Design and characterization of GRC-1: A soil for lunar terramechanics testing in Earth-ambient conditions

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Journal of Terramechanics Journal of Terramechanics 47 (2010) 361–377 www.elsevier.com/locate/jterra

Design and characterization of GRC-1: A soil for lunar terramechanics testing in Earth-ambient conditions H.A. Oravec a, X. Zeng a, V.M. Asnani b,* a

Department of Civil Engineering, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA b NASA Glenn Research Center, 21000 Brookpark Road, MS 23-3, Cleveland, OH 44135, USA Received 5 June 2009; received in revised form 23 April 2010; accepted 25 April 2010 Available online 9 June 2010

Abstract Earth experiments must be carried out on terrain that deforms similarly to the lunar terrain to assess the tractive performances of lunar vehicles. Most notably, terrain compaction and shear response underneath the lunar vehicle wheels must represent that of the Moon. This paper discusses the development of a new lunar soil simulant, Glenn Research Center lunar soil simulant #1 (GRC-1), which meets this need. A semi-empirical design approach was followed in which the soil was created by mixing readily available manufactured sands to a particle size distribution similar to the coarse fraction of lunar soil. By varying terrain density, a broad range of in situ cone penetration measurements collected by the Apollo mission astronauts can be replicated. An extensive set of characterization data is provided in this article to facilitate the use of this material. For reference, the index and geotechnical properties of GRC-1 are compared to the lunar soil and existing lunar soil simulants. Published by Elsevier Ltd. on behalf of ISTVS. Keywords: Apollo; Lunar soil simulant; Moon wheels; NASA; Penetrometer; Roving vehicle

1. Introduction The National Aeronautics and Space Administration (NASA) has been developing surface vehicles for exploration and construction operations on the Moon [1,2]. This has created the need to characterize the tractive performances of these vehicles in terrain that deforms like lunar terrain. Terrain deformation in response to vehicle loading is, in general, controlled by the composition and compactness of the surface material, atmospheric conditions, and gravity. The majority of the lunar surface is covered by finely reworked, highly fractured, dry regolith material consisting predominately of impact melt breccias and agglutinates [3]. The mean particle size distribution of the sub centimeter fraction of the regolith ranges from 40 to 800 lm, with the majority averaging between 60 and 80 lm. The individual particles range in shape from round to elongated, subangular *

Corresponding author. Tel.: +1 216 433 3992; fax: +1 216 433 3954. E-mail address: [email protected] (V.M. Asnani).

0022-4898/$36.00 Published by Elsevier Ltd. on behalf of ISTVS. doi:10.1016/j.jterra.2010.04.006

to angular, and have irregular reentrant surfaces [4]. Additionally, the bulk density of the lunar regolith is estimated to range from 1.45 to 1.55 g/cm3 over the first 15 cm in depth. To date, the lunar regolith is not completely characterized and is assumed to regionally vary in composition, structure, and stratigraphy. Nevertheless, lunar soil simulants, such as Minnesota Lunar Simulant-1 (MLS-1), Johnson Space Center-1 (JSC-1), and Johnson Space Center-1A (JSC-1A), have been developed to approximately represent its composition in specific regions [5–10]. Theoretically, such materials could be used to represent the lunar terrain strength if used in a vacuum chamber that was accelerated to off-set the gravity differential between the Moon and Earth (e.g. by using a centrifuge or aircraft). However, this method is not practical for evaluating full terrain–vehicle systems. To fill the need for terrain to evaluate lunar vehicle tractive performances, the authors have developed a readily obtainable sand mixture (GRC-1) that can be prepared to represent lunar terrain strength in measured regions. At specific densities, GRC-1 matches the in situ cone penetration

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data measured by Apollo astronauts on the Moon. The development of GRC-1 and comparison to the in situ measurements is first described. Following this, a comprehensive data set is presented to facilitate its use for characterization of lunar vehicle tractive performance, as well as terramechanics model validation experiments. 2. Design of GRC-1 soil 2.1. Problem formulation In his seminal treatise of the early 1960’s, MG Bekker asserted that vehicle mobility on any planet is controlled by the stress–strain relationships of the terrain in compaction and shear [11,12]. The compaction strength of terrain was considered the main factor influencing wheel sinkage, while shear strength controlled wheel slip. Correspondingly, two terrains of different composition that have the same measured response to compaction and shear loading would be analogous. For the purpose of soft terrain modeling, compaction can be represented by the equation [13],   kc p¼ þ k / zn ; ð1Þ b where p is the pressure applied to a grounded plate, z is the resulting terrain sinkage, b is a geometric factor, and the remaining parameters are empirically determined compaction factors derived from a series of direct terrain measurements using an instrument called a bevameter. Additionally, shear strength, sb, of loose granular terrain may be represented by the equation developed by Janosi and Hanamoto [14],   sb ¼ ðcb þ rb tan /b Þ 1  ej=K ; ð2Þ in which rb is the normal pressure on a grounded plate, j is the resulting shear displacement, and cb, /b, and K are empirically determined shear factors, again based on bevameter measurements. Because of the form of this equation, cb is considered to represent terrain cohesion or the strength in absence of normal load, and /b is correspondingly the friction angle that relates normal pressure to shear pressure. The factor K, otherwise denoted as the modulus of shear deformation, is an indication of the displacement necessary to achieve maximum shear strength. Unfortunately, explicit compaction and shear measurements of the lunar surface are not available to compare with terrain conditions in Earth based lunar vehicle experiments. However, Apollo 15 and 16 mission astronauts did take direct terrain strength measurements using a cone penetrometer [15–19]. The resulting pressure data (Fig. 1), or cone index (CI) values, are a measure of the local compaction and shear strength of the terrain versus depth. Though compaction and shear strength cannot be separately determined by this measurement, the US Army has used this instrument to characterize terrain trafficability for over 40 years [20–22], owning to its ease of use. It has been found that the gradient (G) of CI versus depth correlates

well with the drawbar pull force that a lightly loaded lunar wheel can generate in dry sandy terrain [23]. Accordingly, the authors have utilized the G values estimated from the Apollo CI measurements [17,18] to calibrate a test bed for lunar vehicle driving experiments. The vertical spikes shown on the penetration curves in Fig. 1 are representative of sudden unloading and reloading resulting from intermittent application of pressure to the cone penetrometer. As noted by Mitchell et al. [18], these anomalies can be ignored in the interpretation of the test results. It was also noted that the depth of penetration is somewhat uncertain because the surface reference pad of the penetrometer tended to ride up the shaft during tests [17]. In the Apollo 15 Preliminary Science Report [17] Mitchell et al. suggest that due to the error in ground reference, the resulting penetration curves provide an upper bound on the depth of penetration for the corresponding applied force. This, in turn, provides a conservative estimate for the slope or G of the penetration curve with respect to vehicle mobility. Table 1 summarizes the lunar G values1 estimated by Mitchell et al. [17,18]. As shown, the value of G varies by location from approximately 3– 10 kPa/mm. 2.1.1. Objectives  The primary objective of this investigation is to create soil, which in the Earth environment deforms similarly under vehicle loading as lunar terrain. Similarity is evaluated by comparing G over the range of soil density to the range of G estimated from in situ lunar measurements.  The secondary objective is to provide a comprehensive set of data to facilitate use of this soil in lunar vehicle terramechanics characterization and model validation experiments. These data are to include soil index values, standard geotechnical strength measurements, and bevameter terrain parameters.

2.1.2. Scope  To be practical for large-scale vehicle testing, the materials utilized in the soil design must be readily available, inexpensive, and have a particle size range that does not create an overwhelming amount of dust.  Additionally, vehicles being evaluated must apply the same ground pressure as they would on the Moon, in order to create similar deformation. Thus, the test vehicles are intended to have equal wheel sizes and equal weight distribution between wheels.

1

It should be noted that data provided in Table 1 correspond to penetration measurements taken with a 323 mm2 base area cone tip. Additional lunar cone penetration data is available for a 130 mm2 cone tip as well as for a 3226 mm2 rectangular plate, but these data are not provided in this report. For information on these data refer to [19].

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Cone Penetration Resistance (CI), kPa

Apollo 15: Adjacent to Trench Apollo 15: Rover Track Apollo 15: Adjacent to Track Apollo 16: Uphill on Top Part of Crater Apollo 16: Near Rover Track

Relative Depth, cm Fig. 1. Apollo 15 and 16 cone penetration data sets (323 mm2 cone base area) [19]. Note that the horizontal axis is labeled “Relative Depth” since the absolute depth is uncertain.

Table 1 Lunar cone index gradient terrain estimates near Apollo 15 and 16 landing sites (323 mm2 cone base area) [17,18]. Mission

Location

Estimated depth (cm)

Cone index gradient, G (kPa/mm)

Apollo Apollo Apollo Apollo Apollo

Adjacent to trench In rover track Adjacent to rover track Uphill, top of crater Near rover track

8.25 5.25 <11.25 20 8a

4.06 4.36–7.59 >2.98 3.37–3.86 6.30–9.85

a

15 15 15 16 16

Penetrometer may have hit rock [18].

2.1.3. Assumptions  For reasons explained in the design method (Section 2.2), it is assumed that the G values derived from lunar cone penetrometer measurements are highly sensitive to the frictional component of terrain strength and relatively insensitive to cohesion. Experimental cone penetration studies conducted by the US Army in Earth gravity support this notion. For example, measurements in dry desert sand show that small changes in friction angle are associated with large changes in CI [24]. Corresponding measurements in lean and heavy clays show that CI measurements are not significantly affected by relatively small changes in cohesion forces in the range that may exist in lunar terrain (0.1–1 kPa [4]) [25]. Since there is no empirical data about the sensitivity of G to cohesion in lunar gravity, the authors have evaluated this relationship using two well known mathematical models for CI: (1) the ultimate bearing capacity model created by Terzaghi and modified by Meyerhof for a conical-shape foundation [15,26] and (2) the cavity expansion model developed by Rohani and Baladi [27]. Refer to the Appendix for details on this evaluation. The Meyerhof method indicates that G is not influenced by cohesion in lunar gravity, while the

Rohani and Baladi method indicates that G is significantly influenced by small amounts of cohesion in lunar gravity. Despite this uncertainty, this assumption is relied upon in the present work.  Additionally, it is assumed that if a dry granular terrain is designed to mimic the lunar cone penetration measurements, as indicated by the G metric, then the material will also respond similarly to vehicle loading in terms of the compaction (Eq. (1)) and shear resistance (Eq. (2)) that control vehicle mobility. 2.2. Design method and results To design this soil, a frictional, cohesionless, root material was selected based on practical considerations and then its strength was tuned to match the in situ lunar cone penetration G values by adjusting the soil density. If the assumption that the G values only represent frictional strength is true, then this approach would result in a soil that has similar frictional strength to lunar terrain, but lacks the cohesive strength. This would be a conservative approach, given that the soil would be slightly weaker and would therefore have slightly lower trafficability.

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The first step was to select a frictional material that could be manufactured repeatably on a large-scale, was relatively inexpensive, and would be available for years to come. A local company in Chardon, Ohio, USA, called Best Sand Corporation (BS), offered a suitable material in several particle size distributions. Multiple samples were evaluated for consistency in particle size distribution following the American Society for Testing Materials (ASTM) standards. For the second step, the target particle size distribution was set to be the estimated mean of lunar surface material

(Fig. 2a), excluding the fraction below 75 lm (Fig. 2b). The lunar soil particle size distribution was a rational starting point for the design, and the exclusion of small particles was done to prevent dust generation during large-scale laboratory testing. Four different standard sand blends from BS, with the measured particle size distributions shown in Fig. 3, were recombined to match the target. The specific formula was 36% BS110, 8% BS530, 24% BS565, and 32% BS1635. This sand mix, called GRC-1, is depicted in Fig. 4. Its particle size distribution is shown along with the target distribution in Fig. 2b.

100 Lunar Soil Upper Bound

90

Percent Finer by Weight, %

Lunar Soil Lower Bound

80

Mean Lunar Soil

70 60 50 40 30 20 10 0 10

1

0.1

0.01

0.001

Particle Size, mm Fig. 2a. Mean lunar soil particle size distribution shown together with ±1 standard deviations [7]. 100 GRC-1 Sample 1

90

GRC-1 Sample 2 Coarse Fraction - Mean Lunar Soil

Percent Finer by Weight, %

80 Coarse Lunar Soil Upper Bound Coarse Lunar Soil Lower Bound

70 60 50 40 30 20 10 0 10

1

0.1

0.01

Particle Size, mm Fig. 2b. Lunar particle size distribution excluding the sub 75 lm fraction compared to GRC-1 soil mix. GRC-1 samples 1 and 2 refer to two initial mixtures of GRC-1, a small and large sample, respectively. Both have mixtures of 36% BS110, 8% BS530, 24% BS565, and 32% BS1635. For more details see [28].

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100 BS1635

90

BS530 BS565

Percent Finer by Weight, %

80

BS110

70 60 50 40 30 20 10 0 10

1

0.1

0.01

Particle Size, mm Fig. 3. Particle size distribution of the four BS materials used in the GRC-1 soil design.

In the third and final design step, cone penetration data was collected and compared to the in situ lunar measurements. A total of 181 cone penetration tests were performed on GRC-1 at various densities (refer to Section 3.1.3 for discussion on density) to determine the range of strength of GRC-1 in terms of G. Soil was prepared in a rigid soil bin large enough to ignore boundary effects. To ensure homogeneity throughout the sample, the soil was evenly distributed into the bin using a hopper set to a consistent height; approximately 3–6 cm from the soil surface. Specific densities were then achieved by compacting the soil using a horizontal vibration table. Example cone penetration measurements are shown for a low (0% relative density, 1.60 g/cm3) and high (72.4% relative density, 1.80 g/ cm3) density, in comparison to the Apollo measurements in Fig. 5. Additionally, Fig. 6 shows a plot of all 181 data points along with a linear trend line, which was fit using the

least squares method. The trend line is described by the equation, G ¼ 0:0834ðDR Þ þ 1:5811;

ð3Þ 2

which has a goodness of fit or R value of 0.7637. For comparison with the lunar terrain, the full range of estimated G values is plotted with the GRC-1 data in Fig. 7. Within the range of density tested, GRC-1 covers the seven lowest lunar terrain G values. Above this density, the cone penetrometer could not be pushed by hand to the full measurement depth of 18 cm. As a result, there is one lunar G value that lies outside of the measured range of GRC-1. In this case it was noted that the penetrometer cone may have hit rock [18]. Because the GRC-1 soil design was intended for vehicle mobility testing, where weak terrain is more of a concern than strong terrain, it was decided not to pursue the G versus density relationship in this region of relatively high terrain strength. Moreover, the initial blend of GRC-1 was considered to meet the primary objective to deform similarly to lunar terrain. 3. Properties of GRC-1, lunar soil, and lunar soil simulants A comprehensive set of index properties, geotechnical data, and terramechanics data are provided to facilitate the use of GRC-1 for vehicle tractive performance characterization and model validation experiments. Where possible, corresponding lunar soil and lunar soil simulant data are provided for comparison. 3.1. Basic and index properties

Fig. 4. Photo depicting GRC-1 grain geometry and particle size.

3.1.1. Classification In order to classify GRC-1 using the Unified Soil Classification System (USCS) [29] it was necessary to determine the grain sizes D10, D30, and D60, where D denotes the size

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GRC-1: 0 % Relative Density

Cone Penetration Resistance (CI), kPa

GRC-1: 72.4 % Relative Density Apollo Cone Penetration Measurements

Relative Depth, cm Fig. 5. Example cone penetration measurements for GRC-1 prepared to 0% (1.60 g/cm3) and 72.4% (1.80 g/cm3) relative density. Note that Apollo penetration curves are shown here excluding anomalies created by intermittent application of pressure.

Cone Index Gradient (G), kPa/mm

12

10

8

6

4

2

0 0

10

20

30

40

50

60

70

80

Relative Density (DR), % Fig. 6. Results of cone penetration tests performed on GRC-1.

or apparent diameter of the soil particles and the numeric subscript refers to the percentage that is smaller according to the particle size distribution curve. For GRC-1, D10 is approximately equal to 0.094 mm, D30 equals 0.160 mm, and D60 equals 0.390 mm (Table 2). Therefore, the coefficient of uniformity, CU, which is an indication of the range of particle sizes represented by the equation [29,30], CU ¼

D60 ; D10

ð4Þ

is approximately 4.15 for GRC-1. The coefficient of curvature, CC, a measure of the shape of the particle size

distribution curve between the D60 and D10 grain sizes represented by the equation [29,30], D230 CC ¼ ; ð5Þ D10 D60 is approximately 0.70 for GRC-1. Using the USCS, GRC-1 is classified as a poorly graded sand (SP) with little to no fines (refer to Figs. 2b and 4). Based on the lunar grain size distribution (Fig. 2a), the lunar soil is classified as a well graded silty sand to silt material (SW–SM to ML) due to its high composition of fine grained particles. Similarly, lunar soil simulant JSC-1 is classified as a well graded sand to silty sand material (SW–SM), while MLS-1 and JSC-1A

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367

Unmeasured Region

Cone Index Gradient (G), kPa/mm

12

10 Apollo 16: Near Rover Track

8

Apollo 15: Rover Track Apollo 16: Near Rover Track

6 Apollo 15: Rover Track

4 Apollo 15: Adjacent to Track

2

Apollo 16 : Uphill on Top Part of Crater Apollo 15: Adjacent to Trench

0 0

20

40

60

80

100

Relative Density (DR), % Very Loose

Loose

Medium Dense

Dense

Very Dense

Fig. 7. GRC-1 versus estimated lunar G values from Apollo cone penetration data.

Table 2 Index properties and geotechnical data for GRC-1, lunar soil, and simulants.a Property

Standard

GRC-1

Lunar soil [4,7]

MLS-1 [8,9]

JSC-1 [5,6,9]

JSC-1A [10]

D10 (mm) D30 (mm) D60 (mm) CU CC USCS qmax (g/cm3) qmin (g/cm3) GS emin emax npmin npmax Cc Cs

ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM ASTM – – – – ASTM ASTM

0.094 0.160 0.390 4.15 0.70 SP 1.89 1.60 2.583 0.364 0.613 0.267 0.380 0.03 0.008

0.013 0.034 0.140 10.77 0.64 SW–SM to ML 1.93b 0.87b 2.3 to >3.2 0.605 2.559 0.377c 0.719c 0.3–0.05 –

0.019 0.049 0.150 7.89 0.84 SP–SM 2.20 1.50 3.2 0.456 1.132 0.313 0.531 – –

0.019 0.057 0.150 7.89 1.14 SW–SM 1.91 1.43 2.9 0.517 1.028 0.341 0.507 – –

0.017 0.042 0.110 6.47 0.94 SP–SM 2.03 1.57 2.875 0.416 0.832 0.294 0.454 0.068 0.001

D 2487-83 D 2487-83 D 2487-83 D 2487-83 D 2487-83 D 2487-83 D4253-93 D4254-91 D854-92

D2435-90 D2435-90

a Values for classification data were determined based on the corresponding particle size distribution curves for the lunar soil simulants [5–10] and the mean particle size distribution for the lunar soil [7]. b Values based on Apollo mission data [4]. c Based on GS = 3.1.

are classified as poorly graded sand to silty sand materials (SP–SM) [5–10,28] (refer to Table 2). Additionally, a set of ASTM standard laboratory tests were performed on GRC-1 to determine the specific gravity, maximum and minimum bulk densities, as well as to determine the compressibility of the material. The results of these tests are provided and compared with that of the lunar soil and lunar soil simulants in the following sections.

3.1.2. Specific gravity Standard testing procedure ASTM D854-92 [31] was followed to determine the specific gravity, GS, of GRC-1. The specific gravity of a material is defined as the ratio of the mass density of solid particles to the mass density of pure water at 4 °C. A total of three specific gravity tests were performed and compared. From the three tests it was determined that GRC-1 had an average specific gravity of 2.58 (Table 2).

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In comparison, the specific gravity of the lunar soil ranges from 2.3 to greater than 3.2 [4]. However, the lunar soil exhibits subgranular porosity which exists as enclosed voids within the lunar soil particles. Thus, during laboratory specific gravity testing of the soil, water cannot fill the enclosed voids. As a result, the average specific gravity of the soil is lower than typically expected if the enclosed voids did not exist. Taking this subgranular porosity into account, a specific gravity range of 2.9–3.5 may be a more accurate representation of the lunar soil [4]. Similarly, the specific gravity of lunar soil simulant MLS-1 is approximately 3.2 [8], that of JSC-1 is approximately 2.9 [5], and that of JSC-1A is approximately 2.88 [10]. Thus, the specific gravity value of GRC-1, 2.58, falls near the lower bound of the lunar regolith and simulant specific gravity. 3.1.3. Density The tests for the determination of maximum and minimum bulk density of GRC-1 followed the standards described in ASTM D4253-93 [32] and D4254-91 [33], where the minimum density was established by filling a container using a hopper and the maximum density was achieved by vibration with an applied surface load. Three minimum and three maximum density tests were done and the average measured value of maximum density was found to be 1.89 g/cm3 while the average measured value of minimum density was found to be 1.60 g/cm3 (Table 2). These values correspond to relative densities of 100% and 0%, respectively (Fig. 8), as determined by the equation [30],

Bulk Density (ρ), g/cm3

1.89 1.87

DR = (ρ-1.60)/(0.29)*(1.89/ρ)*100

1.84 1.81 1.78 1.75 1.72 1.69 1.66 1.63 1.6 0

20

40

60

80

100

Relative Density (DR), % Very Loose

Loose

Medium Dense

Dense

Very Dense

Fig. 8. GRC-1 bulk density versus relative density.

DR ¼

qmax q  qmin   100; q qmax  qmin

ð6Þ

where qmax and qmin are the maximum and minimum bulk density, respectively, and q is the in situ density of the sample. Using the average specific gravity of the GRC-1 in combination with the average maximum and minimum bulk density of the soil, other engineering properties such as porosity, np, and void ratio, e, of GRC-1 are calculated. The bulk density, specific gravity, and porosity of a soil are related by the equation [30], q np ¼ 1  ; ð7Þ GS qw where qw is the density of water (1 g/cm3). This equation is representative of the ratio of the volume of the voids to the total volume of the soil sample. The void ratio of a soil is defined as the ratio of the volume of the voids to the volume of the soil solids. Mathematically it is related to the soil porosity by the following equation [30], np e¼ : ð8Þ 1  np Based on the maximum and minimum densities and the average specific gravity of GRC-1, the void ratio of the soil is between 0.364 and 0.613. Additionally, the porosity of GRC-1 ranges from 0.267 to 0.380. Comparison of the void ratio and porosity of GRC-1 to the lunar soil and lunar soil simulants can be found in Table 2. Approximations of the in situ lunar soil bulk density with respect to depth are provided in the Lunar Sourcebook [4] as shown in Table 3. Generally speaking, the bulk density of the lunar soil tends to increase with depth (over the first 60 cm of soil) from 1.45 to 1.79 g/cm3, while the top 15 cm of lunar soil has an average bulk density of 1.50 g/cm3. Similarly, the bulk density of lunar soil simulant MLS-1 ranges from 1.50 to 2.20 g/cm3 [8] while the bulk density of JSC-1 ranges from 1.43 to 1.91 g/cm3 [6], and that of JSC-1A ranges from 1.57 to 2.03 g/cm3 [10]. It is noteworthy, also, that the in situ lunar density was determined from measurements in lunar vacuum conditions, while the densities of the simulants were measured in Earth-ambient conditions. It has been reported that a significant decrease in atmospheric pressure (increase in vacuum) leads to an increase in porosity (decrease in bulk density) [34]. This may explain why the low end of lunar density seems less than that of the simulants. The range in bulk density that can be achieved by GRC-1 is 1.60–1.89 g/cm3. The minimum density is slightly higher than the lunar soil and simulants, likely because GRC-1 is less angular and

Table 3 Estimated in situ lunar soil parameters [4]. Depth (cm)

Bulk density, q (g/cm3)

Relative density, DR (%)

Avg. porosity, np (%)

Avg. void ratio, e

Soil description

0–15 0–30 30–60 0–60

1.50 ± 0.05 1.58 ± 0.05 1.74 ± 0.05 1.66 ± 0.05

65 ± 3 74 ± 3 92 ± 3 83 ± 3

52 ± 2 49 ± 2 44 ± 2 46 ± 2

1.07 ± 0.07 0.96 ± 0.07 0.78 ± 0.07 0.87 ± 0.07

Med. to dense Dense Very dense Dense

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therefore less capable of sustaining separation between particles. On the other hand, the maximum density of GRC-1 is lower because it has less fine particles to fill voids. 3.2. Mechanical properties 3.2.1. Compressibility The load-settlement relationship is defined by a onedimensional consolidation test following the standard procedures of ASTM D2435-90 [35]. In a consolidation test, a soil sample is subjected to a series of normal loads increasing in magnitude, while the corresponding deformation or settlement is measured. The results are plotted in terms of void ratio versus the logarithm of the effective stress. From the linear portion of the loading relationship (refer to [35] and Fig. 9) the compression index, Cc, is determined by the equation [35], Cc ¼

ðe1  e2 Þ ; logðp2 =p1 Þ

ð9Þ

where e1 and e2 are the void ratios of the soil corresponding to effective vertical stresses of p1 and p2, respectively. Similarly, the normal loading is gradually reduced in steps and the resulting void ratio is again determined. From the recorded data on the unloading line (Fig. 9), the swelling index, Cs, of the soil can be calculated using the equation [35], Cs ¼

ðe1  e2 Þ ; logðp2 =p1 Þ

ð10Þ

where e1 and e2 are the void ratios of the soil corresponding to effective vertical stresses of p1 and p2, respectively. A total of two one-dimensional consolidation tests were

369

performed on GRC-1 at the initial void ratios of 0.525 and 0.406 (approximately 1.69 and 1.83 g/cm3 or 34.7% and 81.9% relative density), respectively. The results of these tests are shown in Fig. 9 and tabulated along with the available lunar soil and simulant data in Table 2. From the data collected it was found that the compression index of GRC-1 is approximately 0.03 and the swelling index is 0.008. Both values are fairly low, indicating that the soil is less compressible and dilates less than most natural soils including the lunar soil which has an estimated compression index ranging between 0.3 and 0.05 [4]. 3.2.2. Triaxial test For a given density state, the ultimate soil strength is controlled by friction angle and cohesion. These data were derived following the ASTM D2850-87 [36] standard triaxial compression test on samples of GRC-1 prepared to bulk densities ranging from 1.60 to 1.82 g/cm3 or 0% to 78.8% relative density. A total of 10 unconsolidated undrained triaxial test sets were performed. Each set consisted of three tests with GRC-1 prepared to similar densities at confining pressures of 50, 100, and 200 kPa, respectively. A typical result from the triaxial tests performed on GRC-1 is shown in Fig. 10. It is clear that GRC-1 is plastic in nature and maintains a maximum shear stress value when failure is induced, as is typical of loose granular material. The principal stresses, r1 and r3, at failure were used to generate Mohr’s circles [30], from which the failure envelope was drawn (refer to Fig. 11). The Mohr–Coulomb equation [30], s ¼ c þ r tan /;

ð11Þ

was then used to determine the corresponding values of cohesion, c, and angle of internal friction, /, where r is

0.6

0.55

Void Ratio, e

0.5

0.45

0.4

0.35

0.3 1

10

100

log p, kPa Fig. 9. Results of one-dimensional consolidation tests performed on GRC-1.

1000

370

H.A. Oravec et al. / Journal of Terramechanics 47 (2010) 361–377 Table 4 Results of triaxial testing performed on GRC-1.

350 200 kPa 100 kPa

Deviator Stress (Δσ1), kPa

300

50 kPa

250 200 150 100 50 0 0

2

4

6

8

10

Axial Strain, % Fig. 10. Typical triaxial stress versus strain results for GRC-1, shown for an average density of 1.60 g/cm3 (0% relative density) at three normal pressures.

the applied normal pressure on the soil sample and s is the resulting ultimate shear strength of the soil. The results of the triaxial tests are summarized in Table 4. As shown by the data, friction angle of the soil increases with density, ranging from 29.8° to 44.4° for corresponding densities of 1.60 and 1.82 g/cm3 (0% and 78.8% relative density, respectively). This range of friction angle for GRC-1 is similar to the best estimates for the in situ lunar soil based on the Apollo missions which range from 30° to 50° [4]. The typical values for the lunar soil cohesion and friction angle in intercrater areas are summarized in Table 5. In comparison, the angle of internal friction of lunar soil simulant MLS-1 ranges from <41.4° to >49.8° [8] while the angle of internal friction of JSC-1 is approximately 45° [5], and that of JSC-1A ranges from <41.9° to >56.7° [10].

Average density, q (g/cm3)

Relative density, DR (%)

Friction angle, / (°)

1.60 1.62 1.64 1.66 1.71 1.73 1.76 1.78 1.79 1.82

0.00 8.05 15.90 23.56 41.92 48.97 59.25 65.90 69.18 78.78

29.8 30.4 33.3 33.4 33.8 37.2 38.4 42.1 42.4 44.4

The measured cohesion of GRC-1 was too low to draw a meaningful conclusion, as is typical for dry sands. The triaxial tests performed during this investigation were conducted with relatively high effective confining pressures, and thus the cohesive strength (zero-confinement strength) could not be extrapolated accurately. As pointed out by Das [30], the determination of cohesion from triaxial tests may be difficult as a straight line extrapolation of the failure envelope back to the normal stress of zero. It is more likely that the strength envelope is curved in the region of small confining pressures. However, at small confining pressures, triaxial test systems are prone to error resulting from the rubber membrane surrounding the soil sample as well as from the difficulty in maintaining a constant low cell pressure. Thus, the task of accurately determining the cohesion of GRC-1 remains a challenge. 3.3. Terrain strength The terrain strength parameters of GRC-1 were determined using a bevameter system. In contrast to triaxial tests, bevameter tests are intended to mimic the modes of terrain

φ

Failure Envelope

σ1 (Major Principal Stress)

c

σ3 (Minor Principal Stress) Δ σ1 (Deviator Stress)

Fig. 11. Typical Mohr’s circles from triaxial tests performed on GRC-1.

H.A. Oravec et al. / Journal of Terramechanics 47 (2010) 361–377 Table 5 Lunar soil strength parameters (of intercrater regions) with depth [4]. Depth (cm)

Bulk density, q (g/cm3)

Relative density, DR (%)

Avg. cohesion, c (kPa)

Avg. friction angle, / (°)

0–15 0–30 30–60 0–60

1.50 ± 0.05 1.58 ± 0.05 1.74 ± 0.05 1.66 ± 0.05

65 ± 3 74 ± 3 92 ± 3 83 ± 3

0.52 0.90 3.0 1.6

42 46 54 49

failure from vehicle running gear [13]. In other words, the terrain is engaged at the surface without external confinement. Separate plate loading tests are done to determine the stress–strain relationships of the terrain in the normal and shear directions. The plate contact areas and the range of pressure applied to the ground are intended to span the expected vehicle contact and loading conditions. Additionally, the soil bin should be large enough so the boundaries do not affect the terrain response. However, universal practices for bevameter testing have not been established. The same soil preparation procedures used for cone penetration testing were employed here to create repeatable and homogeneous terrain conditions. The soil bin was selected to be as wide and deep as practical (58.4 cm in diameter and 24 cm in depth) in order to minimize boundary effects [28]. Plate sizes (refer to Table 6) were considerably smaller than anticipated lunar wheel contact areas, because the bevameter system had finite load capability and it was considered more important to test in the expected range of ground pressure. For lack of exact engineering criteria, the plate sizes were selected to be similar to those used in lunar wheel investigations by the Army for the NASA Apollo program [23]. 3.3.1. Normal bevameter test The normal bevameter test is intended to establish the normal stress–strain relationship of the terrain used to predict running-gear sinkage. The tests were conducted by applying incremental dead weight to a round plate until a maximum pressure was applied or punching failure occurred. Soil was prepared to an average relative density of 27.3% (1.67 g/cm3) to attain a representative strength of the lunar terrain as determined by cone penetration tests. The applied normal force and corresponding sinkage were measured via a load cell and linear variable differential transformer, respectively. The applied pressure was then deduced based on the normal force and the area of the plate. This test was done with the three plate sizes shown in Table 6 and the pressure and sinkage data were Table 6 Bevameter end effector geometry. Test

Plate diameter (cm)

Contact area (cm2)

Normal bevameter

7.6 10.2 19

45.36 81.71 283.53

Shear bevameter

I.D. 14.0; O.D. 17.9

97.71

371

fit to Eq. (1). A total of five repeat tests were conducted, since there was a significant amount of scatter associated with this test. Fig. 12 shows the raw data, together with the ensemble mean trend for each plate size. Over the range of pressures tested, the shape of these trends change due to changing terrain response patterns. At first the terrain compressed, then general shear failure occurred, and then, in the case of the smallest plate, puncture type failure occurred. Since the model for plate sinkage (Eq. (1)) only has one shape factor, these data were reduced to the pressure range from 0 to 30 kPa. The model was then fit using Wong’s least squares approach [37], modified to account for three plates [28], resulting in the parameters listed in Table 7. The goodness of fit was calculated based on the equation [37], vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u½Pðp p Þ2  m c u t ðN 2Þ P ep ¼ ; pm =N

ð12Þ

where pm is the measured pressure, pc is the calculated pressure, and N is the number of data points used for curve-fitting. As shown in Fig. 13, the curve-fit corresponds well to the experimental data with a goodness of fit of 0.0600 for the 7.6 cm plate, 0.1168 for the 10.2 cm plate, and 0.1809 for the 19 cm plate. For a given pressure, the larger plates sink more than the smaller plates, which makes sense based on general soil mechanics theory. The value of n is approximately 1.23. Since this value is greater than one, it suggests a terrain strengthening behavior. The values for kc and k/ were determined to be 4010 kN/mn+1 and 22,369 kN/mn+2, respectively (Table 7). However, these parameters do not seem to have any physical significance. No additional densities of GRC-1 were tested due to time restrictions for this work. It is recommended that the normal bevameter parameters not be used outside of the range of experimental conditions, because the model is purely empirical. As an example, if one tries to simulate a significantly larger contact area a negative pressure will result. 3.3.2. Shear bevameter test In a shear bevameter test an annular ring is rotated on the terrain surface and the relationship between shear stress and shear displacement at various normal pressures is measured. Shear bevameter tests were performed on GRC-1 prepared to relative densities of 15.9% (1.64 g/cm3), 27.3% (1.67 g/cm3), and 55.9% (1.75 g/cm3), using an annular ring with the dimension shown in Table 6. The contact surface of the annulus was covered with coarse sandpaper to engage the terrain. For each density, tests with normal loads of 5, 7, 10, 20, and 30 kPa were conducted. Dead weight was used to establish the normal load and the annulus was rotated approximately 210°. The applied normal force, torque, and corresponding angular displacement were measured via a load cell, torque cell, and potentiometer, respectively. Shear stress was calculated by dividing

372

H.A. Oravec et al. / Journal of Terramechanics 47 (2010) 361–377 0

1 Mode of failure has changed from general shear to punching type failure.

Penetration, cm

2

3

4 Raw Data Points:

5

Ensemble Mean:

19 cm Plate

19 cm Plate

10.2 cm Plate

10.2 cm Plate

7.6 cm Plate

7.6 cm Plate

6

Bottom Bin Boundary

24 0

50

100

150

200

Pressure, kPa Fig. 12. Results from normal bevameter tests performed on GRC-1 at 27.3% relative density (1.67 g/cm3) together with ensemble mean pressurepenetration curves.

T ; 2  r2 Þ ðr þ r Þpðr i i o 2 o

Table 7 Average parameters from normal bevameter testing of GRC-1.

sb ¼ 1

Density, q (g/cm3)

Relative density, DR (%)

n

kc, kN/mn+1

k/, kN/mn+2

1.67

27.3

1.234

4009.91

22368.57

the measured torque by the product of the average radius and annulus area using the equation [38],

ð13Þ

where T is the measured torque and ro and ri are the outer and inner radii of the annular ring, respectively. Shear displacement was calculated using the relationship,  p r þ r  i o j¼a ; ð14Þ 180 2 where a is the angular displacement of the ring in degrees.

0

0.1

Penetration, cm

0.2

0.3

0.4

0.5 Raw Data Points:

0.6

0.7

0

Bekker Curve-Fit:

19 cm Plate

19 cm Plate

10.2 cm Plate

10.2 cm Plate

7.6 cm Plate

7.6 cm Plate

5

10

15

Pressure,

20

25

30

kN/m2

Fig. 13. Results from normal bevameter tests over a limited pressure range, together with best fit curves to the Bekker model (n = 1.234, kc = 4009.91 kN/ mn+1, k/ = 22368.57 kN/mn+2).

H.A. Oravec et al. / Journal of Terramechanics 47 (2010) 361–377 Table 8 Summary of shear bevameter results for GRC-1. Density, q (g/cm3)

Relative density, DR (%)

Average, K (cm)

Friction angle, /b (°)

1.64 1.67 1.75

15.9 27.3 55.9

2.55 2.42 1.81

33.3 33.7 34.0

373

The parameters in Table 8 were then derived by curvefitting the experimental shear stress and shear displacement data to Eq. (2), using the method described by Wong [37]. A typical experimental result compared with the curve-fit is shown in Fig. 14a. For reference, corresponding sinkage data is shown in Fig. 14b, although these data were not parameterized. The goodness of fit was determined using the equation [37],

20000 5.13 kPa

18000 Curve-Fit

16000 7.08 kPa

Shear Stress, Pa

14000 Curve-Fit

12000 10.30 kPa

10000 Curve-Fit

8000 19.72 kPa

6000 Curve-Fit

4000 29.61 kPa

2000 Curve-Fit

0 0

0.05

0.1

0.15

0.2

0.25

Shear Displacement, m Fig. 14a. Typical shear stress vs. shear displacement curves for GRC-1, shown for a density of 1.75 g/cm3 (55.9% relative density).

Shear Displacement, m 0

0.05

0.1

0.15

0.2

0

Linear Displacement (Sinkage), m

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

Fig. 14b. Corresponding sinkage vs. shear displacement curves.

0.25

374

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u½Pðsm sc Þ2  u t ðN 2Þ P ; es ¼ sm =N

H.A. Oravec et al. / Journal of Terramechanics 47 (2010) 361–377

ð15Þ

where sm is the measured shear stress, sc is the calculated shear stress, and N is the number of data points used for curve-fitting. It should be noted that the range of shear displacement used for curve-fitting (5 cm) was calculated using the largest expected lunar wheel size operating at 20% slip. As shown in Table 8, the average value of K tends to decrease with increasing density. This makes sense because when the density of a soil is higher, it requires less shear displacement for the soil particles to pack and ultimately reach maximum shear strength. A more surprising result was that the increase in density caused the factor /b to vary only slightly, in the range from 33° to 34°, as compared to /. Disparity between friction angles measured by the triaxial and bevameter tests has been reported previously [23,24], and is generally attributed to the differing modes of failure induced. The values of cb for GRC-1 were small, and sometimes negative. Like the triaxial test, these values are not trustworthy, since the cohesive parameter (strength without normal load) is determined by extrapolating from measurement made under finite normal loading. In reality, GRC-1 behaves the same as typical dry sand and does not stick together. Therefore it is assumed that the value of cb is very small, and can be considered to be zero for engineering calculation. 4. Utility of GRC-1

don, Ohio. It has been mixed in quantities ranging from 1000 to 20,000 kg (1–20 metric tons) by the Black Lab Corp of Chardon, Ohio for approximately $250 per metric ton. Thus, the material is readily attainable and costs over 100 times less to purchase than other lunar soil simulants. The GRC-1 soil has been used by laboratories at Case Western Reserve University, Johnson Space Center, Jet Propulsion Laboratory, Glenn Research Center, Goodyear Tire & Rubber Company, Honeybee Robotics, Clemson University, Virginia Polytechnic Institute and State University, and Milliken & Company. As an example, Fig. 15 shows the deformation pattern resulting from replicate Apollo Lunar Roving Vehicle tire tests conducted in GRC-1 at the NASA Glenn Research Center. Fig. 15 also shows a photograph of rover tracks created on the Moon during the Apollo 15 mission, for qualitative comparison. Methods to prepare GRC1 in large soil bins for such tests are described in [39]. 4.2. Closure 4.2.1. Limitations As GRC-1 is designed specifically for use in lunar surface strength tests, it does not replicate all the mechanical properties of the lunar soil, nor does it replicate the mineralogical composition or chemistry. Additionally, it is important to keep in mind that GRC-1 was based on terrain measurements from the Apollo 15 and 16 missions and does not represent the entire strength range of the lunar terrain. However, GRC-1 has proven to be useful to create meaningful terrain conditions for large-scale lunar vehicle traction testing.

4.1. Acquisition and use of GRC-1 GRC-1 is created from a precise mixture of four different silica sands produced by the Best Sand Corporation of Char-

4.2.2. Conclusions and recommendations for future work In conclusion, a soil design called GRC-1 has been developed at the NASA Glenn Research Center, in collab-

Fig. 15. (Left) Replicate LRV tire imprint left in GRC-1 after a traction test at NASA Glenn Research Center (Image credit: NASA GRC/Michelle M. Murphy). (Right) LRV tire imprint left on the Moon during the Apollo 15 mission (Image credit: NASA).

H.A. Oravec et al. / Journal of Terramechanics 47 (2010) 361–377

oration with Case Western Reserve University, for use in lunar vehicle traction testing. A comprehensive series of laboratory tests have been conducted to determine its index, geotechnical, and terramechanics properties for test engineering and model simulation. Based on the results of this investigation the following conclusions can be drawn: 3

1. In the density range up to 72% (1.80 g/cm ), GRC-1 can be prepared to cone index gradient values between 1.58 and 8.25 kPa/mm. Greater strength is possible at higher density, but is difficult to measure using a cone penetrometer. This range of strength completely covers four out of the five gradient values (4.06, 4.36–7.59, >2.98, and 3.37–3.86 kPa/mm) estimated from the Apollo mission cone penetration tests. The fifth value (6.30– 9.85 kPa/mm) represents an exceptionally strong terrain condition, which is not a concern for mobility. 2. Triaxial testing reveals that the angle of internal friction ranges from 29.8° to 44.4° for relative densities up to 78.8% (1.82 g/cm3). This verifies similarity to lunar terrain, where the angle of internal friction is estimated to vary between 30° and 50° [4]. 3. A host of index, mechanical, and terrain strength properties have been provided to facilitate the utilization of GRC-1 for lunar vehicle terramechanics characterization and model validation experiments. These were compared with the available properties of lunar soil and lunar soil simulants, for reference. 4. Overall GRC-1 is a well characterized, low cost, and readily obtainable material that can be used to create meaningful and conservative terrain conditions for lunar vehicle terramechanics testing. Recommendations for future work in this area of study include:

X¼

results would be invaluable for lunar surface systems engineering, and would provide the basis for the development of future lunar soil strength simulants. Acknowledgements The work reported herein was carried out with support from NASA Grant NNC06AA25A and the Ohio Space Grant Consortium Fellowship. The opinions expressed in this paper are those of the authors and do not represent the official policies of the funding agencies. Appendix A. The effect of cohesion on lunar cone penetration measurements The influence of cohesion on lunar cone index gradient (G) data is assessed using two alternative models; the Meyerhof bearing capacity model [15,26] and the cavity expansion model [27]. The Meyerhof bearing capacity model of cone index (CI) is represented by the equation: CI Meyerhof ¼ cN c þ qgRN c þ qgzN q

ð1AÞ

where c and q are the cohesion and bulk density of the soil, respectively, g is the acceleration due to gravity, R is the radius of the cone base, z is the soil depth to the cone base, and Nc, Nc, and Nq are bearing capacity factors dependant on the internal angle of friction of the soil, /. The cavity expansion model of CI is represented by the equation: CI Cavity ¼ c cot / ~ m 3ðtan a þ tan /Þ

2 tan að1 þ sin /ÞG þ X; D 2 3  sin / c tan3 / 2

ð2AÞ where

ð3 þ cðz þ LÞ tan /Þ3m  ðc þ cðz þ LÞ tan / þ ð2  mÞcL tan /Þðc þ cz tan /Þ2m ; ð2  mÞð3  mÞ

 An investigation and analysis of the assumption made in this work (Section 2.1.3) to provide insight into the limitations for use of GRC-1.  Development of relationships between the relative density of GRC-1 and the corresponding Bekker parameters kc, k/, and n, as well as K for the complete range of bulk density of the material. This additional data would enable the soil to be utilized in model validation experiments over a wider range of density.  Simulation of the lunar terrain strength in unexplored regions using small-scale laboratory experiments with lunar soil simulants (e.g. JSC-1A and NU-LHT-2), accounting for vacuum, gravity, density variation, and possible effects of water at cold temperatures. Such

375

m¼

4 sin / ; 3ð1 þ sin /Þ

ð3AÞ

ð4AÞ

and

bz ~ ¼ 0:5 A þ 1  Be G Gshear : 1 þ Bebz

ð5AÞ

In Eqs. (2A–5A), c is the cohesion of the soil, / is the internal angle of friction of the soil, c is the unit weight of the soil (equal to gq), D is the cone diameter, L is the cone length, 2a is the apex angle of the cone, z is the soil depth, Gshear is the shear modulus of the soil, and A, B, and b are constants accounting for the free-surface effect for granular materials [27].

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Table A1 Cone and soil properties for the evaluation of G using Eq. (7A). Soil properties Depth, z Cohesion, c Friction angle, / Shear modulus, Gshear Bulk density, q Unit weight, c

0–15 cm 0 and 1 kPa 40° 5 MN/m3 1500 kg/m3 2.43 kN/m3 (lunar gravity)

Cone dimensions Apex angle, 2a Cone height, L Base diameter, D

30° 0.0378419 m 0.0202794 m

Taking the partial derivative with respect to depth z results in the following two alternative expressions for G: GMeyerhof ¼ qgN q ;

ð6AÞ

and GCavity ¼

1 ~ m cot3 / 24G D2 ð2  mÞð3  mÞc2 ð3  sin /Þ h  ð1 þ sin /Þ tan aðtan a þ tan /Þ c tan /ðc þ cz tan /Þ2m

þ ð3  mÞc tan /ðc þ cðL þ zÞ tan /Þ2m  ð2  mÞc tan /ðc þ cz tan /Þ1m ðc þ Lð2  mÞc tan / i 1 þ cðL þ zÞ tan /Þ þ 2 24 D ð2  mÞð3  mÞc2 ð3  sin /Þ " # bBebz ð1  Bebz Þ bBebz þ  0:5m bz 2 1 þ Bebz ð1 þ Be Þ  

1þm 1  Bebz g g Aþ mcot2 /ð1 þ sin /Þ tan aðtan a 1 þ Bebz h þ tan /Þ ðc þ cðL þ zÞ tan /Þ3m i  ðc þ cz tan /Þ2m ðc þ Lð2  mÞc tan / þ cðL þ zÞ tan /Þ : ð7AÞ

According to the Meyerhof model (6A), the gradient is not influenced by cohesion. On the other hand, the cavity expansion model suggests that cohesion is influential. Specifically, using the lunar soil properties and cone geometry outlined in Table A1, GMeyerhof remains constant, while GCavity is reduced by approximately 45% by changing the value of cohesion from 1 kPa (the estimate upper bound [4]) to zero. Considering that these models yield different results, the sensitivity of lunar G measurements to soil cohesion remains an open issue. References [1] National Aeronautics and Space Administration, 2008. NASA’s newest concept vehicles take off-roading out of this world [online]. [accessed 01.06.09]. [2] National Aeronautics and Space Administration Jet Propulsion Laboratory. The ATHLETE rover [online]. [accessed 01.05.09]. [3] McKay DS, Heiken G, Basu A, Blanford G, Simon S, Reedy R, et al. Lunar regolith. In: Heiken GH, Vaniman DT, French BM, editors. Lunar sourcebook. New York: Cambridge University Press; 1991. p. 285–356.

[4] Carrier III WD, Olhoeft GR, Mendell W. Physical properties of the lunar surface. In: Heiken GH, Vaniman DT, French BM, editors. Lunar sourcebook. New York: Cambridge University Press; 1991. p. 475–594. [5] McKay DS, Carter JL, Boles WW, Allen CC, Allton JH. JSC-1 a new lunar soil simulant. In: Galloway RG, editor. Engineering, construction, and operations in space IV, Albuquerque, New Mexico. New York: ASCE; 1994. p. 857–66. [6] Klosky JL, Sture S, Ko HY, Barnes F. Mechanical properties of JSC1 lunar regolith simulant. In: Johnson SW, editor. Proceedings of the fifth international conference on space, Albuquerque, New Mexico. New York: ASCE; 1996. p. 680–8. [7] Carter JL, McKay DS, Taylor LA, Carrier III WD. Lunar simulant JSC-1 is gone: the need for new standardized root simulants. In: Proceedings of the space resources roundtable VI, Golden, Colorado. Houston (TX): Lunar and Planetary Institute; November 2004. p. 15. [8] Batiste SN, Sture S. Lunar regolith simulant MLS-1: production and engineering properties. In: Lunar regolith simulant materials workshop book of abstracts, Marshall Institute, Huntsville, Alabama; January 2005. p. 12–3. [9] Sibille L, Carpenter P, Schlagheck R, French RA. Lunar regolith simulant materials: recommendations for standardization, production and usage. NASA TP-2006-214605; September 2006. [10] Zeng X, He C, Oravec HA, Wilkinson A, Agui J, Asnani VM. Geotechnical properties of JSC-1A lunar soil simulant. ASCE J Aerospace Eng 2010;23(2):111–6. [11] Bekker MG. Land locomotion on the surface of planets. ARS J 1962:1651–9. [12] Bekker MG. Mechanics of locomotion and lunar surface vehicle concepts. Defense Research Laboratories at General Motors Corp, paper no. 632K. In: Automotive engineering congress; January 1963. [13] Bekker MG. Introduction to terrain–vehicle systems. Ann Arbor: The University of Michigan Press; 1969. [14] Janosi Z, Hanamoto B. Analytical determination of drawbar pull as a function of slip for tracked vehicles in deformable soils. In: Proceedings of the first international conference on terrain–vehicle systems, Torino, Italy; 1961. [15] Costes NC, Cohron GT, Moss DC. Cone penetration resistance test – an approach to evaluating in-place strength and packing characteristics of lunar soils. In: Levinson AA, editor. Proceedings of the second lunar science conference, Houston, Texas. Cambridge (MA): The M.I.T. Press; January 1971. p. 1973–87. [16] Fletcher JC, Costes NC, Sturm RG, Norton RH, Campbell GE. Selfrecording portable soil penetrometer. United States Patent Application 161028. 1971-06-09. [17] Mitchell JK, Bromwell LG, Carrier III WD, Costes NC, Houston WN, Scott RF. Soil mechanics experiment. In: Apollo 15 preliminary science report. NASA SP-289; 1972. p. 7-1–28. [18] Mitchell JK, Carrier III WD, Houston WN, Scott RF, Bromwell LG, Durgunoglu HT, et al. Soil mechanics experiment. In: Apollo 16 preliminary science report. NASA SP-315; 1972. p. 8-1–29. [19] National Space Science Data Center. Apollo 15 and 16 soil mechanics penetrometer data [online]. [accessed 01.05.09]. [20] US Army. Soils trafficability. Department of the Army technical bulletin no. TB ENG 37; 1959. [21] Freitag DR. A dimensional analysis of the performance of pneumatic tires on soft soils. US Army Waterways Experiment Station technical report no. 3-688; 1965. [22] Turnage GW. Mobility numeric system for prediction in-the-field vehicle performance. Report I, historical review, planned development. US Army Waterways Experiment Station misc. paper GL-9512; December 1995. [23] Freitag DR, Green AJ, Melzer KJ. Performance evaluation of wheels for lunar vehicles. US Army Waterways Experiment Station technical report no. M-70-2; 1970. [24] Green AJ, Smith JL, Murphy NR. Measuring soil properties in vehicle mobility research. Report I, strength–density relations of an

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