Development and Constitutive Model of Fluid–Solid Coupling Similar Materials

Abstract

The Cretaceous Zhidan group (K1zh) pore fissure-confined water aquifer in Yingpanhao Coal Mine, Ordos City, China, has loose stratum structure, high porosity, strong permeability and water conductivity. In order to explore the fluid–solid coupling similar material and its constitutive model suitable for the aquifer, a kind of fluid–solid coupling similar material with low strength, strong permeability and no disintegration in water was developed by using 5~20 mm stone as aggregate and P.O32.5 Portland cement as binder. The controllable range of uniaxial compressive strength is 0.394~0.528 MPa, and the controllable range of elastic modulus is 342.22~400.24 MPa. The stress–strain curve and elastic modulus of similar materials are analyzed. It is found that the elastic modulus of similar materials with different water–cement ratios conforms to the linear law, the elastic modulus of similar materials with the same water–cement ratio after soaking treatment and without soaking treatment also conforms to the linear law. Based on the material failure obeying the maximum principal stress criterion and Weibull distribution, combined with the elastic modulus fitting formula, a constitutive model suitable for the fluid–solid coupling similar material was established, and the parameters of the constitutive model were determined by differential method. By comparing the theoretical stress–strain curve with the experimental curve, it is found that the constitutive model can better describe and characterize the fluid–solid coupling similar materials with different water–cement ratios and before and after soaking.

1. Introduction

With the development of China’s national economy, more and more deep underground projects are carried out in water conservancy, hydropower, transportation, energy development and national defense engineering [1,2,3]. For example, the Xiaolangdi Yellow River Diversion Project, Central Yunnan Water Diversion Project and Changdian Hydropower Station Diversion Tunnel Project have a higher buried depth. In global terms, the excavation of tunnels and underground space in China are characterized by large scale, large quantity and complex geological conditions and structural forms. In order to meet the needs of infrastructure construction, there are also more and more tunnels with large burial depth and large span and special length, which are often located in areas with strong geological structure. Complex geological conditions in deep underground engineering often lead to collapse, roof fall, water inrush and other disasters, resulting in significant economic losses and casualties [4,5,6,7].

Experts and scholars from various countries have conducted a lot of research on the prevention and control of underground engineering disasters and have achieved fruitful research results. Aissa Bensmaine [8], using the numerical code FLAC, carried out several numerical simulations in axisymmetric groundwater flow conditions to analyze the seepage failure modes of cohesionless sandy soils within a cylindrical cofferdam. They also indicate the sensitivity of the seepage failure mode to internal soil friction, soil dilatancy, interface friction and cofferdam radius. Moreover, new terms are proposed for the seepage failure mode designations based on the 3D view of the downstream soil deformation. It provides a new idea for studying the seepage failure of soil in cofferdam. For Özcan Çakır [9], the field compilation of the resistivity data is assumed to be completed by the application of the multiple electrode pole–pole array. The actual resistivity assembled underneath the analyzed area is inverted by considering the apparent (measured) resistivity values. Unique forms such as ore body, cavity, sinkhole, melt, salt and fluid within the Earth may be examined by joint interpretation of electrical resistivities and seismic velocities. Dang Van Kien [10] produced a numerical analysis using finite element software conducted to investigate the stability of rock mass surrounding the underground cavern and the system of caverns. The whole stability of surrounding rock mass of underground caverns was evaluated by Rocscience-RS2 software. This provides a reliable way to analyze the stability of the caverns and the system of caverns and will also help in the design or optimization of subsequent support. Bo Li [11], according to historical water inflow observation data of typical coal mines, produced a mine inflow prediction model based on unbiased grey and Markov theory was established. This model can eliminate the inherent bias of the traditional model and the effects of the random fluctuation of data on prediction results and has higher computational accuracy. The relevant research results can provide some basis for the improvement of the mine inflow method. Bo Li [12], according to the hydrogeological characteristics of southwest mines in China, produced twelve evaluation indicators determined from the three aspects of aquifer, aquifuge and geological structure, and an evaluation index system of water inrush risk of the karst aquifer in the coal floor has been constructed. On this basis, further using GIS technology and entropy weight theory, a multi-source information evaluation method for the risk of water inrush from the coal floor was proposed, and the evaluation results were verified.

At present, there are three main methods for stability analysis and disaster prevention of underground engineering: theoretical analysis, numerical simulation and model test. However, the complexity of the physical and mechanical properties of underground rock mass makes it difficult to deal with nonlinear problems in theoretical analysis, and it is difficult to simulate the real process of underground disasters by numerical simulation. Therefore, the results obtained by these two methods usually cannot accurately reflect the situation of diagenetic geological bodies in actual engineering conditions. However, the fluid–solid coupling simulation test can qualitatively or quantitatively reflect the complex construction technology, load action mode and time effect in practical engineering, and can also control the whole process from elasticity to plasticity of engineering stress and finally to the failure mode after the ultimate load. The key factor for the success of the fluid–solid coupling simulation test is to select a reasonable and reliable fluid–solid coupling similar material. The aquifer fluid–solid coupling similar material applied to the fluid–solid coupling simulation test needs to meet the following conditions: strong water permeability; the degree of shrinkage and expansion of the material after meeting water must be small; the material needs to have low strength so as not to soften and disintegrate after encountering water to maintain high integrity. As the basis of fluid–solid coupling simulation tests, the development of similar materials has experienced a tortuous and long development process. In the mid-1960s, Barton studied and manufactured a similar model material of raw material mixture composed of gypsum, red dan sand, coarse aggregate and water; this similar material has one characteristic: low elastic modulus. Jacoby [13] used glycerol and other materials as similar materials for model tests to study the problem of mantle convection and concluded that the upper lithospheric plate highly organized large-scale circulation, while the lower lithospheric plate became unstable at the core-mantle boundary. Ren Mingyang [14] developed a new similar material reflecting the fluid–solid coupling effect with iron powder, barite powder and quartz sand as aggregates, white cement as the cementing agent and silicone oil as the regulator. Zhang Ning [15] made a new similar material by mixing cement, sand, rubber powder, water, water reducer, early strength antifreeze and waterproofing agent, The compressive strength of this material is 15~50 MPa, and the elastic modulus is 2~4.5 Gpa. Zhang Jie [16] solved the problem of solid–liquid two-phase model material collapse in water by using paraffin as cementing agent in the study of fluid–solid coupling similar material. Li Shucai [17] developed similar materials (SCVO), which greatly improved the simulation of similar tests. In order to carry out the model test of the formation of high water pressure floor water inrush channel in deep mining. Sun Wenbin [18] developed similar materials suitable for deep well conditions. Li Shuchen [19] used paraffin wax as a cementing agent to develop a fluid–solid coupling similar material used in tunnel water inrush model test. Chen Juntao [20] developed a fluid–solid coupling similar material for the deep water resisting layer, realizing the similar simulation of the deep floor water resisting layer. Han Tao [21] developed a similar material to simulate porous rock mass and successfully applied it to the coupled model test of porous rock mass and the borehole wall. Dai Shuhong [22] used the orthogonal test design method to study fluid–solid coupling similar materials that can meet the similar physical and mechanical properties and similar water physical properties with talcum powder, gypsum and liquid paraffin as raw materials. Li Zheng [23] used clay, fine sand and glass fiber as raw materials to develop similar materials for surrounding rock, and used cement and carbon slag to prepare materials similar to the grouting environment, using multi-layer woven geotextiles to simulate a lining. Similar materials were successfully applied to tunnel seepage model tests. Wu Baoyang [24] taking quartz sand, barite powder and talc powder as aggregates, C325 white cement as the binder and silicone oil as the regulator, has developed a new type of fluid–solid coupling similar material with low strength, adjustable water absorption, non-disintegration in water and simple production. The feasibility and applicability of the material were verified by the model test of an underground reservoir in a multi coal seam mining coal mine.

In general, the research on fluid–solid coupling similar materials has made a certain degree of progress, but most of the fluid–solid coupling similar materials are mainly based on the study of aquifuge materials, the research on similar materials of aquifers is still lacking and most of the research work on similar materials pays more attention to solving the problem of easy disintegration of materials in water and lacks research on material constitutive models and failure modes. Therefore, it is urgent to carry out the research on fluid–solid coupling similar materials, as well as the research on their mechanical properties, constitutive models, failure modes and properties after water encounter.

2. Development of Fluid–Solid Coupling Similar Materials

2.1. Raw Material Selection

Before determining the raw materials, in order to reduce the workload, based on the principle of material selection, pre-experiment, a preliminary study was carried out to determine the raw materials of similar materials according to the function of the expected material and the physical and mechanical according to the function of the expected material and the physical and mechanical indices.

(1) Aggregate

As the main raw material of similar materials, aggregate plays a skeleton and supporting role in similar materials. If no aggregate is added during the production of the specimen, the specimen will not be formed. Aggregates are usually divided into coarse aggregates and fine aggregates. Coarse aggregates refer to materials with a diameter greater than 5 mm—generally gravel and pebbles. Fine aggregate refers to the material with a diameter of 0.165 mm, such as river sand, ore sand, sea sand, valley sand and quartz sand. The selection of aggregate by domestic scholars is also roughly within the above range. According to the selection principle of similar materials, it is required that the water content is stable, the texture is hard and clean and the grade is reasonable. Based on the above selection principle of similar materials, the aggregate selected in this paper is stone with a particle size of 5~20 mm.

(2) Cementing materials

Cementing material refers to the material with a certain strength that changes its own properties after physical and chemical action and can be closely bonded with other materials. Cement, gypsum, lime, clay, paraffin, rosin, epoxy resin, polyamide, and asphalt and commonly used cementing materials. In the study of fluid–solid coupling similar materials, the cementing materials used by domestic scholars usually include rosin, cement, clay, paraffin, cement, stone blue, latex, etc. In this paper, with reference to the cementing materials used in the physical model tests carried out in the past, and considering the advantages and disadvantages of each cementing agent, P.O32.5 Portland cement was finally selected. On the one hand, considering that the cementing strength of cement is between weak cementing materials such as gypsum and strong cementing materials such as cement, it can better adjust the strength of similar materials; on the other hand, compared with rosin and latex, cement is easy to use and less affected by temperature.

(3) Water

When preparing most similar materials, it is necessary to mix similar materials with water. The role of water in the preparation of similar materials mainly has two aspects. On the one hand, many cementing materials need water (i.e., hydration) when setting and hardening; on the other hand, when preparing similar materials and making similar material models, water must be used to meet the requirements of the production process. The similar materials developed in this paper choose water immersion to verify the performance of similar materials after encountering water.

2.2. Determination of Water–Cement Ratio

Based on the similarity principle, the strength of similar material is about 0.39~0.53 MPa. Through the strength test of different water–cement ratios, the strength of the material with a water–cement ratio of 0.9:1 is about 0.528 MPa. The test shows that the strength of the material is about 0.50 MPa when the water–cement ratio is 1.0:1, the strength of the material is about 0.46 MPa when the water–cement ratio is 1.1:1 and the material with a water–cement ratio of 1.2:1 is about 0.394 MPa. Therefore, it is finally determined to make specimens in the range of water–cement ratio 0.9:1~1.2:1, and measure the mechanical properties of different specimens.

2.3. Formulation of Similar Materials

In order to test the performance of similar materials with different ratios, six specimens were made in each ratio in the range of water–cement ratio of 0.9:1~1.2:1, and three specimens were in one group. The two groups of specimens were cured at room temperature standard curing conditions for 28 days. One group was directly tested for strength after curing, and the other group was soaked in water for 3~4 days and then tested for strength to test the performance of the specimen under water conditions. The size of the specimen was 150 mm × 150 mm × 150 mm. The test specimens were made as follows.

(1) Prepare a specific mold according to the design requirements, brush the mold with release agent and wait for the release agent to dry;

(2) Aggregate screening;

(3) The water and cement are weighed according to the design ratio, and the weighed water and cement are fully stirred for 5~10 min to make cement slurry;

(4) The sieved aggregate is poured into a uniformly stirred cement slurry and stirred for 5~10 min to ensure that the aggregate surface is uniformly hung with slurry;

(5) Put the stirred material into the mold;

(6) After standing for 48 h, the demolding was carried out, the label was affixed and the standard curing condition was maintained for 28 d.

The preparation process of similar materials is shown in Figure 1.

3. Mechanical Properties Test and Analysis of Similar Materials

The uniaxial compression test of fluid–solid coupling similar materials was carried out on the RMT-150B rock mechanics test system. The axial load was used as the control index to load. The two groups of specimens were loaded until failure. The loading speed was 0.01 kN/s, and the stress–strain curve was recorded.

3.1. Mechanical Property Test of Specimens Not Soaked in Water

Uniaxial compression test is carried out on the test piece not soaked in water, and the stress–strain curve is obtained as shown in Figure 2:

It can be seen from Figure 2 that the uniaxial compressive strength of the intact specimen without water immersion is 0.394~0.528 MPa, and the elastic modulus is 342.22~400.24 MPa. The elastic modulus is relatively stable when it does not reach the peak. The stress–strain trend of similar materials before the peak is approximately linear, indicating that the overall material is dominated by elastic deformation. After the peak, the stress–strain curve of similar materials begins to show more obvious plastic characteristics, indicating that there are new cracks inside the material. Under the action of uniaxial compressive stress, the evolution trend of the axial stress–strain curve of the specimen is similar, which is different from the compression curve of conventional rock materials. The fluid–solid coupling similar material used in this test is mainly elastic deformation before failure, so the stress–strain curve before the peak value shows an approximate linear evolution trend. After the stress passes the end of the elastic stage, it enters the post-peak failure stage. At this stage, the stress gradually decreases with the increase of strain, and there is an obvious nonlinear evolution trend. With the increase of water cement ratio, the peak strength of similar materials and the elastic modulus decrease gradually.

3.2. Mechanical Property Test of Specimens Soaked in Water

The uniaxial compression test is carried out on the specimens soaked in water, and the stress–strain curve is shown in Figure 3:

It can be seen from Figure 3 that the uniaxial compressive strength of the complete specimen after water immersion is 0.370~0.482 MPa, and the elastic modulus is 317.10~360.22 MPa. Compared with the material without water immersion, the peak strength and elastic deformation of the material after water immersion decrease to a certain extent, but the peak strain increases to a certain extent. Combined with previous studies on water chemistry [25,26], the material shows strain softening after water chemical erosion, and the failure mode changes from splitting to shear failure. In addition, after the rock material undergoes hydrochemical action, the particle skeleton reacts with the chemical composition to increase the internal pores. Therefore, under the same load, the displacement of the material soaked in water is larger than that of the material without soaking in water, the peak strain increases and the strength decreases.

3.3. The Peak Stress and Strain Evolution Law of Similar Materials with Different Water Cement Ratio

The evolution law of peak stress and strain of specimens with different water–cement ratios is analyzed. The peak stress and strain of specimens after immersion and those without immersion are shown in Figure 4.

It can be seen from Figure 4 that the peak stress and strain of similar materials gradually decreases with the increase of water–cement ratio. In the same water–cement ratio specimen, the peak stress of the similar material soaked in water is significantly lower than that of the similar material not soaked in water, but the peak strain is slightly higher than that of the similar material not soaked in water. This is due to the chemical action of water, which leads to the reaction of the particle skeleton of the similar material with the chemical composition to increase the internal pores, so that the peak strain of the similar material soaked in water increases.

3.4. Evolution Law of Elastic Modulus of Similar Materials

In order to find the elastic modulus evolution law of similar materials with different water–cement ratios and similar materials before and after immersion, the elastic modulus of similar materials was studied. Figure 5a shows the evolution of the elastic modulus of similar materials with different water–cement ratios. Figure 5b shows the evolution of the elastic modulus of similar materials after soaking treatment and materials without soaking treatment. The results show that the elastic modulus is linear with the water–cement ratio and inversely proportional to the water–cement ratio. By analyzing the elastic modulus of fluid–solid coupling similar materials before and after soaking, it is found that the elastic modulus of the specimen after soaking is linearly related to the elastic modulus of the specimen without soaking.

By fitting the elastic modulus of similar materials with different water–cement ratios and before and after immersion, it is found that it conforms to the linear law, and an empirical formula for fluid–solid coupling similar materials is obtained.

$$E=-193.098\mu +573.7044$$

(1)

In the formula, E is the elastic modulus of fluid–solid coupling similar materials with different water–cement ratios, and μ is the water–cement ratio.

$$E_W=0.74609E+63.58443$$

(2)

In the formula, E_W is the elastic modulus of fluid–solid coupling similar materials after immersion.

4. Constitutive Model

The stress–strain curves of fluid–solid coupling similar materials, especially the curves after the peak, are mainly nonlinear evolution characteristics, which cannot be accurately described and characterized by traditional elastoplastic models. The accurate description of stress–strain curve is of positive significance for understanding the stress evolution law of aquifer in similar model tests of fluid–solid coupling material and for further exploring the stress distribution of aquifer in practical engineering. Therefore, it is necessary to study the constitutive model of fluid–solid coupling similar material.

4.1. Weibull Distribution Damage Constitutive Model

In the mechanical analysis of materials, it is generally believed that there is a large amount of new crack initiation, crack propagation and old crack propagation in the plastic stage of the material; that is, the material has damage in the post-peak stage. In the equivalent strain hypothesis proposed by J. Lemaitre [27], it is shown that the effective stress is equal to the deformation of the damaged material, and the strain relationship of the damaged material can be expressed in the form of the non-destructive material. Replacing the nominal stress [σ] with the effective stress [σ*], the damage constitutive equation of the post-peak stage of the material can be obtained as follows:

$$\left[\sigma \right]=\left[\sigma \ast \right]\left(I-\left[D\right]\right)=\left[H\right]\left[\epsilon \right]\left(I-\left[D\right]\right).$$

(3)

In the formula, [σ] is the nominal stress, [σ*] is the effective stress, I is the unit matrix, [D] is the damage variable matrix, [H] is the elastic modulus matrix of similar materials, and [ε] is the strain matrix.

Assuming that the damage of similar material is isotropic, the one-dimensional damage constitutive relation of similar material can be expressed as:

$$\sigma ={\sigma }^{\ast }\left(1-D\right)=E\epsilon \left(1-D\right).$$

(4)

In the formula, D is the damage variable.

$$D=\frac{n}{N}.$$

(5)

In the formula, n is the number of destroyed elements, and N is the total number of elements of the lossless material.

According to the damage model method of Weibull distribution, the damage evolution law of material after peak load is explored. The probability density function is expressed as:

$$P\left(F\right)=\frac{m}{F_0}{\left(\frac{F}{F_0}\right)}^{m-1}\exp \left[-{\left(\frac{F}{F_0}\right)}^m\right].$$

(6)

In the formula, P(F) is the material element strength distribution function, F is the random distribution variable of element intensity, and m and F₀ are distribution parameters. The material damage variable can be defined as:

$$D={\displaystyle \int P\left(x\right)}dx.$$

(7)

Therefore, the damage variable can be expressed as:

$$D=1-\exp \left[-{\left(\frac{F}{F_0}\right)}^m\right].$$

(8)

Assuming that the micro-element strength obeys the maximum positive strain strength criterion, the damage variable can be expressed as:

$$D=1-\exp \left[-{\left(\frac{\epsilon }{{\epsilon }_0}\right)}^m\right].$$

(9)

In the formula, D is the material damage factor, and m and ε₀ are the parameters related to the physical and mechanical properties of materials.

The material damage constitutive model can be described as:

$$\sigma =E\epsilon \exp \left[-{\left(\frac{\epsilon }{{\epsilon }_0}\right)}^m\right].$$

(10)

4.2. Determination of Constitutive Parameters

Formula (10) can be transformed into:

$$\frac{\sigma }{E\epsilon }=\exp \left[-{\left(\frac{\epsilon }{{\epsilon }_0}\right)}^m\right].$$

(11)

By taking logarithms on both sides of formula (11), we can obtain:

$$\ln \left(\frac{E\epsilon }{\sigma }\right)={\left(\frac{\epsilon }{{\epsilon }_0}\right)}^m.$$

(12)

In this paper, the uniaxial compression stress–strain curve of the fluid–solid coupling similar material is approximately linear before the peak, and there is an extreme point in the strain curve before and after the peak; that is, the slope of the stress–strain curve at the peak is 0:

$$\frac{d{\sigma }_c}{d{\epsilon }_c}=0.$$

(13)

In the formula: ${\sigma }_c$ and ${\epsilon }_c$ represent peak stress and strain.

Substituting Formula (12) into Formula (13), we can get:

$$E\exp \left[-{\left(\frac{{\epsilon }_c}{{\epsilon }_0}\right)}^m\right]\left(1-m{\left(\frac{{\epsilon }_c}{{\epsilon }_0}\right)}^m\right)=0.$$

(14)

We arrange the formula (14) to obtain:

$${\left(\frac{{\epsilon }_c}{{\epsilon }_0}\right)}^m=\frac{1}{m}.$$

(15)

We arrange the formula (15) to obtain:

$$m=\frac{1}{\ln \left(\frac{E{\epsilon }_c}{{\sigma }_c}\right)}.$$

(16)

Substituting Formula (16) into Formula (15), we can get:

$${\epsilon }_0={\epsilon }_c{m}^{\frac{1}{m}}.$$

(17)

Substituting Formulae (16) and (17) into Formula (10), we can get:

$$\sigma =E\epsilon \exp \left[-{\left(\frac{\epsilon }{{\epsilon }_c{m}^{\frac{1}{m}}}\right)}^{\frac{1}{\ln \left(\frac{E{\epsilon }_c}{{\sigma }_c}\right)}}\right].$$

(18)

According to Formula (18) and (1), the constitutive model of fluid–solid coupling similar materials with different water cement ratio is:

$$\sigma =(-193.096\mu +573.7044)\epsilon \exp \left[-{\left(\frac{\epsilon }{{\epsilon }_c{m}^{\frac{1}{m}}}\right)}^{\frac{1}{\ln \left(\frac{\left(-193.098\mu +573.7044\right){\epsilon }_c}{{\sigma }_c}\right)}}\right].$$

(19)

According to Formulae (18) and (2), the constitutive model of fluid–solid coupling similar material after immersion is:

$$\sigma =(0.74609E+63.58443)\epsilon \exp \left[-{\left(\frac{\epsilon }{{\epsilon }_c{m}^{\frac{1}{m}}}\right)}^{\frac{1}{\ln \left(\frac{\left(0.74609E+63.58443\right){\epsilon }_c}{{\sigma }_c}\right)}}\right].$$

(20)

As shown in Figure 6, the stress–strain curve of similar materials with water–cement ratio of 1.1:1 is taken as an example to compare the experimental curve with the theoretical curve of the constitutive model. Taking Figure 6a as an example, in the stress stage of 0.155~0.355 MPa, the material deformation is elastic deformation, and the test curve is basically consistent with the theoretical curve. In the stage of stress 0.355~0.448 MPa, the test curve is slightly different from the theoretical curve, indicating that the material is not in complete elastic deformation before the peak, and there is a certain plastic deformation. After reaching the peak stress of 0.448 MPa, the material has obvious nonlinear deformation characteristics, and the experimental curve is approximately coincident with the theoretical curve. The results show that the constitutive model can better describe the stress–strain curve of fluid–solid coupling similar materials.

4.3. Failure form Analysis

Through the analysis of the model test results, it can qualitatively or quantitatively reflect the action mode and time effect of the load in the actual project and control the whole process of the elastic to plastic and the failure form after the ultimate load. Therefore, the study of the failure form of fluid–solid coupling similar materials is of positive significance for understanding the stress concentration and failure mechanism of aquifer in fluid–solid coupling model test.

Figure 7 and Figure 8 show the morphology of similar materials with different water–cement ratios after failure. It can be seen from the figure that the larger the water–cement ratio, the worse the integrity of the material after failure. The reason for this phenomenon is that the larger the water–cement ratio, the smaller the cohesion between the particles of the material, and the looser the structure after failure. It can be seen from the figure that the specimens after immersion are the same as those without immersion. With the increase of water–cement ratio, the number of damaged blocks gradually increases. Comparing the test data and failure modes of the two specimens, the compressive strength and elastic modulus of the specimens after immersion were lower than those of the specimens without immersion. The structure of the specimens after immersion was looser than that of the specimens without immersion. This is due to the strain softening of the material after chemical erosion, and the failure mode is transformed from splitting to shear failure. In addition, after the rock material undergoes hydrochemical action, the particle skeleton reacts with the chemical composition to increase the internal pores.

4.4. Damage Analysis

It can be seen from Figure 9 that with the increase of strain, the damage–strain curves of similar materials show a nonlinear evolution trend. When the strain is equal, the greater the water cement ratio, the greater the damage. When the peak strain is reached, the damage occurs, and the damage growth rate is fast. With the increase of strain, the damage growth rate decreases and gradually becomes stable. When the material is close to failure, the damage growth rate of the material decreases again.

It can be seen from Figure 10 that with the increase of stress, the damage–stress curves of similar materials have nonlinear characteristics. When the stress is equal, the greater the water–cement ratio, the smaller the damage. The stress after the peak value of the material decreases with the increase of the damage. At the initial stage of the damage, the damage increases approximately linearly, and the growth rate is large. With the decrease of the stress, the damage growth rate also decreases, and gradually tends to be stable.

5. Conclusions

(1) A fluid–solid coupling similar material suitable for simulating the aquifer with loose formation structure, high porosity, strong permeability and water conductivity has been developed. The material has low strength, strong water permeability, and does not disintegrate when it meets water. The raw material is easy to obtain, and the production process is simple, which enriches the research means for aquifers with loose structure and strong water permeability.

(2) The peak stress and strain of similar materials gradually decrease with the increase of water–cement ratio; the elastic moduli of similar materials with different water–cement ratios follow the linear law, and the elastic moduli of similar materials before and after immersion also follow the linear law. Among the similar materials with the same water–cement ratio, the peak stress of the similar materials after immersion is significantly lower than that of the similar materials without immersion, but the peak strain is slightly higher.

(3) Based on Weibull distribution, the constitutive model of fluid–solid coupling similar material is established. The parameters of the constitutive model are further determined by the differential method. The constitutive model of fluid–solid coupling similar material is established by using the elastic modulus of similar material with a different water–cement ratio before and after immersion. Using Weibull distribution damage variable analysis, it is found that when the strain of fluid–solid coupling material is equal, the greater the water–cement ratio, the greater the damage caused by the material, and when the stress is equal, the greater the water–cement ratio, the smaller the damage caused by the material.

Although the constitutive model is obtained from the elastic modulus of fluid–solid coupling similar materials after immersion in water, there are still some deficiencies in the study of water rationality of similar materials, In this paper, the performance of similar materials is tested by immersing them in water, which verifies that they do not disintegrate when they meet water, but no specific permeability coefficient is given. In the next stage of research, we should focus on the water rationality of materials.