A Novel Material for In Situ Construction on Mars: Experiments and Numerical Simulations
CCenter for Sustainable Engineering of Geological and Infrastructure Materials (SEGIM)
Department of Civil and Environmental EngineeringMcCormick School of Engineering and Applied ScienceEvanston, Illinois 60208, USA
A Novel Material for In Situ Construction on Mars:Experiments and Numerical Simulations
Lin Wan, Roman Wendner, Gianluca Cusatis
SEGIM INTERNAL REPORT No. 15-12/487A
Accepted for publication in Construction and Building Materials May 2016 a r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Novel Material for In Situ Construction on Mars:Experiments and Numerical Simulations
ByLin Wan , Roman Wendner , Gianluca Cusatis ∗ PhD, Researcher, Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Rd.Evanston IL, 60208 USA. E-mail: [email protected] Director Christian Doppler Laboratory LiCRoFast, Department of Civil Engineering and Natural Hazards, Universityof Natural Resources and Life Sciences (BOKU) Vienna. E-mail: [email protected] Corresponding Author: Associate Professor, Department of Civil and Environmental Engineering, Northwestern Univer-sity, 2145 Sheridan Rd. Evanston IL, 60208 USA. E-mail: [email protected], Phone: (847)-491-4027 bstract: A significant step in space exploration during the 21st century will be human settlement on Mars.Instead of transporting all the construction materials from Earth to the red planet with incredibly highcost, using Martian soil to construct a site on Mars is a superior choice. Knowing that Mars has longbeen considered a “sulfur-rich planet”, a new construction material composed of simulated Martian soiland molten sulfur is developed. In addition to the raw material availability for producing sulfur concreteand a strength reaching similar or higher levels of conventional cementitious concrete, fast curing, lowtemperature sustainability, acid and salt environment resistance, 100% recyclability are appealing supe-rior characteristics of the developed Martian Concrete. In this study, different percentages of sulfur areinvestigated to obtain the optimal mixing proportions. Three point bending, unconfined compression andsplitting tests were conducted to determine strength development, strength variability, and failure mecha-nisms. The test results show that the strength of Martian Concrete doubles that of sulfur concrete utilizingregular sand. It is also shown that the particle size distribution plays an important role in the mixture’sfinal strength. Furthermore, since Martian soil is metal rich, sulfates and, potentially, polysulfates are alsoformed during high temperature mixing, which might contribute to the high strength. The optimal mixdeveloped as Martian Concrete has an unconfined compressive strength of above 50 MPa. The formulatedMartian Concrete is simulated by the Lattice Discrete Particle Model (LDPM), which exhibits excellentability in modeling the material response under various loading conditions.
Sulfur has been used as a molten bonding agent for quite a long time in human history. The use ofsulfur was mentioned in literature of ancient India, Greece, China and Egypt [7]. For example, sulfur wasone of the raw materials to manufacture gunpowder by ancient Chinese [29]; sulfur was also used to anchormetal in stone during the 17th century [6]. Starting in the 1920s, sulfur concrete has been reported tobe utilized as a construction material [24]. Various researchers and engineers studied and succeeded inobtaining high-strength and acid-resistant sulfur concretes [1, 2, 3]. In the late 1960s, Dale and Ludwigpointed out the significance of well-graded aggregate in obtaining optimum strength [4, 5].2hen elemental sulfur and aggregate are hot-mixed, cast, and cooled to prepare sulfur concrete prod-ucts, the sulfur binder, on cooling from the liquid state, first crystallizes as monoclinic sulfur (S β ) at238 ◦ F (114 ◦ C). On further cooling to below 204 ◦ F (96 ◦ C), S β starts to transform to orthorhombic sulfur(S α ), which is the stable form of sulfur at ambient room temperatures [8]. This transformation is rapid,generally occurring in less than 24 hours and resulting in a solid construction material. However, sinceS α is much denser than S β , high stress and cavities can be induced by sulfur shrinkage. Hence, durabilityof unmodified sulfur concrete is a problem when exposed to humid environment or after immersion inwater. In the 1970s, researchers developed techniques to modify the sulfur by reacting it with olefinichydrocarbon polymers [9, 16], dicyclopentadiene (DCPD) [10, 12, 11, 15, 17], or other additives and stabi-lizers [13, 14, 18] to improve durability of the product. Since then, commercial production and installationof corrosion-resistant sulfur concrete has been increasing, either precast or installed directly in industrialplants where portland cement concrete materials fail from acid and salt corrosion [24].For earth applications, well developed sulfur concrete features (1) improved mechanical performance:high compressive & flexural strength, high durability, acid & salt water resistant, excellent surface finishand pigmentation, superior freeze/thaw performance; (2) cost benefits: faster setting-solid within hoursinstead of weeks, increased tolerance to aggregate choice; and (3) environmentally friendly profile: reducedCO footprint, no water requirements, easily obtainable sulfur as a byproduct of gasoline production,recyclable via re-casting, compatible with ecosystem, e.g. for marine applications. Current pre-cast sulfurconcrete products include, but are not limited to, flagstones, umbrella stand, counterweights for highvoltage lines, and drainage channel [38].For example, in January 2009, around 80 meters sewage pipeline in the United Arab Emirates wasremoved and replaced by sulfur concrete. In the same time period, a total of 215 fish reef blocks made ofsulfur concrete (2.2 tons/block) were stacked at a depth of 15 meters, 6 kilometers off the coast of UAE[35]. With regular concrete fish reefs, the growth of algae and shells takes time because concrete is alkaline.However, since sulfur concrete is practically neutral in alkalinity, algae and shell growth was observed soonafter installation.While sulfur concrete found its way into practice as an infrastructure material, it is also a superiorchoice for space construction considering the very low water availability on the nearby planets and satellites323]. After mankind stepped on the lunar surface in 1969, space agencies have been planning to go back andbuild a research center on the moon. Since local material is preferred to reduce expenses, starting in theearly 1990s, NASA and collaborative researchers studied and developed lunar concrete using molten sulfur.Around the year 1993, Omar [20] made lunar concrete by mixing lunar soil simulant with different sulfurratio ranging from 25% up to 70% and found the optimum mix with 35% sulfur to reach a compressivestrength of 34 MPa. Later he added 2% of steel fibers to the mixes and increased the optimum strength to43 MPa. However, lunar concrete has serious sublimation issues because of the near-vacuum environmenton the moon. In 2008, Grugel and Toutanji [31, 33, 41] reported experimental results of two lunar concretemixes: (1) 35% sulfur with 65% lunar soil simulant JSC-1, and (2) 25% sulfur and 20% silica binder mixturewith 55% JSC-1. The two mixtures, similar in strength ( ∼
35 MPa), revealed a continuous weight lossdue to the sublimation of sulfur when placed in a vacuum environment, 5 × − torr, at 20 ◦ C for 60days. Based on the measurements, it was predicted that sublimation of a 1 cm deep layer from the twosulfur concrete mixes would take 4.4 and 6.5 years respectively. The sublimation rate varied from rapid atthe high lunar temperatures ( < ◦ C) to essentially nonexistent at the low lunar temperatures (-180 ◦ Cto -220 ◦ C). However, the low temperature on the moon is too harsh to maintain intact the mechanicalproperties of sulfur concrete. After cycled 80 times between -191 ◦ C (-312 ◦ F) and 20 ◦ C (68 ◦ F), thesamples failed at about 7 MPa under compression, which is about 1/5 of the average strength, 35 MPa,of the non-cycled samples.While the moon is the closest and only satellite of earth, its near-vacuum environment, broad tem-perature range and long day-night rhythm, about 30 earth days, are not the most adequate for humansettlement. Venus is the closest planet to Earth, however it is also the hottest planet in the solar systemwith an average surface temperature over 400 ◦ C [45], making it uninhabitable for humans. Mars, on theother hand, is not too hot or too cold, and has an atmosphere to protect humans from radiation. Itsday/night rhythm is very similar to that on Earth: a Mars day is about 24 hours and 37 minutes [25].Thus, Mars is the most habitable planet in the solar system after Earth. In recent years, many countries,including the U.S., China, and Russia, announced to launch manned Mars missions in the next decades.Due to the dry environment on Mars, sulfur concrete concept is a superior choice for building a humanvillage on the red planet. Studies of Martian meteorites suggest elevated sulfur concentrations in the inte-4ior, and Martian surface deposits contain high levels of sulfur (SO up to 37 wt%, average 6 wt%), likelyin the forms of sulfide minerals and sulfate salts [37]. Except of the easiest option of finding a sulfur mineon Mars, like the one in Sicily on Earth, elemental sulfur can be extracted from sulfides or sulfates throughvarious chemical and physical processes, for example, by heating up the sulfur compounds [19]. NASAhas advanced programs on In Situ Resources Utilization (ISRU) [30] for this specific purpose. Moreover,the atmospheric pressure (0.636 kPa) [34] as well as temperature range ( ≤ ◦ C) are highly suitable forthe application of sulfur concrete. As shown in Fig. 1 [31], the most possible construction site on Marshas environmental conditions in the Rhombic (stable) state of sulfur and is three orders of magnitude inpressure above the solid-vapor interface. Thus, sublimation is not an issue and a relatively warm area canbe selected as the construction site. Furthermore, with the temperature on Mars lower than 35 ◦ C, thedrawback of sulfur concrete melting at high temperature will not be an issue for initial constructions suchas shelters and roads while certainly might be of concern for long term settlements in which fire resistancewould be important.To let the thoughts become facts, a new construction material using simulated Martian soil and moltensulfur is developed in this study. Different percentages of sulfur are studied to obtain the optimal mixingproportions. Through mechanical tests, it is found that Martian Concrete have much higher strengths thansulfur concrete utilizing regular sand. Sieve analysis and chemical analysis provide possible explaination forthe higher strength of Martian Concrete: the Martian soil simulant has a better particle size distribution,it is also rich in metal elements, which react with sulfur, forming polysulfates and possibly enhancingstrengths. Mechanical simulations of Martian Concrete are then carried out using the state-of-art LatticeDiscrete Particle Model with excellent simulation of Martian Concrete mechanical properties.5igure 1: Sulfur phase diagram with labeled environmental conditions on Mars and Moon [31]6
Experimental Study of Martian Concrete
Sulfur concrete products are manufactured by hot-mixing sulfur and aggregate. The sulfur binder firstcrystalizes as monoclinic sulfur (S β ), and then the mixture cools down while sulfur transforms to the stableorthorhombic polymorph (S α ), achieving a reliable construction material. While sulfur is commerciallyavailable, Martian soil simulant JSC Mars-1A [32] was obtained in replacement of Martian soil to developa feasible Martian Concrete. Table 1 lists the major element composition of the simulant. As seen, theMartian soil simulant, resembling the actual Martian soil [22], is rich with metal element oxides, especiallyaluminium oxide and ferric oxide. In this study, various percentages of sulfur are mixed with JSC Mars-1Ain a heated mixer at above 120 ◦ C. Temperature measurements are performed during mixing to ensuresulfur melting. Then the mixture is transferred to 25.4 × ×
127 mm (1 × × ◦ C. Martian soil simulant Mars-1A of maximum 5 mm aggregate size wasfirst used for casting, however the specimens showed many voids and uneven surfaces due to the largeaggregate, see Fig. 2a. Sulfur cannot be ensured to fill the large number of big voids or to surroundand bind all large aggregates, especially on the specimen surface. Afterwards, only Mars-1A of maximum1 mm aggregate size was utilized to achieve Martian Concrete (MC) with flat and smooth surfaces, seeFig. 2b. Mechanical tests were conducted after 24 hours, and these included unconfined compression,notched and unnotched three-point-bending (TPB), and splitting (Brazilian) tests. Beams of dimensions25.4 × ×
127 mm (1 × × ) 34.5-44Titanium Dioxide (TiO ) 3-4Aluminum Oxide (Al O ) 18.5-23.5Ferric Oxide (Fe O ) 9-12Iron Oxide (FeO) 2.5-3.5Magnesium Oxide (MgO) 2.5-3.5Calcium Oxide (CaO) 5-6Sodium Oxide (Na2O) 2-2.5Potassium Oxide (K O) 0.5-0.6Manganese Oxide (MnO) 0.2-0.3Diphosphorus Pentoxide (P O ) 0.7-0.9 Unconfined compression tests were performed in a closed loop servo-hydraulic load frame with a maximumcapacity of 489 kN (110 kips). Stroke/displacement control with a loading rate of 0.003 mm/s was applied.In order to ensure consistent and accurate test results, a Standard Operation Procedure (SOP) for testingwas created. The test protocol was first filled with the relevant details, which include Vernier Calipermeasurements of each dimension (average of 2 ∼ × ×
127 mm (1 × × ± ∼
63 MPa, which is roughly a 20 ∼
30% increase, see Fig. 4 labeled as “Mars1A 1mm R.”.Furthermore, better mixing and applying pressure while placing the material in formwork facilitates ma-8a) (b)Figure 3: Cube specimen (a) before and (b) after unconfined compression testterial strength. In the experimental campaign of this study, a well distributed pressure was manuallyadded to the mixture in formwork, and thus the pressure was not quantified. Making the mixture compactfacilitates formation of sulfur bonds and also reduces the number and size of cavities of the final product.Average compressive stress-strain curves for MC with sulfur ratio ranging from 40% to 60% are plottedin Fig. 5a. Stress is calculated as P / A , where P is load and A is the area of the cross section; strainis calculated as ∆ h/h , where h is the height of the specimen. The stress-strain curves feature a typicalalmost-linear behavior up to the peak and a long stable softening post-peak.While Martian Concrete has a high strength of over 50 MPa with relatively high percentage of sulfur,sulfur concrete made of regular sand (Sand Concrete, SC) was cast and tested as well for comparison.With the same dimension of 25.4 mm (1 in), SC cubes were cast with a sulfur ratio in the range of 15% ∼ t% Sulfur C o m p r e ss i v e S t r e n g t h ( M P a ) Mars1A 1mmMars1A 1mm R.Sand 11 mmSand 1 mmSand1A 1 mm
Figure 4: Compression strength variation as a function of percentage of sulfur for Martian Concrete(a)
Strain [-] S t r e ss < [ M P a ] Compression
40% Sulfur45% Sulfur47.5% Sulfur50% Sulfur52.5% Sulfur60% Sulfur (b)
Nominal Strain [-] N o m i n a l S t r e ss [ M P a ] Notched TPB
40% Sulfur45% Sulfur47.5% Sulfur50% Sulfur52.5% Sulfur60% Sulfur
Figure 5: Comparison of the response for Martian Concrete with various sulfur ratio by (a) compressionand (b) 50% notched three point bending tests 10 ormalized Sieve Size [-] P a ss i n g P e r ce n t ag e [ % ] ASTM 9.5mmASTM 12.5mmASTM 19mmASTM 25mmAASHTO 4.75mmMars1A 1mmSand 11mmFuller
Figure 6: Particle size distribution (PSD) study of Martian soil simulant and regular sand as well as ASTMand AASHTO recommended PSD for mixing sulfur concrete
While 25% of elemental sulfur works the best for both mixes with regular sand, they also both have muchlower strength compare to Martian Concrete. To study the influence of aggregates and the correspondingparticle size distribution (PSD) on material strength, sieve analyses of Mars-1A (maximum 1 mm aggregatesize) as well as regular sand (maximum 11 mm aggregate size) were conducted. Also included in the PSDanalysis were the recommended PSDs by ASTM and AASHTO standards for mixing sulfur concrete[24]. In Fig. 6, the normalized distributions of Mars-1A, regular sand, the ASTM D 3515 and AASHTOrecommended PSD ranges as well as Fuller’s law with power 1/2 are plotted and compared. Overall, thePSD of Mars-1A falls well in the recommended PSD range according to standards and is relatively closeto Fuller’s law, while the PSD of regular sand misses the recommended PSD range and also deviates fromFuller’s law. While this finding explains partly the difference in the measured strength of MC and SC, itcannot justify the more than doubled strength of MC compared to SC.
In addition to the PSD of aggregate, other factors must play a role concerning the final strength obtainedin MC experiments. Fig. 7 & 8 show the microscope study of Martian Concrete (MC) and sulfur concretewith regular sand (SC) with optimal compositions. By comparing the particles of MC and SC in the11a) (b)Figure 7: Microscopy study of sulfur concrete on 1 mm scale with compositions of (a) 50% sulfur and 50%Martian soil simulant (b) 25% sulfur and 75% regular sand and a maximum particle size of 1 mmmesostructure pictures, a few observations are in order. Firstly, the visible average particle size of MCis much smaller than that of SC after hot mixing, although both mixes use aggregate with maximumparticle size up to 1 mm. After casting and curing, the aggregate particles and their sizes can be welldistinguished for SC; on the contrary, the majority of MC particles are below 500 microns. Secondly, theMC mix has many red areas, dark spots and almost no voids, while the SC mix shows distinguishablyyellow areas of sulfur, opaque orange to dark red spots related to sand particles and a number of voidsof around 200 microns. These observations, along with preliminary X-ray photoelectron spectroscopy(XPS) tests, suggest that the metal elements in Mars-1A react with sulfur during hot mixing, formingsulfates and polysulfates, and altering the PSD of aggregates to lower ends, which further enhance theMC strength. SC does not have such phenomena because silica sand does not react with sulfur at theaforementioned casting conditions. In other words, in MC aggregate is chemically active whereas in SCis inert and sulfur only serves as “glue” for the sand particles. The existence of sulfates and polysulfatesin MC are qualitatively confirmed by XPS by analyzing the chemical state of sulfur and individual metalelements within 900 micron-diameter areas of a thin MC sample. Definitely, further research is needed toclearly identify the chemical products characterizing MC internal structure.
To complete the mechanical characterization of MC, its fracturing behavior is studied in this section andthe next. Beam specimens with nominal dimensions 25.4 × ×
127 mm (1 × × µ m scale with compositions of (a) 50% sulfur and50% Martian soil simulant (b) 25% sulfur and 75% regular sand and a maximum particle size of 1 mmthree-point-bending (TPB) tests. The beam specimens featured a half-depth notch at midspan cut with adiamond coated band-saw machine. Testing notched samples is customary in fracture mechanics to controlthe fracture onset and to capture post-peak behavior. Dimension and weight measurements were recordedon specifically optimized TPB protocols. Centerline on top of specimen, and support lines at the bottomwere pre-marked then aligned within the servo-hydraulic load frame, which had a capacity of 22.2 kN(5 kip). The adopted TPB test setup is shown in Fig. 9a. The nominal span (distance between bottomsupports) was 101.6 mm (4 in). An extensometer sensor was glued to the bottom of the specimens with thenotch in between its two feet. After applying a pre-load of up to 5% of the expected peak, the specimenswere loaded in crack mouth opening displacement (CMOD) control with a loading rate of 0.0001 mm/sec,which was increased in the post-peak section to limit the total testing time while ensuring a fully recordedsoftening behavior. Typical crack propagation and fracture surface after failure are presented in Fig. 9b&c.The crack starts at the notch tip and develops upward along the ligament.Notched (50%) fracture test stress-strain curves of MC with sulfur ratio in the range of 40% ∼ σ = 3 P L/ bh , where P is load,and L , b , and h are span, width, and depth of the specimen respectively; the nominal strain is calculatedas (cid:15) =CMOD/ h . The optimal percentage of sulfur is found to be 50% ( ± , as shown in Fig. 10b. When mixed with lower or higher sulfur ratio than 50%, MC has lowerfracture energies, see Fig. 5b and Fig. 10b. Same as for compressive strength, recast and applying pressurecan as well improve material flexural strength thanks to more compact sulfur bonds. Splitting tests on 25.4 mm (1 in) cubes were performed by the same load frame as for compression.Roughly 1 mm diameter bars were placed on the top and at the bottom of the specimen. A loading rateof 0.003 mm/s was applied until failure of the specimen at peak load. Only recast Martian Concrete with47.5%, 50%, and 52.5% were tested, and provided splitting tensile strength of 3.6 MPa ± Wt% Sulfur
40 45 50 55 60 N o m i n a l S t r e n g t h ( M P a ) CastRecast (b)
Wt% Sulfur
40 45 50 55 60 F r a c t u r e E n e r g y [ J / m ] CastRecast
Figure 10: Best percentage of sulfur for Martian Concrete by TPB test results (a) nominal flexural strength,and (b) fracture energy ± ±
26% respectively. The splitting tensile strength is calculated as σ = 2 P/πbh ,where P is load, b and h are the depth and height of the cube specimen respectively. In agreement withcompression and TPB test results, splitting tests again confirm that MC with 50% of sulfur have thehighest performance. The splitting nominal stress-strain curves, until failure at peak load, of the optimumMC are shown in Fig. 16b, where nominal strain is calculated as vertical displacement divided by thespecimen height.Modulus of rupture (MOR) tests were carried out for MC with the optimum mix, 50% sulfur and 50%Martian soil simulant. Unnotched beams with dimensions 25.4 × ×
127 mm (1 × × σ = 3 P L/ bh , where P is load, L , b , and h are span, width, and depth of thespecimen respectively; the nominal strain is calculated as vertical displacement divide by specimen depth. For design and analysis purposes it is important to formulate and validate a computational model for thesimulation of Martian Concrete. This is pursued within the theoretical framework of the Lattice DiscreteParticle Model (LDPM).In 2011, building on previous work [26, 27, 28], Cusatis and coworkers [39, 40] developed LDPM, amesoscale discrete model that simulates the mechanical interaction of coarse aggregate pieces embedded15n a binding matrix. The geometrical representation of concrete mesostructure is constructed by randomlyintroducing and distributing spherical shaped coarse aggregate pieces inside the volume of interest andzero-radius aggregate pieces on the surface. Based on the Delaunay tetrahedralization of the generatedparticle centers, a three-dimensional domain tessellation creates a system of polyhedral cells (see Fig. 11)interacting through triangular facets and a lattice system. The full description of LDPM geometry isreported in Cusatis. et. al. [39, 40].Figure 11: One LDPM Cell around an aggregate piece.In LDPM, rigid body kinematics is used to describe the deformation of the lattice particle system andthe displacement jump, (cid:74) u C (cid:75) , at the centroid of each facet is used to define measures of strain as e N = n T (cid:74) u C (cid:75) (cid:96) ; e L = l T (cid:74) u C (cid:75) (cid:96) ; e M = m T (cid:74) u C (cid:75) (cid:96) (1)where (cid:96) = interparticle distance; and n , l , and m , are unit vectors defining a local system of referenceattached to each facet. A vectorial constitutive law governing the material behavior is imposed at thecentroid of each facet. In the elastic regime, the normal and shear stresses are proportional to the corre-sponding strains: t N = E N e ∗ N = E N ( e N − e N ); t M = E T e ∗ M = E T ( e M − e M ); t L = E T e ∗ L = E T ( e L − e L ),where E N = E , E T = αE , E = effective normal modulus, and α = shear-normal coupling parameter;and e N , e M , e L are mesoscale eigenstrains (if any present). For stresses and strains beyond the elastic limit,the LDPM formulation considers the following nonlinear mesoscale phenomena [26, 27, 39]: (1) fractureand cohesion; (2) compaction and pore collapse; and (3) internal friction. Fracture and cohesion due to tension and tension-shear.
For tensile loading ( e ∗ N > e ∗ = (cid:112) e ∗ N + α ( e ∗ M + e ∗ L ), and stress, t = (cid:112) t N + ( t M + t L ) /α , which define the normal and shear stresses as t N = e ∗ N ( t/e ∗ ); t M = αe ∗ M ( t/e ∗ ); t L = αe ∗ L ( t/e ∗ ). The effective stress t is incrementally elastic ( ˙ t = E ˙ e ) and must satisfy the inequal-16ty 0 ≤ t ≤ σ bt ( e, ω ) where σ bt = σ ( ω ) exp [ − H ( ω ) (cid:104) e − e ( ω ) (cid:105) /σ ( ω )], (cid:104) x (cid:105) = max { x, } , and tan( ω ) = e ∗ N / √ αe ∗ T = t N √ α/t T , and e ∗ T = (cid:112) e ∗ M + e ∗ L . The post peak softening modulus is defined as H ( ω ) = H t (2 ω/π ) n t , where H t is the softening modulus in pure tension ( ω = π/ ω = 0) with parabolic variation for strength given by σ ( ω ) = σ t r st (cid:16) − sin( ω ) + (cid:112) sin ( ω ) + 4 α cos ( ω ) /r st (cid:17) / [2 α cos ( ω )], where r st = σ s /σ t is the ratio of shearstrength to tensile strength. Compaction and pore collapse from compression.
Normal stresses for compressive loading( e ∗ N <
0) must satisfy the inequality − σ bc ( e D , e V ) ≤ t N ≤
0, where σ bc is a strain-dependent boundarydepending on the volumetric strain, e V , and the deviatoric strain, e D = e N − e V . The volumetric strain iscomputed by the volume variation of the Delaunay tetrahedra as e V = ∆ V / V and is assumed to be thesame for all facets belonging to a given tetrahedron. Beyond the elastic limit, − σ bc models pore collapseas a linear evolution of stress for increasing volumetric strain with stiffness H c for − e V ≤ e c = κ c e c : σ bc = σ c + (cid:104)− e V − e c (cid:105) H c ( r DV ); H c ( r DV ) = H c / (1 + κ c (cid:104) r DV − κ c (cid:105) ); σ c is the mesoscale compressiveyield stress; r DV = e D /e V and κ c , κ c are material parameters. Compaction and rehardening occur beyondpore collapse ( − e V ≥ e c ). In this case one has σ bc = σ c ( r DV ) exp [( − e V − e c ) H c ( r DV ) /σ c ( r DV )] and σ c ( r DV ) = σ c + ( e c − e c ) H c ( r DV ). Friction due to compression-shear.
For compression dominated loading conditions ( e ∗ N < t M = E T ( ˙ e ∗ M − ˙ e ∗ pM ) and ˙ t L = E T ( ˙ e ∗ L − ˙ e ∗ pL ), where ˙ e ∗ pM = ˙ ξ∂ϕ/∂t M ,˙ e ∗ pL = ˙ ξ∂ϕ/∂t L , and ξ is the plastic multiplier with loading-unloading conditions ϕ ˙ ξ ≤ ξ ≥
0. Theplastic potential is defined as ϕ = (cid:112) t M + t L − σ bs ( t N ), where the nonlinear frictional law for the shearstrength is assumed to be σ bs = σ s + ( µ − µ ∞ ) σ N [1 − exp( t N /σ N )] − µ ∞ t N ; σ N is the transitional normalstress; µ and µ ∞ are the initial and final internal friction coefficients.Each meso-level parameter in LDPM governs part of the mechanical material behavior. The normalelastic modulus, which refers to the stiffness for the normal facet behavior, E , , along with the couplingparameter α , govern LDPM response in the elastic regime. Approximately, the macro scale Young’smodulus E and Poisson’s ratios ν can be calculated as E = E (2 + 3 α ) / (4 + α ) and ν = (1 − α ) / (4 + α ).Typical concrete Poisson’s ratio of about 0.18 is obtained by setting α = 0.25 [40]. The tensile strength, σ t ,and characteristic length, (cid:96) t , govern the strain softening behavior due to fracture in tension of LDPM facets1740], with the relation G t = (cid:96) t σ t / E , where G t is the mesoscale fracture energy. Calibration of σ t and (cid:96) t is typically achieved by fitting experimental data, e.g. the nominal stress-strain curves of TPB tests. Theyielding compressive stress, σ c , defines the behavior of the facet normal component under compression.The softenig exponent, n t , governs the interaction between shear and tensile behavior during softeningat the facet level and it governs the macroscopic compressive behavior at high confinement. One obtainsmore ductile behavior in both compression and tension by increasing n t , however the increase is morepronounced in compression than in tension. The initial internal friction, µ , mainly govern the mechanicalresponse in compression at low confinement and have no influence on tensile behavior. Descriptions ofeffects and functions of other LDPM mesoscale parameters and further discussions can be found in Cusatiset. al. [40] and Wan et. al. [48].LDPM has been utilized successfully to simulate cementitious concrete behavior under various loadingconditions [39, 40]. Furthermore, the framework has been extended to properly account for fiber reinforce-ment [42, 43] and has the ability to simulate the mechanical behavior of ultra high performance concrete(UHPC) [44, 46, 48] and long term behavior of concrete with fastening applications [47].Although Martian Concrete has sulfur bonds instead of calcium-silicate-hydrate gels, it shares withcementitious concrete the heterogeneous internal structure, which is the basis of the LDPM formulation.Thus, LDPM is adopted to simulate the mechanical behavior of the Martian Concrete. The numerical sim-ulations presented in this paper were performed with the software MARS, a multi-purpose computationalcode, which implements LDPM, for the explicit dynamic simulation of structural performance [36]. Asaforementioned, the particle size of aggregate in MC is shifted to lower ends after casting, however, the ex-act distribution cannot be obtained and simulating the smallest particles would result in significantly highcomputation cost. Thus, the discrete particles are generated randomly with aggregate piece of 0.5 to 1 mmand Fuller’s law to the power 1/2 for each type of specimen. The utilized mesoscale parameters for MCwith the best sulfur ratio (50%) are listed in Table 2. The TPB experimental data was primarily utilizedto calibrate the LDPM parameters governing elastic as well as fracture behavior, which include normalmodulus, tensile strength, shear strength ratio, tensile characteristic length, and softening exponent. Notethat the normal modulus is calibrated by the TPB test data because the nominal strain (CMOD/ h ) isdirectly measured on the specimen, while all other tests include the effect of the test machine compliance.18ompression experimental data was then used to calibrate the shear strength, the softening exponent andthe initial internal friction. The other parameters’ values, relevant to confined compressive behavior, aredetermined based on calibrated sets for typical concrete materials available in the literature [40, 48] andare assumed to work also for Martian Concrete in absence of specific experimental data. The adoptedvalues are densification ratio = 1, asymptotic friction = 0, transitional stress = 300 MPa, volumetric devi-atoric coupling coefficient = 0, deviatoric strain threshold ratio = 1, and deviatoric damage parameter =5. After all LDPM parameters had been calibrated and determined, prediction simulations for unnotchedTPB tests and splitting tests were carried out and compared to experimental data as validation.The LDPM simulation setup, typical failure type and crack propagation of notched TPB, unconfinedcompression, splitting, and unnotched TPB tests are shown in Fig, 12, 13, & 14 respectively. Notethat in the notched and unnotched TPB simulation setup (Fig. 12 & 14), the specimen is composed oflattice discrete particles at the center and classical elastic finite elements on the two sides, where onlyelastic deformation is expected to occur, to save computational time. In the unconfined compression testsimulation, high friction parameters for typical concrete-steel slippage interaction [40] are utilized: µ s =0.13, µ d = 0.015, and s = 1.3 mm, to simulate friction between the specimen ends and the steel loadingplatens, assuming a slippage-dependent friction coefficient formulated as µ ( s ) = µ d + ( µ s − µ d ) s / ( s + s ).The fitted stress-strain curves can be found in Fig. 15 & 16. Fig. 15a shows the nominal stress-strain curvesfor 50% notched TPB tests and the material has total fracture energy, G F , of 67.0 J/m . The mesoscaleinitial fracture energy calculated from LDPM parameters, G t = (cid:96) t σ t / E = 37.6 J/m , is approximatelyhalf of G F . This is due to the fact that even under macroscopic mode I fracture the mesoscale response ischaracterized by both shear and tension. Fig. 15b presents the experimental and simulated stress-straincurves of unconfined compression test. Young’s modulus E is back calculated as the aforementionedequation E = E (2 + 3 α ) / (4 + α ) and has an average value of 6.5 GPa. This value is then used to removethe machine compliance in experimental compression test data.Brittle failure is observed both in experiments and simulations for unnotched TPB and splitting tests,as shown in Fig. 16 a & b respectively. The compliance in splitting and unnotched TPB experimental datais removed according to calibrated simulations. As pure predictions, the simulation peaks highly agreewith the average strengths of the experiments. This indicates the superior ability of LDPM to simulate and19igure 12: LDPM simulation notched TPB test setup and zoomed-in view of crack propagation(a) (b)Figure 13: LDPM simulation typical crack propagation in (a) unconfined compression test and (b) splitting(Brazilian) testFigure 14: LDPM simulation unnotched TPB test setup and typical crack propagation19Figure 12: LDPM simulation of notched TPB test setup and zoomed-in view of crack propagationpredict the mechanical behavior of not only cement based concrete but also the novel waterless Martianconcrete materials. Table 2: Parameters for Martian Concrete LDPM SimulationsNormalModulus [GPa] 10DensificationRatio [-] 1TensileStrength [-] [MPa] 3.7YieldingCompressiveStress [MPa] 300ShearStrengthRatio [-] 4TensileCharacteristicLength [mm] 55SofteningExponent [-] 0.2InitialHardeningModulusRatio [-] 0.12TransitionalStrainRatio [-] 4InitialFriction [-] 0.120a) (b)Figure 13: LDPM simulation of typical crack propagation in (a) unconfined compression test and (b)splitting (Brazilian) testFigure 14: LDPM simulation of unnotched TPB test setup and typical crack propagation(a) Nominal Strain [-] N o m i n a l S t r e ss [ M P a ] < u =1.65MPa ' G F =67.0J/m ' L =101.6mm ' b =25.7mm ' h =25.6mm ' Notched TPB
EXPEXP AveSIM (b)
Strain [-] S t r e ss [ M P a ] < u =54.4MPa ' h =25.5mm ' d =24.9mm ' w =25.6mm ' E = 65.0GPa ' Compression
EXPEXP AVESIM
Figure 15: Experimental results and LDPM simulations for calibration and validation: (a) 50% notchedthree-point-bending tests (b) unconfined compression tests21a)
Nominal Strain [-] N o m i n a l S t r e ss [ M P a ] < u =7.24MPa ' L =101.6mm ' b =26.2mm ' h =25.7mm ' Unnotched TPB
EXPEXP AveSIM (b)
Strain [-] S t r e ss [ M P a ] < u =3.9MPa ' b =25.7mm ' h =25.6mm ' Splitting
EXPEXP AVESIM
Figure 16: Experimental results and LDPM simulations for validation: (a) unnotched three-point-bendingtests (b) splitting tests
In conclusion, the developed sulfur based Martian Concrete is feasible for construction on Mars for its easyhandling, fast curing, high strength, recyclability, and adaptability in dry and cold environments. Sulfuris abundant on Martian surface and Martian regolith simulant is found to have well graded particle sizedistribution to ensure high strength mix. Both the atmospheric pressure and temperature range on Marsare adequate for hosting sulfur concrete structures. Based upon the experimental and numerical resultspresented in this paper, the following conclusions can be drawn: • The best mix for producing Martian Concrete (MC) is 50% sulfur and 50% Martian soil simulantwith maximum aggregate size of 1 mm. The developed MC can reach compressive strength higherthan 50 MPa. • The optimum particle size distribution (PSD) of Martian regolith simulant is found to play a role inachieving high strength MC compared to sulfur concrete with regular sand. • The rich metal elements in Martian soil simulant are found to be reactive with sulfur during hotmixing, possibly forming sulfates and polysulfates, which further increases MC strength. Simultane-ously, the particle size distribution of aggregate is shifted to lower ends, resulting in less voids andhigher performance of the final mix. • With the advantage of recyclability, recast of MC can further increase the material’s overall perfor-22ance. • Applying pressure during casting can also increase the final strength of MC. Sulfur shrinks when iscooled down. By reducing the mixture’s volume during casting, the number and size of cavities ofthe final product are decreased. • Although developed for conventional cementitious concrete, the Lattice Discrete Particle Model(LDPM) shows also excellent ability in simulating the mechanical behavior of MC under variousloading conditions.
Acknowledgement
The work was financially supported with Northwestern University internal funding. The authors wouldlike to thank laboratory coordinator Dave Ventre and undergraduate student Timothy Clark for theircontribution to material preparation in the experimental campaign.23 eferenceseferences