft landing sites. Thus, wind erosion due to global dust stormmay not pose an immediate threat to the strength decay of the sulfur concrete. In this

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-180 -140 -100 -60 -20 20 60 100 140 18010-15

10-10

10-5

100

105

Mon

oclin

ic

Liquid

Vapor

Rhombic

MarsMoon

Figure 2: Temperature-pressure phase diagram of sulfur [8, 20].

study, we will primarily consider the effect of temperature variation.

2 Numerical Modeling

2.1 Contact Model

Numerical analysis in this work is performed using the discrete element code ParticleFlow Code (PFC3D) [9]. The contact model is modified from the default parallel bondmodel option by including a softening force-displacement relationship. A parallel bondin PFC can be envisioned as a series of elastic springs distributed over the contact areabetween a pair of particles in contact. Schematics of the particle-particle interactionsare shown in Figure 2.2. In addition to the normal and shear contact forces, bendingmoments can be transmitted through the contact between particles.

The default parallel bond contact model has two components and can be described bytwo groups of micro-scale parameters: 1) particle-particle contact (point contact): normaland shear stiffnesses, Kn and Ks ([F/L]), and friction coefficient µ; 2) the parallel bond(area contact): apparent normal and shear stiffnesses, kn and ks ([F/L3]), the normaland shear bond strengths, σc and τc ([F/L2]), and the parallel bond radius multiplierλ. The radius multiplier λ defines the contact area radius for the parallel-bond viaR = λmin(RA, RB), where RA and RB are the radii of the two particles in contact.These two types of contact act in parallel. Since the stiffnesses for the two types of

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contact differ in dimensions, it is more convenient to specify apparent moduli as theinput parameters instead. For example, the normal stiffnesses Kn for the point contactbetween particles and kn for the parallel-bond can be determined from,

Kn = 2Ec(RA +RB) kn =Ec

RA +RB

(1)

where Ec and Ec are the apparent moduli for the particle-particle contact and the parallel-bond, respectively. Assuming compression positive, the point contact model relates theforces and displacements through,

Fn = −Knδn ∆Fs = −Ks∆δs (2)

and follows Coulomb’s law of friction,

|Fs| ≤ µFn if δn≤0, Fn = Fs = 0 if δn > 0 (3)

where Fn and Fs denote the normal and shear contact forces in the point contact, respec-tively; δn is the overlap (δn > 0 indicates a gap at the contact) and δs is the slip betweena pair of particles.

For the area contact component, before reaching the softening condition, the contactforces, Fn and Fs, and the bending moment, M , follow the linear relationships with theparallel bond stretch δn, slip δs and the angle of relative particle rotation θ,

Fn = −knAδn ∆Fs = −ksA∆δs ∆M = −knI∆θ (4)

where A is the cross sectional area of the parallel bond, A = 2Rt (2D; t = 1) or A = πR2

(3D), and I is the moment of inertia, I = 2R3t/3 (2D) and I = πR4/4 (3D).The softening force-displacement relationship is implemented in the normal compo-

nent of the contact (see Figure 3). Softening occurs when the normal contact force Fn ina parallel bond reaches a limit defined by the normal bond strength, i.e.,

Fn max = −σcA (5)

The force-displacement relationship during the softening stage can be expressed as,

δn =σckn

+σc + Fn/A

βkn(6)

where the softening coefficient β defines the ratio between the loading and softeningstiffnesses, i.e., β = ku/kl and kl = knA. The perfectly brittle case when β → ∞ isthe default parallel bond option in PFC and has often been used in DEM studies in the

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¹Fn max

¹kl

¹±¤

¹Fn

1

¹ku1 E

¹±1¹±n

¹±2E

0

¹kl

1 B

A

o

Figure 3: Force-displacement law.

literature [?, ?]. The parallel bond fails if one of the criteria below is satisfied,

δn + R∣∣θ∣∣ ≥ δc or

∣∣Fs

∣∣A≥ τc (7)

If we use the beam theory as an analogy for the parallel bond, the normal bond failurecriterion means that the bond fails if the stretch at the edge of the bond reaches thethreshold value δc. In this model, we set,

δc = δ2 =δckn

(1 + β

β

)(8)

When the parallel bond breaks, the bond stretch at a contact is,

δn = δ∗ =δckn

(1 + β

β

)− R

∣∣θ∣∣ (9)

Since the rotational contribution is included in the bond failure condition (Eq. 7), forlarge β, it is possible that the bond failure condition actually precludes the occurrence ofsoftening. Both the normal and shear forces, Fn and Fs, in the parallel bond reduce tozero, when the bond fails.

In this work, breakage of a parallel bond, when the failure criteria, Eq. 7, are met ata contact, is termed a micro-crack event. Note that the micro-scale failure mechanism ofwhether the bond fails in tension or in shear does not directly translate to a tensile orshear failure mechanism at the macro-scale. The micro-scale bond strengths affect themacro-scale failure behaviors via macro-scale properties such as the strength ratio σc/σt[14]. For the sake of simplicity in formulating the contact model, we assume that themicro-scale failure mechanism is inherently tensile, which is reasonable for quasi-brittle

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materials such as sulfur concrete. Therefore, the softening model is only implementedin the normal direction. Only the coefficient β in addition to the normal bond strengthσc and kn is needed to describe the softening behavior. The softening law accounts forthe progressive failure of the bonds and also increases the range of interaction betweenparticles.

2.2 Thermal Expansion Model

The effect of diurnal temperature change on the sulfur concrete strength is simulatedby implementing a thermal expansion model [26]. In this thermal model, it is assumedthat the temperature change only affects the particle size while other material properties,including friction coefficient and stiffness, remain constant. The variation of particleradius with temperature change is determined by,

∆R =1

3αR0∆T (10)

where R0 is the particle radius at current temperature; ∆T is temperature change; andα is the coefficient of volumetric thermal expansion. Thermal expansions will change theoverlaps between particles. Consequently, both the contact force and bond force will beupdated according to Eqs. 2 and 4.

2.3 Model Setup

A series of uniaxial compression and tension tests with a cylindrical sample of D ×H =

40 × 80 mm is performed to evaluate the strength of the material. A set of baselinemicro-scale parameters for the particles and contacts is listed in Table 1. Particles ofa uniform size distribution are generated randomly within the cylindrical domain. Thebond strengths follow Gaussian distributions, where the standard deviations are 10% ofthe means, see Table 2. The shear bond strength is chosen to be large enough to ensurethat all the micro-scale failures are tensile in nature. The mean normal bond strength isset to be σc =10 MPa. The thermal expansion coefficient is α = 1× 10−5 1/◦C [3, 15].

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Table 2: Bond strengths in the contact model and macro-scale material properties.β 0.4

Normal bond strength σc (MPa) 10.0±1.0Shear bond strength τc (MPa) 320.0±32.0

Elastic modulus E ′ (GPa) 42.5Poisson’s ratio ν ′ 0.29

Uniaxial compressive strength σc (MPa) 33.4Uniaxial tensile strength σt (MPa) 3.4

Strength ratio σc/σt 9.8

Table 1: Micro-scale parameters.Particle radii (mm) 0.8-1.66Density ρ (kg/m3) 2400Gravity g (N/kg) 3.711

Point contact modulus Ec (GPa) 8Stiffness ratio kn/ks 4.0Friction coefficient µ 0.5

Thermal expansion coefficient α (1/◦C) 1× 10−5

Parallel bond modulus Ec (GPa) 8Bond stiffness ratio kn/ks 4.0

Radius multiplier λ 1

We first benchmark the micro-scale parameters by performing the uniaxial compres-sion and tension tests without temperature change. The macro-scale material propertiesare summarized in Table 2. The stress-strain curve is shown in Figure 4. In the pre-peakregime, the stress-strain relationship is approximately linear. A sudden stress drop isobserved in the post-peak regime. The shape of the curve is comparable to experimentalresults presented in [20]. The elastic modulus of the “digital rock” is 45 GPa, which iswithin the common range for sulfur concrete [10]. Note that the peak stress is also relatedto the gradation of the aggregate. Due to the lacking of data for the Martian soil particlesize distribution, we assume the particle size is in the range of 0.8 < R < 1.66 mm fol-lowing uniform distribution. The compressive to tensile strength ratio is approximatelyσc/σt =9.8. which is very close to the experimental results reported in [16].

3 Simulation Results

In this study, we primarily investigate two temperature change scenarios. In the firstscenario, the temperature change is in long-term that simulates seasonal temperaturechange. In the second, the temperature change is in short-term, simulating daily temper-

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0 0.2 0.4 0.6 0.8 1

10-3

0

5

10

15

20

25

30

35

Figure 4: Stress-strain relationship in baseline simulation with ∆T = 0.

ature cycles on Mars.We denote σc0 as the compressive strength of the material when temperature change

is zero. When temperature decreases or increases by ∆T , the normalized compressivestrength varies with ∆T as shown in Fig. 5. As temperature decreases, the strengthis significantly decreased. However, the strength variation is independent temperatureincrement up to 200 ◦C. In this study, we only consider the thermal expansions andcontraction. When the final temperature exceeds 96 or 120 ◦C, phase transfer of thesulfur will govern the strength variation. According to Fig. 2, sulfur remains in the solidphase under Martian environmental conditions.

When temperature changes relatively faster, the strength variation is rather inde-pendent of the temperature cycle, as shown in Fig. 6. In the simulations, we increaseor decrease the temperature by ∆T and then resume the original state. The strengthremains roughly the same through the process.

4 Discussion

Compare the simulation results from Figs. 5 and 6, it shows that the strength variationis very sensitive to low temperatures. The strength can be reduced by approximately50% when the temperature is lowered by 150 ◦C. Considering this scenario may occuron Mars under extreme conditions, the effect of the temperature change must be takeninto consideration during design phase. However, the effect of temperature increment to

10

-150 -100 -50 0 50 100 150 2000

0.2

0.4

0.6

0.8

1

1.2

Figure 5: Strength variation with temperature change.

-200 -150 -100 -50 0 50 100 150 2000

0.2

0.4

0.6

0.8

1

1.2

Figure 6: Strength variation with temperature cycle.

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strength decay is negligible.Careful examination of Martian environmental conditions suggests that the effect of

wind erosion due to seasonal dust storm is not a concern in terms of sulfur concretecompressive strength. Preliminary investigation shows that the dust consists of very fineparticles that no clear evidence of transporting material can be identified [2].

In this study, we assume the temperature change occurs in a relatively short periodof time. However, data collected from direct observation [4, 6] shows that remarkabletemperature variation on the surface of Mars occurs in Martian days or even years. Nu-merical simulation of long-term sulfur concrete behaviors requires a more comprehensivemodel and a powerful computer.

The temperature variation can also change the mechanical behaviors of the sulfur con-crete through other mechanisms, such as changing the stiffness or micro-fabrics. However,numerical study is hindered by the lacking of experimental data to further calibrate themodel.

5 Conclusion

In this study, we propose a three-dimensional discrete element method model to simulatethe behaviors of Martian regolith concrete under extraterrestrial conditions. This DEM-based multiphysics simulation model can be used to assessment of the performance ofMartian concrete under in-situ conditions. Simulation results show that the compressivestrength is sensitive to the temperature change rather than temperature variation cy-cles. Implementation of this research provide structural engineers with a predictive andproactive tool to estimate the response of Martian concrete under various conditions anddesign parameters, enhancing confidence in the safety and efficiency of the design, andwill inform decisions to modify sulfur ratio or improve the mix design. Most importantly,by providing structural engineers with a quantitative, science-based understanding of theperformance of Martian concrete under extreme conditions, the decision-making processduring both design and maintenance will be more seamless and defensible. The issuespertaining to this topic, such as the effect of temperature on material stiffness, detailedparticle size distribution, and sulfur behavior under low pressure, requires further exper-imental studies.

Acknowledgment

This project received seed funding from the Dubai Future Foundation through Guaana.comopen research platform (Grant #: VC1450). The completion of this study was not pos-sible without the contributions of many individuals. Special thanks to Dr. T. MatthewEvans for his valuable comments and suggestions, which make this work more decent and

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complete. These supports are gratefully appreciated and acknowledged.

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