1. Introduction
With the rapid development of national economic construction, basic projects such as water conservancy and hydropower, transportation, and energy mines have gradually developed [
1]. In the process of development, each project also gradually encountered some complex engineering geological problems (hydraulic–dynamic coupling problems) [
2]. For example, traffic construction has gradually shifted from plain areas to mountainous, hilly, and coastal areas [
3]. Tunnels in mountainous areas often face complex geological structures, frequent earthquakes, and concentrated heavy rainfall phenomena [
4,
5] which are prone to problems such as water inrush and landslides. With the development and utilization of marine resources, problems such as hydraulic change [
6], wave shock [
7], and plate vibration [
8] are often encountered in the process of ocean construction. Water conservancy and hydropower projects have often been affected by earthquakes and reservoir drainage since their construction [
9]. Coal mine projects are prone to water inrush, mud outbursts, and collapse accidents in water-rich areas [
10]. With the development of energy cleanliness, underground reservoirs are gradually built in coal mines in arid areas which are highly sensitive to mine earthquakes and water action [
11].
Figure 1 shows some of the disasters caused by hydraulic–dynamic coupling in various fields.
In summary, an increasing number of engineering projects are facing the problem of multi-field coupling. Some scholars have used fiber concrete to improve the properties of engineering materials [
12,
13]. Some scholars also use low-strength materials as backfill or high-strength materials in coal mines [
14,
15,
16]. However, the study of the above materials is considered from the perspective of protection and reinforcement and has no reference significance for the stability analysis and instability mechanism under hydraulic and dynamic action. At present, theoretical analysis [
7], numerical simulation [
17], and physical model tests [
18] have become the main research methods to study the above problems, aiming at engineering problems such as the disaster evolution process, stability analysis, and prevention and control of complex rock mass under hydraulic–dynamic coupling. Nevertheless, the theoretical analysis requires many simplifications and assumptions of the prototype, which is not suitable for the study of complex geological problems. The study of the damage evolution mechanism by numerical simulation is limited and verification by model tests and field tests is lacking [
9]. Additionally, the physical model test has become an important method to study the disaster mechanism of engineering rock masses under complex conditions because it can truly restore the failure evolution process and instability mode of complex rock masses [
18]. In particular, accurately obtaining the similarity between similar materials and real rock mass materials becomes the key to accurately reflecting the failure process of rock mass model tests [
19]. This work intends to use physical model tests to study engineering problems under hydraulic–dynamic action so research on new similar materials is an important basic work at present.
Meanwhile, many scholars have carried out relevant research on similar materials of rock mass physical modes. Some scholars have used MLPS or gypsum to study the anchorage characteristics and crack propagation of rock-like materials [
20,
21] but the above studies are based on certain materials in specific engineering studies rather than a class of similar materials with a wide range of changes.
In consideration of the parameter range and characteristics of similar materials, Li et al. [
22,
23] developed a series of new fluid–structure coupling materials such as SCVO and PSTO based on the fluid–structure coupling similarity theory of continuous media. Shen et al. [
6] developed a similar material suitable for sand formation conditions in deep-sea environments by using standard sand, petroleum jelly, and other materials. Zhang et al. [
19] derived similar criteria for fluid–solid coupling under high osmotic pressure and high ground stress and developed a new fluid–solid coupling material with white cement, silicone oil, and other materials. However, the above similar materials are prepared with paraffin, silicone oil, petroleum jelly, and other oily liquids, so it is difficult to avoid the use of alcohol lamps for heating and melting treatment which can easily cause danger. Furthermore, Xu et al. [
24] successfully developed similar materials suitable for simulating the development and evolution of tunnel lining cracks by using gypsum, quartz sand, diatomite, and fly ash. Wang et al. [
25], based on the Xianglushan tunnel, developed similar materials that could simulate the failure modes of concrete and rock masses. But Xu and Wang’s paper only discussed the failure mode of similar materials and the instability state of tunnel lining and did not consider the hydraulic and dynamic characteristics of similar materials. Additionally, some scholars have developed a series of similar materials suitable for fluid–structure coupling models using conventional materials such as quartz sand, cement, gypsum, and barite powder and successfully applied them to the simulation of cretaceous sandstone aquifer [
26], red layer soft rock simulation [
27], karst landform, and other physical model tests [
28]. However, the above model tests only consider the permeability coefficient and the conventional physical and mechanical parameters. In terms of the dynamics of similar materials, Li et al. [
29] and Tian et al. [
30] conducted dynamic and static tests on rock samples composed of quartz sand, cement, and other materials but failed to deeply explore the hydrodynamic characteristics and the evolution law of dynamic parameters. At the same time, Cao et al. [
18] and Yang et al. [
31] designed and completed the shaking table model of slopes with weak interlayers under the action of rainfall. However, in the whole test process, only the saturation of the interlayer material was considered and the softening characteristics of the interlayer material in water and the change law of the dynamic parameters were ignored. Thus, there would be certain difficulties in the theoretical analysis in the later stage [
32].
In summary, previous studies on similar materials have mainly focused on the physical and mechanical properties of materials under the influence of single factors such as seepage, dynamics, and failure phenomena. However, with the widespread occurrence of multi-field coupling phenomena such as hydraulic and dynamic fields, only studying the material properties of a single factor cannot meet the physical model test. Thus, it can be noted that the development of a new type of similar material that considers both hydraulic and dynamic properties is an urgent problem for the physical model test under multi-field coupling. Considering that traditional research on similar materials does not include both hydraulic and dynamic parameters, this work aims to obtain new similar materials. First, based on the dimensional analysis method and Buckingham π theorem, the similarity relationship of physical model tests under percolation–dynamic coupling is derived. Then, through an orthogonal test, with quartz sand and barite powder as aggregates, cement and sodium silicate as cementing materials, and rosin and glycerine as modulators, similar materials considering of both hydraulic and dynamic properties were developed. The sensitivity analysis and statistical analysis of the physical parameters and failure modes of specimens with different proportions were carried out. Finally, the fitting formulas of different parameters are obtained based on multiple regression analysis, which can provide a reliable basis for physical simulation tests of slopes or tunnels under the action of hydraulic and dynamic coupling.
2. Similarity Theory and Similarity Relation
According to the requirements of similarity theory, the coupling model test of statics, percolation, and dynamic field should satisfy the similarity of geometrical dimensions, mechanical properties, force conditions, hydraulic properties, and dynamic parameters. According to dimensional analysis, for any physical system, if it contains n physical quantities and k fundamental dimensions, the remaining (n-k) physical quantities can be expressed in fundamental dimensions [
25,
33].
The main physical quantities involved in the static percolation–dynamic field coupling model include the density ρ, geometric dimension L, elastic modulus E, Poisson’s ratio μ, cohesion force c, internal friction angle φ, stress σ, strain ε, time t, frequency ω, displacement x, velocity v, acceleration a, gravitational acceleration g, damping ratio λ, dynamic elastic modulus Ed, dynamic Poisson’s ratio μd, external force F, permeability coefficient k, and softening coefficient η for a total of 20 parameters. Meanwhile, the Poisson’s ratio, internal friction angle, strain, damping ratio, dynamic Poisson’s ratio, and softening coefficient are dimensionless parameters, that is Cμ, Cφ, Cε, Cλ, Cμd, and Cη are all 1. The experiment adopts an absolute dimension system with density ρ, geometric dimension L, and acceleration a as the basic dimensions. Then, the π function is
According to the method of dimensional analysis and Buckingham’s π theorem, the general form of all physical parameters constituting the dimensionless π number is
Substituting the dimensions of E, c, σ, t, ω, x, v, g, Ed, F, and k into Equation (2) yields
From the principle of dimensional consistency, similar invariants can be obtained by solving Equation (3):
In the derivation process, ρ, L, and a are determined as the basic dimensions and the similarity relationship of the remaining physical quantities is shown in
Table 1.
In addition, because the percolation–dynamic coupling model is located in the gravitational field, Cg = Ca = 1; thus, the similar invariants of permeability coefficients derived from the dimensional analysis method and Buckingham π theorem are consistent with the similar criteria derived from the fluid–structure coupling model with uniform continuous media.
5. Damage Pattern Analysis of Similar Materials
To ensure that specimens made of similar materials and natural rocks have similar failure characteristics under loading, the failure forms and characteristics of specimens with different proportions under uniaxial compression are statistically analyzed. The failure patterns of 25 groups of tests are shown in
Figure 16. The statistics of the failure patterns of the samples in each group are shown in
Table 6.
As shown in
Figure 16 and
Table 6, there are 10 groups of tensile and splitting failure, 8 groups of conical failure, 5 groups of oblique shear failure, and 2 groups of composite failure modes. These phenomena show that different material ratios can simulate different types of failure modes.
Meanwhile, the reasons for the above phenomena are as follows: under ideal conditions, the test specimen is in a one-dimensional compression state under vertical pressure, that is, under vertical pressure and transverse expansion. Since the tensile strength of the brittle material is far less than the compressive strength, the test specimen will undergo tensile splitting failure. In the actual test, the test specimen produces a conical fracture surface due to the friction between the end and the pressure plate and the fracture surface splits the remaining part under the action of pressure, that is, the test specimen has conical failure. Therefore, 18 specimens exhibit tensile splitting and conical failure, accounting for 72% of the 25 similar materials with different proportions. Furthermore, when the end of the test block has local tensile shear cracks and the cracks extend into the main shear fracture plane, the test block will experience inclined shear failure, which is relatively rare. In the course of the test, the compound failure form may be due to the existence of more sodium silicate or glycerin in the specimen itself, which makes it exhibit a certain dilatancy effect.
6. Discussions
Previous studies have generally focused on the impact of a single factor, such as dynamic (earthquake, blasting, etc.) or hydraulic (rainfall, groundwater level, etc.) factors, on engineering projects; the similar materials developed thus mainly consider the impact of a single factor. However, as more and more engineering construction projects begin to face the problem of multi-field coupling such as pertaining to hydraulic and dynamic parameters, it is urgent to develop new similar materials that consider hydraulic and dynamic properties. In view of this, this paper designed the relevant experiment. Compared with previous studies, this experiment not only considered the hydraulic characteristics of the material but also studied the multi-field physical and mechanical parameters of the material.
According to the similarity relation formula in
Section 2, the similarity relation of major physical parameters of similar materials is derived based on the dimensionless criterion and the Buckingham π theorem (
Table 1). The formula can provide a basis for the calculation of physical model materials under hydraulic–dynamic coupling. The formula is consistent with the permeability coefficient similarity relationship derived by Zhang et al. based on the fluid–structure coupling equation. Based on the orthogonal test, a test scheme of six factors and five levels was designed. A new type of similar material with quartz sand and barite powder as aggregates, cement and sodium silicate powder as cementing materials, and rosin and glycerin as modulating agents was developed. The hydrodynamic properties, dynamic properties, and basic physical parameters of the material were fully studied. The developed similar materials have a wide range of parameters, with densities ranging from 1.597 to 2.261 g/cm
3. The compressive strength is 121.8~1771.5 kPa; the elastic modulus 4.63~100.65 MPa; the cohesion is 20.95~358.85 kPa; the internal friction angle is 9.21~49.55°; the softening coefficient is 0.22~0.98; the permeability coefficient is 1.07 × 10
−9~4.28 × 10
−6 m/s; the dynamic elastic modulus is 2.56~9.36 GPa; and the dynamic Poisson’s ratio ranges from 0.195 to 0.271. The sensitivity of the physical parameters of similar materials was analyzed by range analysis. The results show that the main parameters affecting the compressive strength, elastic modulus, and cohesion of similar materials are the content of barite powder. The main parameter affecting density and the dynamic Poisson ratio was the cement content. The rosin content has a certain influence on the internal friction angle and dynamic elastic modulus of similar materials. The particle size of quartz sand mainly affects the softening coefficient of similar materials. The change in the permeability coefficient is mainly controlled by cement and sodium silicate.
All these results show that the newly developed similar materials can satisfy the physical model tests under the action of hydrodynamic coupling. For example, the surrounding rock and lining structures can be constructed with similar materials of different proportions to study the dynamic response characteristics of the water-rich tunnel. Slope rock masses with cracks can be constructed by laying blocks with similar materials in advance and the infiltration characteristics of slopes under the action of rainfall can be studied. In the field of coal mining or backfill, the instability of underground reservoirs or the failure phenomenon under the coupling action of reservoir water and mine earthquakes can be simulated. In addition, although this study has conducted relevant research on the hydraulic and dynamic characteristics of new similar materials, there are still shortcomings in the coupling analysis of materials. In the later stage, the mechanical properties of similar materials under different water contents can be explored so as to obtain the physical and mechanical properties under different water contents, laying the foundation for the theoretical calculation of the later physical model.