Effects of Earth–Rock Dam Heterogeneity on Seismic Wavefield Characteristics

Abstract

Earth–rock dams are typical soil–rock mixtures with high heterogeneity. Mastering the effect of dam heterogeneity on seismic wavefields is the premise of accurately detecting hidden risks in dams. In this paper, based on the soil–rock mixture characteristics of actual dams, a soil–rock mixture model that can reflect the heterogeneity of dams is established through local segmentation and reassignment of random disturbances. The influence of local area size on model heterogeneity is described. The seismic wavefield in a soil–rock mixture dam is numerically simulated through a staggered-grid finite-difference algorithm with second-order accuracy in time and sixth-order accuracy in space. Then, the effect of dam heterogeneity on effective wavefields is analyzed. The results show that the heterogeneity of the earth–rock dam can lead to scattered waves in the seismic wavefield, and the scattered waves are mainly generated by Rayleigh surface waves. In the seismic record, scattered waves with strong energy appear in the region below the surface waves. The scattered wave energy is weak and close to that in the homogeneous media in the region above the surface waves. As the rock content in the dam increases, the scattering of seismic wavefields and the energy of scattered waves weaken gradually. The scattered waves generated by the heterogeneity of the dam significantly impact the reflected longitudinal wave and converted wave but, affect the reflected shear wave less. The numerical simulation results are consistent with the acquired seismic wavefield from the field test, proving the effectiveness of the numerical simulation for the seismic wavefield propagation characteristics of the earth–rock dam.

1. Introduction

Earth–rock dams are one of the most widely used types in hydraulic engineering. Their safety is essential for the regular operation of various water conservancy projects. However, after decades of operation, many dams suffer from potential safety hazards such as leakage and low-speed loose layers due to low early design standards, backward construction techniques, and the lack of effective management and maintenance during operation [1,2]. If these risks are not detected and addressed in time, they will seriously affect the safety of dams [3,4,5,6]. As a fast and non-destructive geophysical detection method, the seismic wave method can be used to collect data with rich geological information to accurately reflect the geotechnical parameters of strata. Therefore, this method can be applied to effectively detect hidden risks in earth–rock dams [7,8]. Mastering the kinematic and dynamic characteristics of seismic wave propagation inside earth–rock dams is a prerequisite for accurately detecting hidden risks in dams. In recent years, many scholars have studied the characteristics of seismic wave propagation inside earth–rock dams through theoretical analysis and field tests [9,10,11].

Earth–rock dams, mainly composed of soil and rock and filled by throwing and rolling, have high heterogeneity. However, most scholars have approximated them as homogeneous media when studying their seismic wavefield characteristics. The effect of medium heterogeneity on the wavefield is not considered. When seismic waves propagate in inhomogeneous media, scattered waves with strong energy are generated. The superposition of the scattered wave and the effective wavefield can significantly impact the detection results of hidden risks. Therefore, earth–rock dams cannot be regarded as homogeneous media. Based on the theory of random media, many scholars have studied the propagation characteristics of seismic wavefields in heterogeneous media by establishing a random medium model [12,13,14,15]. Li et al. [16] pointed out that the heterogeneity of random media increases with the increasing autocorrelation length. Liu et al. [17] proposed that higher heterogeneity of random media indicated greater scattering attenuation. Lei et al. [18] investigated the relationship between the normalized scale parameter and the scattered seismic wavefield. However, the above scholars failed to consider the influence of Rayleigh surface waves on scattered wavefields. In the actual seismic detection, there are strong energy Rayleigh surface waves in the acquired seismic data due to the free boundary between the surface and the air. In the detection of hidden risks in earth–rock dams, surface waves are strong interference waves. They can cover the effective wavefield and reduce the signal-to-noise ratio of seismic data, posing difficulties to the processing and interpretation of seismic data. Therefore, the influence of surface waves cannot be ignored when studying the seismic wavefield characteristics of earth–rock dams.

The random medium model is established by adding random disturbance to the traditional geological model. The variation in physical parameters such as longitudinal wave velocity, shear wave velocity and density of the model is small, and the percentage of various media cannot be reflected. Earth–rock dams are mainly composed of multiphase media, such as soil and rock, and they are typical soil–rock mixtures. There are apparent differences in the physical parameters between soil and rock in the dam, causing a strong heterogeneity of the earth–rock dam in terms of physical properties [19,20]. In addition, there is a precise soil–rock ratio of earth–rock dams during filling, and the mechanical characteristics of the dam with different soil–rock ratios are also different [21]. Therefore, the conventional random media cannot accurately reflect the heterogeneity of earth–rock dams.

To realistically reflect the propagation characteristics of the seismic wavefield inside earth–rock dams, this paper proposes a soil–rock mixture modeling method that can reflect the heterogeneity of earth–rock dams based on the conventional random medium modeling methods. A staggered-grid finite-difference method is used to simulate the seismic wavefield of the soil–rock mixture dam model. The characteristics of the scattered wavefield inside the dam are analyzed, and the influence of dam heterogeneity on the effective wavefield is studied, which provides a theoretical basis to detect hidden risks in earth–rock dams by the seismic wave method.

2. Establishment and Characteristic Analysis of the Soil–Rock Mixture Model

2.1. Soil–Rock Mixture Modeling Method

Earth–rock dams are composed of a mixture of soil and rock, and the distribution of soil and rock inside the dam is discrete and random. Therefore, to accurately reflect the heterogeneity of the actual earth–rock dam, the established soil–rock mixture dam model should not only reflect the difference in soil–rock physical parameters, but should also meet the conditions of discrete and random distribution of soil and rock inside the dam. In this paper, an algorithm was used to obtain the second-order stationary random process during the conventional random medium modeling. Firstly, random disturbances with zero means and a specific variance were calculated. Then, the random disturbance was divided and sorted. Finally, the random disturbance was reassigned according to a certain soil–rock ratio to obtain the soil–rock random mixture dam model.

The random disturbance in statistical mathematics can be regarded as a random sequence. Since the random sequence cannot be Fourier transformed in theory, an autocorrelation function is needed to describe the Fourier transform of this random sequence. Thus, the mixed elliptic autocorrelation function φ(x, z) was used to cause the random disturbance and can be expressed as [22,23]:

$$\phi (x,z)=\exp \left[-{\left(\frac{x^2}{a^2}+\frac{z^2}{b^2}\right)}^{\frac{1}{1+r}}\right]$$

(1)

where x and z are horizontal and vertical coordinates, a and b are horizontal and vertical autocorrelation lengths to describe the homogeneous average scale in each direction, and r is the roughness factor.

The amplitude spectrum D(k_x, k_z) was obtained by Fourier transforming the mixed autocorrelation function φ(x, z), while the independent random field θ(k_x, k_z) with uniform distribution in the interval [0,2π) was generated by a random number generator. Then, the random power spectrum F(k_x, k_z) was calculated as:

$$\mathrm{F}(k_x,k_z)=\sqrt{\mathrm{D}(k_x,k_z)}·e^{i\theta (k_x,k_z)}$$

(2)

The random power spectrum F(k_x, k_z) was inverse Fourier transformed to obtain the random disturbance ψ(x, z), and the mean μ and variance d of ψ(x, z) were calculated. Then, the random disturbance was normalized and multiplied by the disturbance standard deviation ε to obtain a random disturbance model σ(x, z), which can be expressed as:

$$\sigma (x,z)=\frac{\epsilon }{d}\left[\psi (x,z)-\mu \right]$$

(3)

The random disturbance model σ(x, z) is segmented by a local area of R × R, where R denotes the number of grid points, to rank the model values of each grid node in the local area. Assuming that the percentages of soil and rock content in the dam are P_soil and P_rock, respectively, the model values in the top P_rock of the local area are replaced by the physical parameters of rock, such as longitudinal wave velocity, shear wave velocity, and density, and the remaining model values are replaced by the physical parameters of soil, as shown in Figure 1.

Since earth–rock dams are compacted during construction, the gaps in the dam are very small. Therefore, the proportion of air is not considered in the modeling, and the sum of P_soil and P_rock is one. If the proportion of air needs to be considered, the model values of local areas can also be replaced by the physical parameters of soil, rock, and air according to the above method. The local area of R × R is slid along the horizontal and vertical directions, and the entire random disturbance model is reassigned to obtain a soil–rock mixture media model that satisfies the percentage of soil and rock content in the dam. Figure 2 shows the process of soil–rock mixture media modeling.

2.2. Characteristic Analysis of the Soil–Rock Mixture Model

To verify the correctness of the soil–rock mixture modeling method, we built a soil–rock mixture model of longitudinal wave velocity according to the procedure in Figure 2, with the model grid size nx = nz = 100, grid spacing dx = dz = 0.5 cm, autocorrelation length a = b = 1, roughness factor r = 1, and random disturbance standard deviation ε = 10%. After the random disturbance calculation, a window of local size R = 5 was selected to segment the random disturbance. Then, the values of the random disturbance grid nodes were replaced by the longitudinal wave velocity of soil and rock according to the proportion of 80% soil and 20% rock.

Table 1. Physical parameters of earth–rock dam media.

Media Types	Longitudinal Wave Velocities Vp (m/s)	Shear Wave Velocities Vs (m/s)	Density ρ (kg/m3)
Soil	800.0	200.0	1700.0
Rock	2000.0	1150.0	2000.0

shows the soil and rock longitudinal wave velocities, and Figure 3a shows the established soil–rock mixture model.

In the soil–rock mixture model, soil and rock are randomly distributed in a ratio of 4:1. When seismic waves propagate in any direction in the model, they spend 20% of the time propagating in the rock and 80 % in the soil. Therefore, the background velocity of the seismic wave propagating in the soil–rock mixture model should be the weighted average of soil–rock wave velocities with a weighted ratio of 4:1, and the background velocity of the longitudinal wave in the soil–rock mixture model is 1040 m/s. Based on the background velocity, the random medium model with the same random characteristic parameters is shown in Figure 3b.

Figure 3 shows the significant random variation in the longitudinal wave velocity of the media within both models. The velocity distribution of the two models at Z = 0.25 m is shown in Figure 4. Figure 3 and Figure 4 show that the velocity values of the random media are distributed around the background velocity of 1040 m/s, with little overall velocity variation. In contrast, only the longitudinal wave velocities of the soil and rock exist within the soil–rock mixture model, and the velocity values in the model change significantly.

Figure 5 shows the statistical results of the overall velocity distribution for both models. Figure 5a shows that 80% of the sample in the soil–rock mixture model is the longitudinal wave velocity of soil, and 20% of the sample is the longitudinal wave velocity of rock, which is the same as the soil–rock ratio set during modeling. Figure 5b shows that the velocity distribution in the random medium model is relatively dispersed. The samples with velocity values between 900 m/s and 1150 m/s are 7834, accounting for 78.34% of the total. Gaussian fitting of the statistical results reveals that the velocities in the random medium model are normally distributed, and the extreme value of the curve corresponds to the background wave velocity of 1040 m/s (Figure 5b).

A comparative analysis of the two models shows that the longitudinal wave velocity in the random medium model varies mainly within the disturbance standard deviation of the background velocity, which cannot represent the heterogeneity of the soil–rock mixture. The soil–rock mixture model reflects not only the differences in physical parameters and the random distribution of various media, but also the percentage content of various constituent media.

During the random medium modeling, the random characteristic parameters directly affect the heterogeneity of the model. Because the soil–rock mixture model is established based on random disturbance, the influence of random characteristic parameters on the heterogeneity of the soil–rock mixture model is the same as that of the random media. In the case of the same soil–rock ratio, the heterogeneity of the soil–rock mixture media is mainly manifested in the particle size of the rock in the model. The autocorrelation length is set as a = b = 3, and the soil–rock mixture model is established with the same grid size, roughness factor, and local window size as the model in Figure 4, as shown in Figure 6a. A comparison of Figure 3a and Figure 6a demonstrates that as the autocorrelation length increases, the particle size of the rock in the model becomes larger. The local window size is changed to create a soil–rock mixture model with R = 10 and R = 20, as shown in Figure 6b,c. A comparison of the models with three different local window sizes in Figure 6 indicates that with other random characteristic parameters unchanged, larger local window sizes mean more concentrated grid points of the rock particles in the local window. Therefore, a larger particle size of the rock in the model suggests a stronger heterogeneity.

3. Seismic Wavefield Characteristics of the Earth–Rock Dam

3.1. Numerical Simulation Method

Numerical simulation of seismic wavefields based on the elastic wave equation is a technical means to theoretically calculate the seismic signals received at the surface and generate seismic records under a given geological model. Among the various numerical simulation methods, the staggered-grid finite-difference method has become the most widely used for the numerical simulation of seismic wavefields due to its simple grid division, fast calculation speed and high precision [24,25]. Additionally, it has been proved that the algorithm can be accurately and stably applied to the wavefield simulation of random media when the number of grids per wavelength is greater than 10 [22].

In the soil–rock mixture geological model established in this paper, soil and rock particles are assumed to be isotropic elastic media. Therefore, based on the stress–strain equation of isotropic elastic media, seismic wavefields in soil–rock mixture media are numerically simulated by a staggered-grid finite-difference algorithm with second-order accuracy in time and sixth-order accuracy in space. The stress–strain equation for isotropic elastic media can be written as:

$$\{\begin{array}{l}\rho \frac{\partial v_x}{\partial t}=\frac{\partial {\sigma }_{xx}}{\partial x}+\frac{\partial {\sigma }_{xz}}{\partial z}\\ \rho \frac{\partial v_z}{\partial t}=\frac{\partial {\sigma }_{zx}}{\partial x}+\frac{\partial {\sigma }_{zz}}{\partial z}\\ \frac{\partial {\sigma }_{xx}}{\partial t}=(\lambda +2\mu )\frac{\partial v_x}{\partial x}+\lambda \frac{\partial v_z}{\partial z}\\ \frac{\partial {\sigma }_{zz}}{\partial t}=(\lambda +2\mu )\frac{\partial v_z}{\partial z}+\lambda \frac{\partial v_x}{\partial x}\\ \frac{\partial {\sigma }_{zx}}{\partial t}=\mu (\frac{\partial v_z}{\partial x}+\lambda \frac{\partial v_x}{\partial z})\end{array}$$

(4)

where σ_xx and σ_zz denote normal stresses; σ_xz denotes shear stress; v_x and v_z are velocity components of particle vibration; ρ is medium density; and λ and μ are Lame coefficients.

Boundary treatment is important for the numerical simulation of seismic wavefields in soil–rock mixture media. In this paper, to simulate the Rayleigh surface wave generated during the actual seismic exploration, the upper part of the model was set as the acoustic-elastic boundary approach (AEA) [26,27], and the boundaries of all other regions were set as absorption boundaries according to the actual situation of the dam. Due to the high Poisson’s ratio of earth–rock dams, when there is a free boundary, the multiaxial perfectly matched layer (M-PML) [28,29] was adopted for the absorption boundaries on the left and right sides of the model to ensure the stability of the seismic wavefield calculation. In addition, because the surface waves mainly propagate on the free surface, the surface wave energy at the bottom edge of the model is weak. To reduce the computational effort of numerical simulation, the perfectly matched layer (PML) [30,31] was adopted at the bottom of the model. Figure 7 shows the numerical simulation boundary setting.

3.2. Scattered Wavefields in the Seismic Wavefield

The difficulties of using the seismic wave method to detect hidden risks in earth–rock dams are that the dam media are complex, the scale of hidden risks is small, and the difference in physical parameters between hidden risks and dams is not significant. Therefore, mastering the propagation characteristics of seismic waves in soil–rock mixture dams is a prerequisite for accurately detecting hidden risks. Firstly, the soil–rock mixture dam model is established with a width of X = 60 m and a depth of Z = 25 m. The random characteristic parameters, local sizes, physical parameters, and content percentages of soil and rock are the same as those of the model in Figure 3a. The established longitudinal wave velocity model is shown in Figure 8. The shear wave velocity and density modeling methods were the same as for longitudinal waves. Then, seismic wavefields were numerically simulated. The grid spacing was Δx = Δz = 0.1 m, the source was Ricker wavelet with a dominant frequency of f_m = 100 Hz, and the sampling time interval was dt = 2 × 10⁻⁵ s. The scheme of boundary treatment is shown in Figure 7. The source was set in the middle of the dam, with a trace interval of 1 m. The position of the receiver point is shown in Figure 8.

Moreover, the conventional random medium model is established using the above characteristic parameters, and seismic wavefields in homogeneous media and random media are numerically simulated. The background physical parameters of both models are weighted according to the proportion of soil and rock in the dam. The longitudinal wave velocity, shear wave velocity, and density are shown in

Table 2. Physical parameters of different soil–rock ratio models.

Rock Percentage	Soil Percentage	Longitudinal Wave Velocities Vp (m/s)	Shear Wave Velocities Vs (m/s)	Density ρ (kg/m3)	Rayleigh Wave Velocities VR (m/s)	Rayleigh Wave Wavelength (m)
10%	90%	920	295	1730	280	2.80
20%	80%	1040	390	1760	370	3.70
30%	70%	1160	485	1790	461	4.61
50%	50%	1400	675	1850	641	6.41
10%	90%	920	295	1730	280	2.80

.

Figure 9 shows the 30 ms wavefield snapshots and seismic records of three media obtained by numerical simulation. As shown in Figure 9a–c, there were no scattered waves when the seismic waves propagated in the homogeneous dam, while there were significant scattered waves when they propagated in the random medium dam and the soil–rock mixture dam. The scattered wave mainly existed in the region where the surface waves arrived, and the energy of scattered waves in soil–rock media was stronger than that in random media. Scattered waves also existed between the longitudinal wave (P) and shear wave (S) in random media and soil–rock mixture media, but their energy was weak.

As can be observed from Figure 9d–f, the arrival times of direct and surface waves were the same in the three media, which proves the correctness of the calculation method of background physical parameters for soil–rock mixture media. In the seismic records of random media and soil–rock mixture media, the scattered waves with strong energy appear in the region below the surface waves. The scattered wave energy is weak and close to that in the homogeneous medium in the region above the surface waves. The energy of the scattered waves in the soil–rock mixture media is significantly stronger and lasts longer than that in random media, further demonstrating the higher heterogeneity of the soil–rock mixture media.

A comparison of wavefield snapshots and seismic records of the three media shows that seismic wavefield scattering in random and soil–rock mixture media is mainly related to surface waves. Scattered waves with strong energy appear in the region where the surface waves arrive. It was inferred that the scattered waves in soil–rock mixture media are mainly generated by surface waves. When the surface wave propagates in soil–rock mixture media, the Rayleigh surface wave (R) can effectively identify medium heterogeneity and generate scattered waves with strong energy due to its low velocity, short wavelength, strong energy, and high resolution. The approximate wave velocity and wavelength of the surface wave are shown in Table 2 (VR = 0.95 × VS). Therefore, when studying seismic wavefields in soil–rock mixture dams, the influence of surface waves must be considered. The upper part of the model was set as a free boundary, and the Rayleigh surface waves were simulated numerically.

3.3. Effects of the Soil–Rock Ratio on Seismic Wavefields

Dams with different soil–rock ratios have different elastic mechanical properties. From a seismology perspective, as the rock content increases, the physical parameters such as longitudinal wave velocity, shear wave velocity, and density of earth–rock dams will increase. Table 2 shows the physical parameters of models with different soil–rock ratios. Figure 10a–c shows the soil–rock mixture dam models with 10%, 30%, and 50% rock content, respectively. The random characteristic parameters of the models are the same as those of the model in Figure 8. For better display in the figure, only the 0.5 m × 0.5 m area of the model is intercepted. Figure 10d–f show the seismic records for three models with different rock contents that are numerically simulated with the same calculation parameters in Figure 9.

The scattered waves in seismic records are mainly generated by surface waves. In the case of the constant dominant frequency of the wavelet, the higher the velocity of the Rayleigh surface waves, the longer the wavelength and the lower the resolution. As shown in Table 2, the wavelength of the surface wave propagating in a dam with 50% rock content was one time longer than that of a dam with 10% rock content. Therefore, with the increase in rock content, the scattering of seismic waves and the energy of scattered waves gradually weaken, and the seismic wavefield characteristics of soil–rock mixture media gradually tend to those of homogeneous media.

3.4. Effects of Scattered Waves on Effective Wavefields

During the detection of hidden risks in earth–rock dams by the seismic wave method, the scattered waves generated by the heterogeneity of the dam will be superimposed with the effective waves, which will significantly impact the detection results. Mastering the law of the effect of scattered waves on effective waves can better detect hidden risks and improve detection accuracy.

A bedrock layer with a 5 m thickness was set at the bottom of the dam model in Figure 8. The physical parameters of the bedrock are the same as those of the rock in Table 1. The dam model with bedrock is shown in Figure 11a. Then, the propagation characteristics of the seismic wave in the above model were simulated with the same parameters of the numerical simulation shown in Figure 9. Figure 11b shows the simulated seismic record. In addition to direct waves and surface waves, there were also reflected longitudinal waves (RP), converted waves (CP), and reflected shear waves (RS) at the bedrock interface in seismic records. Due to the small difference in the longitudinal wave velocity between the dam and the bedrock, the energy of the reflected longitudinal waves and converted waves was weak. Affected by scattered waves, the reflected longitudinal waves and converted waves arriving after the surface waves were difficult to identify from the seismic record. Because of the strong energy and low propagation speed of the reflected shear waves, when they reached the receiver point, the energy of scattered waves was greatly attenuated, and the reflected shear waves were less affected by the scattered waves. Therefore, the reflected shear waves can still be identified in the scattering area of the seismic record.

The single-trace signal at 45 m in the seismic record of the soil–rock mixture dam was extracted and compared with that of the homogeneous media. The results of the comparison are shown in Figure 12, which reveals that, affected by the heterogeneity of the dam, the phase of the seismic signal in the soil–rock mixture dam lagged behind that in the homogeneous dam. Before the arrival of the surface wave, the direct wave and the reflected longitudinal wave amplitude in the soil–rock mixture dam were basically the same as those in the homogeneous media, and the converted wave amplitude was attenuated. After the arrival of the surface wave, the reflected shear wave amplitude in the soil–rock mixture media was significantly attenuated compared with that in the homogenous media. Therefore, in detecting hidden risks in earth–rock dams, it is crucial to choose appropriate acquisition parameters so that reflected longitudinal waves and converted waves avoid the influence of scattered waves as far as possible. In addition, shear wave detection can be performed when conditions permit.

4. Seismic Wavefield Tests on the Earth–Rock Dam

To verify the correctness of the above results, a reservoir in Wuhan, Hubei Province, China, was selected to carry out the field test of the seismic wavefield in the earth–rock dam. The dam is 13.67 m in height, and the dam top is 6.5 m in width. The soil–rock ratio of the dam is approximately 7:3. Hammer seismic source excitation was used, and data were acquired at a trace spacing of 1 m for a total of 48 traces. The acquired seismic records are shown in Figure 13b,c.

Due to the free boundary between the dam and the air, there are surface waves with strong energy in the acquired seismic records, which are approximately linearly distributed, with low frequency and wide coverage. Therefore, the surface wave must be considered when studying the seismic wavefield characteristics of earth–rock dams. Reflection waves at the bedrock interface are not found in the seismic records. It is presumed that the wave velocity of bedrock at the bottom of the dam is low, and there are small differences in the physical parameters between the bedrock and the dam. Due to the absorption attenuation of the dam, it is difficult to receive reflected wave signals at the top of the dam. Since the dam is a soil–rock mixture, there are significant scattered waves in the seismic record, and their energy is correlated with the surface wave. In the area below the surface waves, scattered waves with strong energy exist. In the area above the surface waves, the scattered wave energy is weak, close to that in the homogeneous media, which is consistent with the numerical simulation results, proving the effectiveness of the numerical simulation for the seismic wavefield propagation characteristics of the earth–rock dam.

5. Conclusions

In this paper, based on the soil–rock mixture characteristics of the actual dam media, a soil–rock mixture model that can reflect the difference in physical parameters between soil and rock in the earth–rock dam and has a precise soil–rock ratio is established through the segmentation, sorting, and reassignment of the random disturbance model. A staggered-grid finite-difference method is used to simulate the seismic wavefield of the soil–rock mixture dam model. The characteristics of the scattered wavefield inside the dam are analyzed, and the influence of dam heterogeneity on the effective wavefield is studied. The main conclusions are obtained as follows:

(1) A larger window size indicates a larger particle size of rock in the model and a stronger heterogeneous model during establishing the soil–rock mixture model.

(2) The heterogeneity of the earth–rock dam can lead to scattered waves in the seismic wavefield, and the scattered waves are mainly generated by Rayleigh surface waves. In the seismic records, there are scattered waves with strong energy in the area below the surface waves. In the area above the surface waves, the scattered wave energy is weak and close to that in the homogeneous media.

(3) As the rock content increases, the wavelength of surface waves through the dam increases, and the scattering of seismic waves and the energy of scattered waves gradually weaken.

(4) The scattered waves generated by the heterogeneity of the dam significantly affect the reflected longitudinal waves and converted waves, while the effect on reflected shear waves is relatively small.

6. Future Work

The main purpose of studying the seismic wavefield characteristics of the earth–rock dam is to provide a theoretical basis for detecting hidden risks in earth–rock dams. In this paper, we have only studied the propagation characteristics of seismic waves in dams without hidden hazards. To further develop the theory of seismic wave detection for hidden risks in earth–rock dams, dam models with different hidden risks will be established based on the current research and the actual situation of common hidden risks in dams. For example, when there are leakage hazards inside the dam, the leakage area changes from a two-phase medium of soil and rock to a three-phase medium of soil, rock, and water. Higher water content means more serious dam leakage. With the modeling method of soil–rock mixture media proposed in this paper, dam models with different degrees of leakage can be established efficiently. Then, the numerical simulation of seismic wavefields in earth–rock dams with hidden risks is carried out, and their kinematic and dynamic characteristics are analyzed. The influence of the depth and size of hidden risks on detection resolution is studied. The key wavefield characteristics for identifying hidden risks in the earth–rock dam are obtained, which can guide the detection of hidden risks more effectively.