Mechanical properties of quartz sand and gypsum powder (plaster) mixtures: 1 implications for laboratory model analogues for the Earth’s upper crust 2

Granular materials are a useful analogue for the Earth’s crust in laboratory models of 51 deformation. Constraining their mechanical properties is critical for such model’s scaling and 52 interpretation. Much information exists about monomineralic granular materials, such as 53 quartz sand, but the mechanical characteristics of bimineralic mixtures, such as commonly- 54 used quartz sand mixed with gypsum powder (i.e. plaster), are largely unconstrained. We used 55 several mechanical tests (density, tensile, extension, shear) to constrain the failure envelope of 56 various sand-plaster mixtures. We then fitted linear Coulomb and parabolic Griffith failure 57 criteria to obtain cohesions and friction coefficients. Tests of the effects of emplacement 58 technique, compaction and humidity demonstrated that the most reproducible rheology is 59 given by oven-drying, pouring and mechanically compacting sand-plaster mixtures into their 60 experimentation container. As plaster content increases, the tensile strength of dry sand- 61 plaster mixtures increases from near zero (pure quartz sand) to 166±24 Pa (pure plaster). The 62 cohesion increases from near zero to 250±21 Pa. The friction coefficient varies from 63 0.54±0.08 (sand) to 0.96±0.08 (20 weight% plaster). The mechanical behaviour of the 64 resulting mixtures shifts at 20-35 weight% plaster from brittle Coulomb failure along a linear 65 failure criterion, to more complex brittle-plastic Coulomb-Griffith failure along a non-linear 66 failure criterion. With increasing plaster content, the brittle-plastic transition occurs at 67 decreasing depth within a pile of sand-plaster mixture. We infer that the identified transitions 68 in mechanical behaviour with increasing plaster content relate to (1) increasing porosities, (2) 69 increasing grain size distributions, and (3) a decrease in sand-sand grain contacts and 70 corresponding increase in contacts of anisotropic gypsum-gypsum grains. The presented 71 characterisation enables a more quantitative scaling of the mechanical behaviour of sand- 72 plaster mixtures, including their tensile strength. Sand-plaster mixtures can thereby 73 realistically simulate brittle-plastic properties of the Earth’s crust in scaled laboratory models. quantifies the mechanical behaviour of quartz sand mixed with gypsum powder by evaluating different mechanical testing methods. We for the scaling of mechanical properties of analogue granular materials. We test influence of the emplacement compaction on estimate the material porosities. We also test the effect of ambient tensile tests, extensional tests, direct shear tests and ring shear tests, we constrain failure envelopes for each of the end-member sand and plaster materials and mixtures thereof. goodness-of-fit of linear Coulomb


Introduction 80
The Earth's crust is a complex set of geological layers and structures, exhibiting a wide range 81 of physical and mechanical properties. Properties such as rock density, porosity, tensile 82 strength, shear strength, cohesion and internal friction control or relate to deformation of the 83 crust during geological processes (Graveleau et al., 2012;Hubbert, 1951Hubbert, , e.g. 1937Labuz et 84 al., 2018). The mechanical response of rocks to a stress applied externally to the studied 85 volume can take several idealised forms. For an ideal, linearly elastic material, the 86 relationship between stress and strain follows a recoverable sloped linear trajectory, and the 87 material resumes its initial geometrical state after the stress is removed ( Figure 1A) (Jaeger et 88 al., 2007). For an ideal plastic material, the relationship between stress and strain is initially 89 similar to an elastic material, but at a certain shear stress threshold the plastic material 90 undergoes 'yielding', after which the strain is non-recoverable (Jaeger et al., 2007). The strain 91 vs. stress curve then becomes horizontal and defines a stable strength value ( Figure 1A representative of material failure in both model (m) and a natural prototype (g). The internal 216 friction coefficient µ is a direct dimensionless parameter. Dynamic similarity implies that the 217 friction coefficient of the model material must be equal to that in geological natural systems: 218 (1) m = g 219 The cohesion C is combined with density ρ, gravitational acceleration g, and depth or length h 220 (Hubbert, 1945;Merle, 2015) in the dimensionless parameter: 221 This parameter quantifies the balance between the gravitational forces and the cohesive 223 forces; the system will be gravity-dominated if ∏ >> 1 and cohesion-dominated if ∏ << 1. In 224 addition, the model material cohesion Cm required for a model that is subjected to the natural 225 gravity field is calculated by rearranging equation (2): 226 Accordingly, the model cohesion dictates the length scale hg of the model with respect to the 228 natural prototype. Different scales of observation, e.g. basin-scale vs. lithosphere scale, 229 therefore necessitate different model cohesions (Abdelmalak et al., 2016). The length scale h* 230 represents the dimensionless scale ratio between model and nature and equals hm/hg (Table 1). 231 In laboratory models of lithosphere-scale processes, one centimeter typically represents 10 232 km, translating into l* ≈ 10 -6 (e.g. Davy and Cobbold 1991), while in those of basin-scale 233 processes, one centimeter most typically represents 100 to 1000 meters, translating into l* = 234 10 -4 -10 -5 (e.g. Dooley and Schreurs, 2012;Galland et al., 2018;Merle, 2015). Bulk densities 235 of most natural crustal rocks range between 2200 and 3000 kg.m -3 , while analogue granular 236 material bulk densities range between 1200 and 1800 kg.m -3 . This leads to model:nature 237 density ratios ρ* of 0.4-0.8. Cohesions of natural rocks range broadly between 10 6 and 10 8 Pa 238 (e.g. Galland et al., 2018;Schellart, 2000;Schultz, 1996;Voight and Elsworth, 1997). 239 For lithosphere-scale processes, ∏ values then range between 2 and 300, and so cohesions of 240 model rocks should be considerably low, between 0.5 and 80 Pa. This is the case for pure 241 silica sand (Klinkmüller et al., 2016;Schellart, 2000). For basin-scale or volcano-scale 242 processes, ∏ values lie an order of magnitude lower, between 0.2 and 30, and cohesions of 243 model materials should have a range between 40 and 800 Pa. Granular materials with higher 244 cohesion compared to sand are thus needed, by using fine-grained powders or fillers in 245 coarse-grained sand. 246  Figure 2A). The grain size is unimodal, with a mean ~205 µm ( Figure 2B). The 256 plaster is air-dried hemi-hydrate gypsum powder with the brand name Goldband (CaSO4.1 2 ⁄ 257 H2O; Knauf). SEM images show the grains are tabular to plate-shaped, and clustered ( Figure  258 2C). Grain size measurements in water in a laser diffractometer without scintillation at Vrije 259 Universiteit Brussel showed that the grain size distribution is unimodal, with a mean ~22 µm 260 ( Figure 2D). This combines both 1-10 µm-sized individual crystals and 10-80 µm-sized 261 clusters. The crystal hardness of quartz is 7 on the scale of Mohs, while that of gypsum 262 crystals is 4. 263 The sand and plaster were mixed at 0, 5, 10, 20, 35, 50, 70 and 100 weight percent (wt%) of 264 plaster. The quartz sand and gypsum plaster end-member materials and their mixtures are 265 hereafter referred to as 'samples'. Ambient air temperature was registered in all laboratory 266 environments to be 18-25°C. 267

Bulk density estimates and effects of emplacement method 277
The effects of three emplacement methods were assessed: (1) pouring, (2) sieving, and (3) 278 pouring and compaction. The first two methods were assessed by systematically measuring 279 the bulk density ρ of sand-plaster mixtures with 0, 10, 20, 50 or 100 wt%. plaster in ring shear 280 tests (see Section 3.2.3). The air-dried granular materials were placed into a ring-shaped shear 281 cell, either by sieving through a 400 µm mesh, or by pouring from an open pitcher. The shear 282 cell is 4 cm high, 1.10 -3 m³ (1 liter) in volume and of a mass of 2186.5 g. The samples were 283 emplaced from ~20 cm height, which was previously found to be the most efficient height for 284 obtaining a most compact quartz sand packing (Lohrmann et al., 2003). Surplus material was weighing the filled test cell on a balance. 287 The third emplacement method, and the effects of humidity, were examined through a second 288 set of identical mixtures that were oven-dried for 24 hours at 90°C, poured in the shear cell 289 from ~20 cm height and compacted by preloading with a normal load of 20000 Pa on the ring 290 shear tester. The ring shear test procedure includes the estimation of material density before 291 and during the test, which provided a means of assessing the effect of material compaction 292 during deformation (see Section 3.2.3). 293 294

Porosity estimates 295
The bulk porosity φ of each granular material was estimated through the equation: 296

Ring shear tests 303
We generally followed the ring shear test protocol for measuring internal friction with the 304 RST01.pc as described in Klinkmüller et al. (2016). The shear cell containing the sample was 305 placed on the ring shear tester ( Figure 3A) and the lid was lowered into the sample surface. A 306 normal load was then applied by the lid to the air-dried poured or sieved sample under rest, 307 that varied in separate test runs from 500, 1,000, 5,000, 10,000, 15,000 to 20,000 Pa. For 308 comparison with direct shear test data, oven-dried samples were poured and then compacted 309 in the ring shear cell by pre-loading with a normal load of 20,000 Pa for 5 seconds. Then, the 310 normal load was returned to 250, 500, 1,000, 2,000 or 5,000 Pa respectively in separate test 311 runs. 312 The cell was then rotated clockwise at a constant angular velocity of 4.4°.min -1 , or 6 mm.   here, but they are available in the accompanying data publication (Poppe et al., 2021). 344 During shearing, vertical lid movement is measured as a proxy for sample decompaction 345 (positive) or compaction (negative). This measurement allowed us to study the effect of 346 sample decompaction/compaction, and thus density variations, on sample frictional 347 properties. 348 An additional velocity stepping test was carried out on a 90 wt% sand -10 wt% plaster 349 mixture to assess the dependency of measured shear strengths on the shear rate, by decreasing 350 the shear rate after reaching the steady state plateau incrementally from 5 mm.s -1 to 2.5, 1,

Direct shear tests 365
Pressures of <500 Pa are typical in sand-box experiments with a few centimeters of material 366 height (depending on material density -cf. equation 2). Because standard ring shear tests at Hubert-type direct shear tests at normal loads of ~100 to ~1200 Pa. The Hubert-type shear 369 apparatus consisted of an upper PVC cylinder suspended above a fixed lower PVC cylinder, 370 with a cardboard ring maintaining a gap of < 1 mm in between both cylinders ( Figure 3B). 371 To avoid humidity effects on material properties, samples were first oven-dried at 90°C for at 372 least 24 hours, left to cool in a sealed container, weighed on a precision balance and poured in 373 the cylinders of the shear apparatus. A lid was placed on top of the sample, and by manual 374 tapping from above on the lid, the sample was compacted down until a height H of 2.5 cm 375 above the gap between both cylinders to obtain the density pre-determined for that material 376 (ρCompacted in Table 2  The 'silo effect' or 'Janssen effect' is a reduction in the normal load on the shear plane due to 397 friction on the wall of the upper cylinder (Jansen, 1895; Mourgues and Cobbold, 2003). This 398 can be corrected empirically. The upper cylinder of the Hubbert-type shear apparatus was 399 suspended above a precision balance. A cardboard ring maintained a gap of <1 mm between 400 the cylinder and the balance. A sample was then poured and compacted in the suspended cylinder to obtain the same densities as used in the direct shear tests ( Table 2). The cardboard 402 ring was then removed. The mass then registered by the balance was the effective normal load 403 exerted on the failure plane in the direct shear tests. These normal load measurements were 404 repeated at least three times for each of the five normal loads in the direct shear tests, and the 405 average 'corrected normal load' was used instead of the theoretical normal load to construct 406 failure envelopes. 407 408

Tensile tests 409
The tensile strength T0 of oven-dried sand, plaster and sand-plaster mixtures containing 5, 10, 410 20, 35, 50 and 70 wt% plaster, and air-dried plaster was measured at Le Mans Université, 411 France, following the method of Schweiger and Zimmerman (1999). Each material was 412 poured into a container of 108 cm³ in volume and with a square-shaped area of 6x6 cm². It 413 was then compacted by manually tapping a cover from above to obtain the required density 414 The tensile strength test consisted of three steps ( Figure 3C). In step 1, the sample was 418 vertically preloaded by the load cell for five seconds to allow the silicone to adhere to the 419 sample surface. In step 2, the loading was reduced until the tension force sensor measured 0 420 N. In step 3, an increasing vertical tensional force was exerted on the granular material by 421 moving the silicone pad upwards at a constant displacement rate until a peak tension force Ft 422 was reached at failure. A photograph of the post-test silicone pad was orthorectified in 423 ArcGIS software (ESRI), where the area of separated granular material As was traced and 424 quantified. The tensile strength T0 was then obtained through the equation: 425 (6) T0 = Ft/As 426 Tensile strength tests were reproduced ten times for the sand and plaster end-members and 427 each sand-plaster mixture. 428 429

Extension tests 430
On the assumption that the failure envelope of a material is non-linear at negative normal 431 loads and at small positive normal loads, the cohesion of granular materials can be estimated 432 by combining the tensile strength T0 with a vertical cliff height H obtained from extensional 433 tests (Abdelmalak et al., 2016). H was measured at the Vrije Universiteit Brussel, Belgium, in 434 an extensional apparatus that consists of a box with three fixed glass walls and one moving wall connected to a computer-controlled piston ( Figure 3D). Attached to the moving wall was 436 sandpaper that covered half of the box bottom length. 437 A weighed amount of oven-dried sand, plaster or sand-plaster mixtures containing 5, 10, 20, 438 35, 50 and 70 wt% plaster, or air-dried plaster was poured in the box. Sample compaction to a 439 vertical height of 10 cm and the required density (see Table 2) was obtained by manual 440 tapping on a lid from above. By moving the wall laterally outwards at a constant rate of 10 441 cm/hr, the attached sandpaper imposed a velocity discontinuity to the base of the sample pack, 442 which extended until two or more fractures developed, forming a graben-like structure. At The spatial grainsize distribution of a sand-plaster mixture, and thus of mineralogy, is 456 strongly affected by the emplacement method. Pouring a mixture quasi-instantaneously 457 maintained a homogeneous sand and plaster distribution as visually observed in Figure 4A. 458 Sieving the mixture, however, resulted in heterogeneous grain-size and mineralogical 459 distribution as the sand and plaster separated into thin layers ( Figure 4A). 460 461

Material porosity 482
The estimated bulk porosity of the samples relates inversely to the bulk density ( Figure 4C; 483 Table 2). Depending on the emplacement technique, the inferred porosity of quartz sand was 484 varied between 36-54 vol%, whereas that of plaster varied between 67-78 vol%. In mixtures 485 of these end-members, the porosity increased systematically, but non-linearly, with increasing 486 plaster content by weight.   After 72 hours of oven-drying at 90°C, samples showed a cumulative weight loss that 502 increased roughly linearly (R² = 0.93) with increasing plaster content ( Figure 5; Table 2). 503 While plaster lost a cumulative 1.05 wt% of moisture, quartz sand only lost 0.05 wt%. For all 504 samples, more than 90% of the weight loss occurred in the first 24 hours of oven-drying (see 505 data in Poppe et al., 2021), suggesting that drying overnight should be sufficient to remove 506 most of the humidity from granular materials prior to experimentation. 507 508 to a dynamic plateau value without further decompaction. Overall, the peak strengths and 543 post-peak plateau strengths increase with increased normal loads. 544 As the plaster content increases in sieved samples, three alterations to this well-established 545 shearing behaviour are seen (Figure 6, bottom rows). Firstly, the initial peak is wider; i.e. 546 more strain is needed to localise a shear zone. Secondly, the associated stress drop gradually 547 decreases, and a peak is absent from a 50:50 sand-plaster ratio onwards; i.e. the behaviour of 548 plaster-dominated mixtures is more plastic. Additionally, the stable sliding strength at a given 549 normal load generally increases with increased plaster content. Thirdly, the compaction-550 decompaction cycle observable in sand-dominated mixtures (≤ 20 wt% plaster) is replaced by 551 steady compaction during localisation in the plaster-dominated mixtures (≥ 50 wt% plaster). 552 For poured samples, the temporal evolution of shear stress and decompaction is qualitatively 553 similar to what has been observed for sieved samples (Figure 6, top rows). Nonetheless, there 554 are some quantitative deviations. First, the peaks are generally wider (i.e. localisation requires 555 more strain) and stress drops are smaller when poured compared to when sieved. Second, 556 high-frequency noise indicates stick-slip, except for pure sand, and such noise is typically 557 higher in amplitude compared to sieved samples. In sand-dominated samples, a clear initial 558 peak with stress drop occurs again, although it is accompanied by a more subtle compaction-559 decompaction cycle (without net decompaction). In plaster-dominated poured mixtures, such 560 a peak stress is again absent and is replaced by strain strengthening and sample compaction 561 until the dynamic steady state is reached. 562 563 Figure 7 depicts the ring shear test results and dilation curves obtained for oven-dried sand, 565 plaster and sand-plaster mixtures that were poured and mechanically compacted prior to 566 testing. In general, the shear stress curves for these poured and pre-compacted samples are not 567 as noisy as those for their poured and uncompacted equivalents (see Figure 6). 568

Stress and dilation curves for oven-dried compacted samples 564
For sand-dominated mixtures (≤ 35 wt% plaster), initial shear stress peaks are again present at 569 all tested normal stresses. These materials thus display a similar strain hardening to strain tests on air-dried samples and as described by (Panien et al., 2006). 572 573

576
For plaster-dominated mixtures (≥ 50 wt% plaster), a peak stress and compaction-577 decompaction behaviour is also seen at low normal loads. This is more brittle behaviour than 578 the generally plastic behaviour seen in equivalent mixtures that were uncompacted prior to 579 testing (see Figure 5). In addition, stick-slip behaviour is apparent in the stress-displacement

Direct shear tests 611
We performed 143 direct shear tests on oven-dried poured+compacted sand, plaster and sand-612 plaster mixtures and on air-dried poured+compacted plaster (Figure 8). 613

Correction for the silo effect 615
The results of the empirical correction for the 'silo effect' (Jansen, 1895 The tested range of normal stresses overlaps with that of the three lowest normal load steps in 618 the ring shear tests (250, 500 and 1000 Pa). The measured normal stress versus applied 619 normal stress curves deviate from a 45° slope. This deviation is greatest for mixtures with 35 620 and 50 wt% plaster. Therefore side-wall friction decreases the applied normal stress at the 621 shear failure plane in all samples, and these curves enable a correction to obtain the average 622 effective normal stress on the failure plane that was used to plot direct shear test data in 623 plaster content increases to about 20 wt%. With higher plaster contents, however, the shear 634 strengths at the tested normal loads remain slightly higher than those of pure sand. 635 636

Tensile tests 637
We performed 89 unconfined tensile tests on oven-dried and compacted sand, plaster and 638 sand-plaster mixtures ( Figure 9A; Table 3). Sand-plaster mixtures with < 20 wt% plaster 639 display average tensile strengths that are near-zero (2-5 Pa) with little to no data spread. From 640 20 wt% plaster upwards, the tensile strength increases with plaster content along a roughly 641 linear trend (R² = 0.969), up to a mean value 167 ± 23 Pa for pure, oven-dried plaster. The 642 data spread increases with increasing plaster content in a mixture. Non-dried plaster yields a 643 tensile strength of 200 ± 18 Pa, the mean of which is ~33 Pa. This is almost 20% higher than, 644 and statistically distinct from, the mean tensile strength value of oven-dried plaster (α=0.050; 645 p=0.004; t-statistic=4.00, t-critical=2.31). 646 647 4.6 Extension tests plaster mixtures, in which a total of 73 vertical opening-mode fracture portions were 650 measured ( Figure 9B; Table 3). Quartz sand extended in a diffuse manner and developed 651 unmeasurably low cliffs. An arbitrary value of 0.1 cm, representing measurement limit, was 652 therefore assigned here to pure sand. 653

Theoretical background 681
We determined the optimal fit to failure envelopes of sand-plaster mixtures by applying a 682 friction coefficient µc were obtained by a 100-fold linear least-squares regression of the data 709 plus noise to find the optimal fit of the linear Coulomb failure criterion in equation (7). The 710 Griffith cohesion CG was obtained by a 100-fold non-linear least-squares regression of the 711 data plus noise to find the optimal fit of parameters a and T0 in equation (8). 712 We constrained optimal Coulomb and Griffith criteria for each of the oven-dried and 713 compacted end-member materials and their mixtures, and for non-dried poured+compacted 714 plaster (Figure 8). We then choose the best-fitting of these criteria to derive either a Coulomb 715 cohesion (CC) or a Griffith cohesion (CG) value for each material. Since the slope of the 716 Griffith criterion is non-unique, we used by default the optimal Coulomb criterion to derive a 717 friction coefficient (µC) for each material. 718 We used only the peak strength data from the ring shear test results (poured, sieved, oven-719 dried and poured+compacted) to constrain an optimal Coulomb criterion as that is a standard 720 approach in such tests (Klinkmüller et (Table 5) is displayed in Figure 10. For sand and sand-plaster mixtures with 733 plaster contents < 35 wt%, CC values from combinations of tensile strength data and direct 734 shear data ( Figure 10A, green circles) yield the optimal fits (i.e. standard deviations are 735 smaller with respect to the cohesion values, see Table 4). CG values obtained from tensile and 736 extension test data ( Figure 10A, red squares), which are constrained only from data in the 737 tensile field, lie within the double standard deviations of CC values, and increase from < 10 Pa 738 to ~105 Pa ( overestimate the lower part of the failure envelope, whereas CG provides optimal fit ( Figure  748 10, orange circles). For direct shear test data alone in comparison, CC provides larger standard 749 deviations and thus poorer fits (see Table 4). CG values obtained from tensile strength and 750 direct shear data (Figure 10, orange circles) first continue increasing, albeit at a lower rate > 751 50 wt% plaster, until the maximum of ~280 Pa for pure plaster. CG values obtained from 752 tensile and extension tests increase roughly linearly (R² = 0.965) with increasing wt% plaster 753 content until a maximum of ~500 Pa for non-dried compacted plaster (Table 4, Figure 10A). 754 Overall, the CC values derived from ring shear data (Figure 10, green diamonds) are strongly 755 dependent on the higher normal stress data (5000 Pa) and their standard deviations are values are highest of all obtained values for mixtures with plaster content ≤ 50 wt%, but 758 abruptly decrease to values similar to CG values derives from failure envelopes that combine 759 tensile and direct shear test data. CC values derived from direct shear data alone do not show 760 obvious trends, but they systematically have higher standard deviations compared to those 761 obtained from failure envelopes that combine tensile and direct shear test data and are 762 therefore not displayed on Figure 10A. Air-dried plaster yielded a CG value that is ~50 Pa 763 higher compared to oven-dried plaster, and displays relatively higher standard deviations 764 (Table 4, Figure 10A, blue-and-red circle). 765 Friction coefficient values can only be derived using a linear Coulomb criterion ( Figure 10B, 766 Table 5). µC values derived from tensile strengths and direct shear data ( Figure 10B (Table 5). 774 µC values of non-dried plaster obtained either from direct shear data alone, or in combination 775 with tensile test data, agree very well (Table 5, Figure 10B, blue-and-red circle). These values 776 are slightly higher than those obtained for oven-dried plaster as constrained from tensile 777 strength and direct shear test data ( Figure 10B, green circles), and they are lower than those 778 for oven-dried plaster as constrained from ring shear test data ( Figure 10B, diamonds).  (Table 4), but that it slightly 802 increases the friction coefficient (Table 5). 803 For pure plaster, our tests document the opposite behaviour: sieved plaster is less dense, 804 poured plaster more dense ( Figure 4B, Table 2). We propose that friction with air during 805 sieving might result in increased electro-static forces that increase porosity between settled 806 plaster grains (van Gent et al., 2010). Pouring plaster may reduce electrostatic forces and may 807 make plaster-rich packs more susceptible to compaction during emplacement. In terms of 808 mechanical properties, our data show that sieved plaster compacts more at low normal loads 809 compared to poured plaster ( Figure 6). Sieving or pouring of pure, air-dried plaster produced 810 a discernable difference in cohesion (Table 4), and sieving slightly increased the friction 811 coefficient (Table 5). Even if assessed minimal, mineralogical changes due to oven-drying at 812 90°C cannot be ruled out (Vimmrová et al., 2020). Drying in combination with mechanical 813 compaction has a strong effect on the mechanical behaviour of pure plaster, however. In 814 addition to higher bulk density and smoother stress-displacement curves, a more brittle 815 behaviour is seen at low normal loads compared to poured or sieved oven-dried plaster 816 ( Figures 6 and 7), and cohesions and friction coefficients are lower regardless of shear testing 817 approach and fitted failure criterion (Tables 4 and 5). SEM pictures showed that, in contrast to 818 the (sub)rounded quartz sand grains, gypsum crystals are tabular gypsum to blocky. 819 Compaction may thus reorient gypsum crystals toward alignment with the shear plane, thus 820 making grain-grain sliding easier, and/or because reduced moisture content reduces the 821 electrostatic attractions between plaster grains. 822 For a sand-plaster mixture with a plaster content of 50 wt%, there is no significant difference 823 in the density when sieved or poured. In addition, sieving of sand-plaster mixtures results in 824 layered, non-homogeneous grain size distribution throughout packs ( Figure 4A). Thus, 825 sieving devices that are designed to ensure an ideally dense packing of sand (e.g. Maillot 826 2013) would create heterogeneous layering due to density, grain size and grain shape 827 differences between quartz sand and gypsum particles. Similarly, Krantz (1991) showed that 828 emplacement-induced density differences affect the shear strength of mixtures of quartz sand 829 and cement more than the difference in particle density of sand versus cement. Pouring is also 830 not ideal as it creates variations in grain packing density throughout sand-plaster mixtures. 831 We surmise that these effects of pouring or sieving could be seen in our data to some extent. 832 stress-displacement curves (Figure 6), although no clear trends or differences were seen in cohesion and friction values (Tables 4 and 5). Compaction and oven-drying had a strong 835 effect on pure plaster. Smoother stress-displacement curves, a more brittle behaviour (stress 836 drop) at low normal loads, and lower friction coefficients are consistently seen compared to 837 non-dried and non-compacted equivalents (Table 4). 838 The problem of ambient humidity in granular analogues has received little attention, although 839 in quartz sand, moisture is known to increases the bulk strength (van Mechelen, 2004). Sand-840 plaster mixtures in past studies have been used in equilibrium with ambient air humidity in 841 laboratories, which can vary strongly from day to day influenced by the weather. Our data 842 demonstrate that a sand-plaster mixture's humidity increases with increasing plaster content 843 ( Figure 5). The moisture uptake by gypsum powder from ambient humidity was previously 844 measured to be ~2-2.5 wt% over 2. Based on our results, we recommend oven-drying and compacting sand-plaster mixtures prior 869 to their deformation in scaled laboratory models. We did not test chemical effects of heating 870 on our gypsum material. While most significant effects have been shown to occur by heating 871 above 100°C, heating up to 50°C for 24 hours may be tested to completely avoid effects on 872 gypsum chemistry and strength (Park et al., 2010;Vimmrová et al., 2020). In a silo, side-wall friction counteracts gravity forces; this 'silo effect' or 'Jansen effect' 889 reduces the actual normal load acting on the shear plane in a direct shear test (Jansen, 1895). An increase in plaster content also generally leads to a more plastic behaviour of a sand-938 plaster mixture (Figures 6 & 7). The stress drop seen for sand-rich mixtures diminishes and 939 ultimately disappears, especially at high normal stresses (<1000 Pa). An exception is when 940 the mixture is oven-dried and pre-compacted; then a small stress drop persists in plaster-rich 941 materials at low normal stresses (<1000 Pa). Irrespective of handling technique, the stress 942 drop diminishes from about 20-35 wt% plaster content and upward. This general shift to a 943 more plastic behaviour in stress-displacement curves as plaster content increases corresponds 944 to a change in dilation behaviour. Sand-rich mixtures (<35 wt% plaster) compact prior to 945 sample failure then de-compact, as previously observed for pure sand (Panien et al., 2006;946 Ritter et al., 2016). Plaster-rich samples (>35 wt% plaster) undergo compaction throughout 947 shearing. Numerical simulations of deformation of granular materials produce a similar 948 transition to more plastic and compaction-dominated behaviour with increased porosity (cfr. 949 Figure 4 in Schöpfer et al., 2009). Therefore, we tentatively attribute the change to a more 950 plastic behaviour with increased plaster content to increased bulk porosity. This change may 951 occur with more distributed strain localisation in the more porous plaster-rich mixtures, 952 especially at high normal stresses, as the progressive collapse of pore-spaces in the gypsum 953 crystal aggregates inhibits the formation of well-defined shear zones. 954 Sand-plaster mixtures therefore have the capacity, like real rocks, to display a brittle-plastic 955 transition with depth. Considering the normal stress as equivalent to confining pressure of an 956 overburden and assuming the compacted bulk densities in Table 2, that transitional depth 957 would amount to 30 cm height (i.e. at ~5000 Pa) in mixtures with 20 wt% plaster. This depth 958 would be shallower with increased plaster content, and it would lie at ~16 cm (~2000 Pa) with 959 50 wt% plaster and at 11 cm (~1000 Pa) in pure plaster. This brittle to plastic transition 960 primarily represents a change in strain-weakening or strain-strengthening behaviour, and does 961 not necessarily imply a major change in strain localisation (i.e. shear zone vs. distributed 962 flow) with depth within a material. 963 Associations between increased plaster content and a sand-plaster mixture's strength, in terms 964 of cohesion and friction coefficient, are complex and in part dependent on measurement 965 technique. In general, cohesion increases with increasing plaster content, up to about 50 wt % 966 plaster ( Figure 10A, Table 4). Coulomb cohesions thereafter decrease or stabilize, whereas 967 either shows no clear trend with increasing plaster content (ring shear test data) or shows an initial slight increase at 0-20 wt% plaster followed by overall decrease at 20-100 wt% plaster 970 ( Figure 10B, Table 5). Uniaxial compressive strength of quartz crystals at room temperature 971 and pressure is around 190-300 MPa (and references therein Scholz, 1972 Such crystal strengths far exceed the differential stresses applied in our material tests. The 976 friction coefficient of granular materials in a regime of no grain fracture is known to increase 977 with increased grain surface roughness (angularity) and particle size distribution (Mair et al., 978 2002), and it is known to decrease with increased porosity (Schöpfer et al., 2009). Moreover, 979 stick-slip behaviour in deformed granular materials is associated with smoother grain surfaces 980 (Mair et al., 2002;Rosenau et al., 2009). Therefore, we interpret that cohesions and friction 981 coefficients at plaster contents of up to 20-50 wt % initially increase because of increased 982 particle size distribution on mixing relatively coarse quartz sand with relatively fine gypsum 983 powder ( Figure 2). Increased inter-crystal attraction forces in gypsum may also play a role in 984 that initial strength increase (see below). Cohesion and friction coefficient subsequently 985 decrease or stabilize at plaster contents of up to 50-100 wt % because of increased porosity 986 ( Figure 4) and possibly also the capability of gypsum grains to align and to slip past each 987 other along their relatively smooth crystal faces. The latter factor can also account for the 988 short-frequency noise and stick-slip events observed in plaster-rich mixtures (Figure 6 & 7). 989 Increasing plaster content of sand-plaster mixtures is clearly associated with increased tensile 990 strength. This has been known qualitatively from the occurrence of opening mode fractures in 991 such mixtures compared to the absence of such fractures in pure quartz sand, and has formed 992 a main reason for use of plaster veneers or sand-plaster mixtures previously (e.g. Byrne