Fused quartz was used as the skeleton of TCS. Iskander and Liu (2010) first used fused quartz as the material representing the skeleton of a transparent sand. Ezzein and Bathurst (2011) found that fused quartz is similar to natural sand in terms of the structure and shape and can replace sand in meso-structural terms. Other experimental studies (Kong et al., 2013; Guzman et al., 2014; Kong et al., 2014) show that fused quartz has similar mechanical properties to sand and can replace sand in terms of the mechanical properties. The fused quartz used (purchased from Xinyi Wanhe Mining Co., Ltd, and shown in Figure 1A) was classified into three groups according to particle sizes of 0.2–0.5, 0.5 to 1.0, and 1.0–2.0 mm. The specific gravity and refractive index of the particles separately are 2.2 and 1.4585 in each group. In the natural state of accumulation, the dry densities of three groups of fused quartz are 1.40, 1.25, and 1.10 g/cm³, and their void ratios are 36, 43, and 50%, respectively.

Mixed mineral oil containing n-dodecane and 15# white oil was used as the pore fluid of TCS. To prevent refraction of light between the pores and skeleton to ensure high transparency of TCS, it is necessary to prepare a pore fluid whose refractive index is consistent with that of fused quartz. At 26°C, the refractive indexes of n-dodecane and 15# white oil (both were purchased from Guangdong Wengjiang Chemical Reagent Co., Ltd) are 1.424 and 1.469, respectively. The refractive index of mixed mineral oil increases with increasing temperature. In general, when the mass ratio of n-dodecane to 15# white oil is 1:3.5 to 1:8, the refractive indexes of mixed mineral oil and fused quartz are consistent or similar. The refractive index of mixed mineral oil can be reduced by adding n-dodecane when it is higher than that of fused quartz and can be increased by adding 15# white oil as it is lower than that of fused quartz.

Nano-scale hydrophobic fumed silica powder was utilized as cement of TCS. The method for preparing transparent soil by adding (micron-scale) silica powder into mixed mineral oil was proposed by Stanier et al. (2014) and it has been proved that the transparent soil has similar mechanical properties to natural soft clay. Limited by the inconsistent refractive indexes of silica powder and fused quartz, the combination of fused quartz and transparent clay is opaque. By contrast, the nano-scale hydrophobic fumed silica powder used in the study (purchased from Bengbu Jingxi Glass Products Co., Ltd, and shown in Figure 1B) is a modified fumed silica, which is a white powder with particle sizes of 15 nm and finer, a density of about 0.07 g/cm³ in its natural state, a high specific surface area, and good dispersibility. Most importantly, the refractive index of silica powder is similar to that of fused quartz, which means that the mixture of silica powder, fused quartz and mixed mineral oil has high transparency. Moreover, such silica powder is hydrophobic (lipophilic) and can adsorb the mixed mineral oil, therefore can be adsorbed onto the surface of fused quartz after mixing with fused quartz and mixed mineral oil. The fused quartz particles can bind to each other due to the surface adsorbed with silica powder, thus manifesting the properties of clay particles.

The process of preparing TCS can be divided into the following five steps:

1) The mixed mineral oil of n-dodecane and 15# white oil was prepared to make the refractive index 1.458 5. The fused quartz (Figure 1A) was cleaned and dried to remove impurities and water on the surface. The mixed mineral oil and the fused quartz were sealed for later use.

To ascertain the effects of the content and mass ratio of silica powder, particle size and gradation of fused quartz on the geotechnical properties of TCS, 11 groups of TCS with different shear strengths were synthesized and UU triaxial shear tests were conducted by using SJ-1A.G triaxial shear apparatus. The test scheme and basic information pertaining to the TCS are summarized in Table 1, where the amount of mixed mineral oil in the specimens was determined by Formula 1. The particle size distribution in each group of TCS is shown in Figure 2. The proportioned TCS was placed into a geotechnical instrument for specimen preparation according to a certain mass, and specimens measuring 39.1 mm in diameter and 80 mm in height were prepared with an air-void ratio of 8–19% and saturation of about 80%. The confining pressures set in triaxial shear tests were 50, 100, and 200 kPa considering the low stress state in the model tests, and the rate of vertical compression displacement was 0.368 mm/min.

Previous studies have proved that particle characteristics affect the shear strength of soils (Ganju et al., 2021; Lu et al., 2021). For example, the angle of internal friction was found to increase with increasing particle size in natural sand through triaxial compression tests using sand with different particle sizes (Li, 2013; Vangla and Latha, 2015). Moreover, various shear strength expressions of sandy soils were fitted based on the correspondence between the gradation parameters (such as the coefficients of uniformity C u and the coefficients of curvature C c ) and the shear strength (Belkhatir et al., 2012; Bayat and Bayat, 2013; Sezer, 2013; Havaee et al., 2015). It is clear from these studies that the particle characteristics are an indicator of the shear strength of soils and can be used to predict the soil shear strength.

Since mechanical properties of TCS are significantly affected by gradation characteristics (Section 4.1.2), establishing expressions of mechanical properties varying with the gradation will be helpful for the preparation of TCS with target mechanical properties. Figure 16 illustrates the variations of cohesion and internal friction angle of TCS with different gradations in Table 1. As suggested in previous studies (Belkhatir et al., 2012; Bayat and Bayat, 2013; Sezer, 2013; Havaee et al., 2015), the coefficient of uniformity, C u , is employed as an indicator of the gradation characteristics of TCS, and it is calculated using the following equation: C u = D 60 D 10 (2) where D 10 and D 60 are the particle diameter at 10 and 60% passing, respectively. The particle diameters required to calculate coefficients of uniformity in Figure 16 are determined by reading the particle size distribution curves in Figure 2. As shown, the cohesive c (Figure 16A) and internal friction angle φ (Figure 16B) of TCS gradually decrease with increasing logarithm of coefficient of uniformity log ( C u ) . The variations of cohesive c and internal friction angle φ are fitted by the following equations: c = − 102.34 × log ( C u ) + 91.33 (3) φ = − 53.61 × log ( C u ) + 62.06 (4)

Based on Eqs 2–4, TCS with the target strength can be prepared by adjusting the particle gradation in the future.

The similarity of the stress–strain relationship is the basis of using TCS as a substitute for natural clay. It can be seen from Figures 3–6 that the shape of stress–strain curves of TCS is ideal elastoplastic type or strain softening type, which is similar to that of natural clay (Huang et al., 2016). Figure 17 illustrates the envelopes of the stress–strain curves of TCS prepared according to 11 schemes in Table 1. As shown, (1) under different particle sizes and gradations of fused quartz and different mass ratios of silica powder, the stress–strain curves of TCS change significantly. By adjusting the particle size of fused quartz and the mass ratio of silica powder, the stress–strain curves of TCS match those of natural clay. (2) Compared with several existing typical transparent geomaterials, such as transparent granular soil (Li et al., 2020), TCS (Wei et al., 2019), transparent glass soil (Kong and Lu, 2014), transparent glass sand (Kong et al., 2013) and Transparent silica gel (Iskander et al., 2002b) used in model tests, the TCS prepared in the present work has a similar stress–strain relationship to them. The difference is that the stress–strain curves of TCS used in this research can be controlled across a wider range, thus TCS has stronger applicability in simulating different natural clays.

The changes in geotechnical parameters (Figures 7, 8, 10, and 11) show that the geotechnical parameters of TCS change with large ranges: cohesion varies from 5 to 65 kPa, the angle of internal friction varies from 25 to 44°, and Young’s modulus from 5 to 17 MPa ( σ 3 = 50  kPa ), 6–22 MPa ( σ 3 = 100  kPa ), and 9–42 MPa ( σ 3 = 200  kPa ). In addition, by changing the air-void ratio or bulk density of TCS, it can be predicted that the range of geotechnical parameters of TCS will increase further. In terms of the ranges of parameters obtained through testing, they cover those of most mechanical parameters of clay (Huang et al., 2016; Chen and Guo, 2019), such as loess, expansive soil, soft soil, frozen soil, red clay, saline soil, etc. Therefore, such TCS can be used as a substitute for natural clay in model tests.

The failure of the TCS specimens under triaxial compression (Figures 13–15) is mainly due to shearing, and the distribution, number, and dip angle of the shear zones in the specimens are similar to those in natural clay (Huang et al., 2016), so TCS can be used to simulate failure process of natural clay.

TCS differs from rock in terms of its mechanical properties, so it cannot be directly used as a substitute for rock. To expand the applicability of TCS in model tests, the feasibility of using TCS as similar materials to soft rock in model tests was explored based on the principle of similar mechanical properties of hard soil and soft rock. Subscripts P and M separately represent the prototype and model, and η   denotes the similarity ratio of physical quantities between the prototype and the model. The conditions for TCS as similar material to soft rock must satisfy the requirements delineated below.

Ignoring the self-weight of a rock mass, the main physical similarity constants of TCS are as follows: η σ = σ P σ M (5) η E = E P E M (6) η ε = ε P ε M (7) where, σ , ε , and E   denote the stress, strain, and Young’s modulus, respectively; η σ , η ε , and η E   separately represent the similarity constants of stress, strain, and Young’s modulus.

Based on the requirement that the stress–strain relationships in the prototype and the model should be expressed by the same equation, the following formulae are derived: E P = σ P ε P (8) E M = σ M ε M (9)

By substituting Formulae 5–7 into Formula 8, Formula 8 can be rewritten as follows: η E E M = η σ σ M η ε ε M (10)

If Formulae 9, 10 are equal, the similarity index is: η E = η σ η ε (11) and as ε   is dimensionless and the similarity constant of strain is η ε = 1, then η E = η σ (12)

The similarity constant of stress can be selected at will without considering the self-weight.

When considering the self-weight of both rock and soil, the similarity constants of the materials should include η γ = γ P γ M (13) where, γ   and η γ   represent the bulk density and its similarity constant, respectively.

Based on principles of elastic mechanics and similarity, the similarity index can be calculated as follows: η σ η L = constant (14) η σ η L η γ = 1 (15) where, η L   represents the similarity constant of size (length) and η L = L P / L M ( L P and L M separately indicate the sizes of the prototype and the model). Meanwhile, Formula 12 should be satisfied.

In similarity model tests, besides that Formulae 12, 14, and 15 governing the main similarity constants should be satisfied, the requirement for a similar strength should also be met. The strength of TCS is expressed as the Mohr–Coulomb shear strength and its parameters include the cohesion and angle of internal friction. The shear strength is consistent with the dimension of stress. When selecting the strength index of simulated materials, it can be converted according to the following formulae: c M = c P η L η γ (16) η c = c P c M = η L η γ (17) where, c P and c M   denote the apparent cohesions of the prototype and the model, respectively.

The angle of internal friction φ   is dimensionless, so the similarity index should satisfy: η φ = φ P φ M = 1 (18) where, η φ represents the similarity constant of the angle of internal friction; and φ P and φ M   represent the angles of internal friction of the prototype and the model, respectively.

In conclusion, in the similarity model tests of TCS, the similarity index must satisfy: η E = η σ = η c η σ = η L η γ η φ = 1 } (19)

In accordance with Formula 19, if the geometric similarity constant is 100, the geotechnical parameters of the prototype materials corresponding to TCS materials can be obtained (Table 2) from where it can be seen that TCS is applicable as a similar material to soft rock, such as dolomite (Liu et al., 2021), marl (Ferrero and Migliazza, 2009), shale (Geng et al., 2016), siltstone (Su et al., 2007), or claystone (Hu et al., 2014).

TCS is usually required to reach a fully saturated state to realize their high transparency in physical model tests, therefore, measuring the mechanical properties of saturated TCS is the premise to the development of physical model tests using TCS (Iskander et al., 2015; Ganiyu et al., 2016). When measuring the shear strength parameters of saturated soil specimens, consolidated undrained (CU) or consolidated drained (CD) triaxial compression tests should be conducted; however, during the consolidation or drainage of saturated TCS specimens, the pore fluid (mixed mineral oil) drained from the specimens will corrode rubber products (such as the latex membrane and rubber O-ring seals), resulting in a failure of the test and even instrument damage. Therefore, CU or CD tests of TCS specimens with complete saturation were not performed in the study, but as an alternative, UU tests on specimens with a saturation ratio of about 80% were conducted. There is a certain difference in mechanical properties between TCS with saturation ratios of about 80 and 100% (the study of unsaturated silt clay (Kererat, 2019) with similar micro-structure to TCS shows that the difference is within 15% in terms of strength parameters), but this small difference does not affect the investigation of the mechanical characteristics such as strength, stiffness, and failure of TCS.

The cementation arising from use of silica powder is the key element that distinguishes TCS from transparent sand and work on the cementation mechanism is significant for further study of the mechanical behavior of TCS. Although Yang et al. (2020) used scanning electron microscopy to study the micro-structural characteristics of TCS and ascertained the changes in the cement and skeleton of TCS before and after compression, the cementation mechanism of silica powder remains unclear: The mechanism of action of silica powder in adsorbing mixed mineral oil warrants further study.