A Model of a Gravity Dam Reservoir Based on a New Concrete-Simulating Microparticle Mortar

Abstract

To address the challenge that traditional dam model materials are difficult to simultaneously meet the requirements of microstructural similarity, dynamic damage simulation, and environmental friendliness, a novel microparticle mortar simulated concrete was developed. This new material consists of cement, sand, gypsum, mineral oil, water, and baryte sand. Through systematic material mechanical tests, the effects of each component on the material’s strength, density, and elastic modulus were revealed, and the optimal mix ratio was determined. This enabled precise control of low elastic modulus and had a high density, while the material is environmentally friendly, non-toxic, and compatible with direct contact with natural water. Its mechanical properties are highly similar to those of the prototype concrete. Based on a 1:70 geometric scale, a shaking table model test of the concrete gravity dam-reservoir system was conducted. The dynamic response and damage evolution under empty and full reservoir conditions were compared and analyzed. The study shows that this material can accurately simulate the stress-strain relationship and failure mode of prototype concrete. Under the full reservoir condition, the dam’s fundamental frequency showed only a 2.72% deviation from the numerical simulation, and as the seismic excitation amplitude increased, the changes in the fundamental frequency effectively reflected the accumulation of damage. Under the design seismic motion, the measured accelerations and stress responses for both empty and full reservoir conditions were in good agreement with numerical calculations. Under overload conditions, the acceleration amplification factor at the dam crest decreased with damage accumulation, and the dam neck was identified as the seismic weak zone. As the peak ground acceleration (PGA) increased from 0.15 g to 0.70 g, the fundamental frequency changes effectively reflected the damage accumulation process in the dam, while the hydrodynamic pressure at the dam heel showed a linear increase (457% increase). The experimentally measured hydrodynamic pressure distribution was between the rigid dam and elastic dam hydrodynamic pressures, reflecting the real fluid-structure interaction effect. This study provides a reliable material solution and data support for dam seismic physical model testing.

1. Introduction

Shaking table model tests are an essential tool for investigating the seismic performance of structures, as they can effectively simulate the structural response of high dams under complex seismic excitation. However, challenges persist in model testing. Due to the limitations of the size and performance of shaking table excitation equipment, physical models simulating the actual concrete high dams and reservoir systems are generally scaled down. The reservoir is typically simulated using natural water, and therefore, the material density scale is approximated as 1. To ensure that the primary low-frequency modes of the scaled model fall within the effective frequency range of the excitation equipment, and to achieve similarity in inertial forces between the model and prototype under seismic loading, it is necessary to simulate the entire dynamic response process of the dam-from elastic deformation and damage cracking to instability failure. This requires that the model material of the dam possesses a low dynamic elastic modulus and exhibits a stress-strain relationship similar to that of prototype dam, maintaining a good similarity in terms of brittle failure modes. Consequently, the development and optimization of high-performance, environmentally friendly, and cost-effective model materials have been a key research focus in the field of dam seismic model testing.

Current development of dam model materials primarily focuses on three core objectives: “low elastic modulus, high density, and similarity.” However, balancing environmental friendliness and mechanical performance remains a common challenge. Early studies, such as those by Oberti and Castoldi [1], used a saturated zinc chloride solution with a density of 2200 kg/m³ and baryte slurry to simulate reservoir water, in order to meet the density scale requirements. However, the compressibility and fluidity of this solution differ significantly from natural water, resulting in a distortion of the fluid-structure coupling effect. To overcome the limitations of liquid simulation, later researchers focused on adjusting the density of solid materials. Gutidze [2] and Harris et al. [3] increased the material density by adding lead particles and adjusted the strength with bentonite, successfully using natural water to simulate the reservoir water. However, lead materials are expensive, highly toxic, and difficult to dispose of, raising environmental concerns. Zou [4] and Gong [5] optimized the physical and mechanical properties of the model by introducing iron powder, baryte, or resin particles with lead cores, but the issues of heavy metal contamination and cost remain unresolved. Additionally, microstructural similarity poses a significant challenge. Zhou et al. [6] developed a model material using cement, river sand, baryte sand, baryte powder, iron powder, and water, suitable for 1:350 small-scale models. However, the inability to simulate the aggregate gradation of real concrete led to significant differences in the stress intensity factor compared to mass concrete. Wang et al. [7,8] used a mixture of barium sulfate, lead oxide, and talc powder to create specialized bricks, adjusting the mixture ratio and compaction pressure to control the material’s properties. The dam model was built using these bricks and bonded with adhesive. Due to significant differences in the micro-mechanical properties between the model material and prototype concrete, failure test results are often limited to qualitative conclusions, making it difficult to precisely reveal the damage and cracking mechanisms of the dam.

The primary goal of researchers in the development and optimization of simulated concrete materials is to successfully apply them in physical model tests. Whether the material performs reliably or not needs to be verified through reasonable experimental design. In the design of seismic dam model tests, the method of vibration excitation for the dam body and the method of reservoir water simulation are key factors influencing the test design. To realistically replicate the dynamic response, damage evolution, and failure modes of the prototype dam under seismic loading, many researchers have conducted extensive and in-depth explorations of model test designs.

The choice of vibration excitation method directly affects the simulation accuracy of dam seismic tests. The main methods currently in use include ambient excitation, shaker excitation, and shaking table excitation. Ambient excitation uses random loads, such as natural wind, traffic disturbances, or artificial hammer strikes, as inputs. Sensor data is then collected to analyze the dam’s dynamic parameters. Sevim et al. [9,10] studied the impact of reservoir water level on the natural frequencies and damping ratios of arch dams using this method. It is low-cost, easy to operate, and does not damage the structure. However, the excitation signal is uncontrollable, and modal parameter extraction can be interfered with by environmental noise. It is also difficult to simulate nonlinear responses and failure modes under strong seismic conditions, making it suitable for identifying dynamic characteristics in the elastic stage and detecting light damage. Shaker excitation involves applying controllable excitation signals, including frequency, amplitude, and phase, to the dam structure. The collected response signals are then analyzed using transfer function analysis and modal parameter identification algorithms to obtain dynamic characteristics. This method was used by Oberti and Castoldi [1] to validate reservoir-structure interaction on a 1:100 scale arch dam model. While this method offers strong signal control, it is difficult to simulate crack propagation and failure modes under strong seismic conditions and does not meet the requirements for ultimate state research. The shaking table excitation method, on the other hand, reproduces seismic motion time histories, allowing direct observation of the model’s nonlinear response and failure modes. Aldemir [11] and Zhang et al. [12] used this method to study the base shear characteristics of gravity dams and the seismic damping performance of hollow concrete gravity dams with saturated sandy soil. Although Qiu et al. [13] did not consider reservoir water due to shaking table size limitations, they also explored the correlation between dam damage and dynamic parameters. This method provides the most realistic excitation scenario and serves as the most direct basis for seismic design and safety assessment.

Additionally, the dynamic coupling between the reservoir water and the dam body is another key factor affecting the accuracy of seismic response simulation. Existing research on reservoir water simulation methods mainly falls into two categories: the added mass method and the natural water method. The added mass method, based on Westergaard’s theory, models hydrodynamic pressure as a concentrated mass fixed on the upstream face of the dam [14,15]. Zhu et al. [16], Kadhim et al. [17], and Wang et al. [18] have conducted dynamic model tests using spring systems, added mass blocks, and lead blocks, respectively. This method has a simple setup, avoids erosion caused by liquid leakage, and resolves the issue of selecting liquid materials under density scaling constraints. However, it neglects the compressibility of water and surface wave effects, making it unable to accurately reflect the real coupling mechanism under full reservoir conditions. The natural water method injects natural water into the model reservoir, directly simulating the dynamic coupling effect between the reservoir water and the dam body. Li et al. [19], under the condition that both acceleration and density scaling are equal to 1, pointed out through comparative experiments that the added mass method tends to be conservative in the elastic stage. To prevent water seepage from altering material properties, Li et al. [19] and Mridha and Maity [20] covered the dam face with polyethylene film. Chen et al. [21] and Altunışık et al. [22] used natural water in shaking table tests for gravity dams and arch dams, respectively, and validated the rationality of different scaled models. Wang et al. [23,24] found significant coupling effects in overflow dam segment tests and proposed a hydrodynamic pressure correction formula through comparative analysis. Xu et al. [25] also used this method to study the instability peak acceleration of a reinforced concrete gravity dam. Overall, the natural water method realistically incorporates water compressibility and crack water filling effects, offering higher simulation accuracy than the added mass method, making it more suitable for studying nonlinear damage in dams under strong seismic loading.

Numerical simulation is one of the main methods for seismic research on gravity dams. Currently, it is mainly based on the Finite Element Method (FEM), combined with concrete plastic damage models, fracture mechanics models, and others, to achieve quantitative analysis of the dam’s dynamic response and damage evolution. In the study of dam-foundation interaction and geometric parameters, Mange et al. [26], based on the Rocscience 2D finite element platform, analyzed the effects of seismic coefficients and downstream slope angles on dam stress and displacement using the Cheruthoni gravity dam in India as an example. Xu et al. [27] combined the modal decomposition response spectrum method and Westergaard’s added mass formula to conduct a seismic safety review of a gravity dam segment. In the areas of reservoir water simulation and fluid-structure coupling algorithms, researchers have made significant contributions. Wang et al. [28] compared the added mass method, incompressible water body, and compressible water body potential flow method, systematically revealing the impact of different reservoir simulation methods on seismic response. Santosh et al. [29] used finite element and Eulerian methods to quantify the effects of dam face slope and reservoir bottom topography on hydrodynamic pressure. In terms of optimizing solution algorithms, Rasa et al. [30] proposed a coupled model based on the Lagrangian method and infinite elements, achieving efficient solution of dynamic equations in the Laplace domain. Additionally, Patra et al. [31] compared the calculation results of three software programs—EAGD-84, ADRFS v1, and Abaqus 6.14—and clearly pointed out that the Abaqus acoustic element method provides higher accuracy in capturing fluid-structure interaction effects.

In summary, the mechanical properties of simulated concrete materials are key factors determining the model similarity scale, experimental design, and testing costs. The closer the simulated concrete material is to prototype concrete, the higher the fidelity in simulating its microstructure and damage mechanisms. However, two major limitations exist in commonly used dam model materials: ordinary cement mortar, while low in cost, fails to simultaneously meet the density and elastic modulus similarity requirements of prototype concrete, resulting in distortions in simulating the dynamic damage process; while heavy materials containing lead, chromium, and other heavy metal aggregates can meet the density requirements, they face significant challenges due to their toxicity, difficult recyclability, and large deviations in their brittle characteristics compared to prototype concrete. To address these shortcomings, this study developed a microparticle mortar simulated concrete composed of cement (Zhangjiakou Hengtai Cement Co., Ltd., Hebei, China), sand, gypsum (BBMG Coating Co., Ltd., Beijing, China), mineral oil (Sinopec Lubricant Co., Ltd., Beijing, China), water, and baryte sand (Yikang Raditation Protection Equipment Co., Ltd., Shandong, China). Through the synergistic adjustment of multiple components, this material successfully achieves a precise match of low elastic modulus and high density. Not only does it possess environmentally friendly, non-toxic, and water-resistant physical properties, but it also accurately replicates the dynamic stress-strain relationship and damage evolution process of prototype concrete, effectively bridging the gap between mechanical similarity and environmental friendliness in traditional materials.

This study aims to overcome the mechanical matching and environmental shortcomings of traditional dam model materials by developing a novel microparticle mortar simulated concrete that integrates accurate simulation performance with environmentally friendly properties. The study comprehensively applies shaking table tests of gravity dam-reservoir systems and analyzes the results using the fluid-structure coupling method in Abaqus software (2020), investigating the dam’s dynamic response characteristics, damage evolution laws, and hydrodynamic pressure distribution patterns. This work provides a reliable material solution and data support for dam seismic physical model tests. The research methodology is shown in Figure 1. The structure of the subsequent chapters is arranged as follows: Section 2 introduces the component design and mechanical performance testing of the novel simulated material, clarifying the impact of components on material performance and determining the optimal mix ratio; Section 3 presents the construction of the 1:70 scaled gravity dam-reservoir system shaking table test model, loading conditions, and data collection plan; Section 4 analyzes the dam’s dynamic response and damage evolution, comparing the results with numerical simulations for validation; Section 5 summarizes the research findings and main conclusions.

2. Model Similarity Relations and Model Material Testing

For a gravity dam with a height of 105 m, crest width of 15 m, and downstream slope ratio of 1:1.4, model tests were conducted on a shaking table with a surface area of 3.1 m × 3.1 m, maximum load capacity of 20 t, and working frequency range of 0.1–100 Hz. The tests aimed to study the dynamic characteristics and dynamic response of the dam. Model tests must satisfy similarity ratio requirements, with similarity relations between the model and prototype primarily controlled by geometric scale, mass density scale, and elastic modulus scale.

Considering limitations in the shaking table surface size and the need to simulate reservoir water, the geometric scale $C_L = 1:70$ of the model relative to the prototype was determined. Since natural water is used to simulate the reservoir, the material mass density scale $C_{\rho } = 1:1$ should be maintained as closely as possible. To ensure an experimental acceleration scale $C_a = 1:1$, the elastic modulus scale $C_E$ should be selected to closely match the geometric scale. Additionally, a lower elastic modulus of the model material ensures that the primary low-frequency modes of the model dam fall within the working frequency range of the shaking table.

To meet similarity ratio requirements, a novel microparticle mortar simulated concrete was developed as the model material. Material testing was conducted to evaluate its strength, elastic modulus, and mass density.

2.1. Novel Microparticle Mortar Simulated Concrete

The model material is a key factor for effective dam shaking table tests. The material used in this study is a newly developed microparticle mortar simulated concrete, which must meet model similarity requirements—including mechanical properties such as strength, mass density, stress-strain curve, and Poisson’s ratio. Additionally, the material should be easy to process, mold, and form, while being environmentally friendly.

The novel microparticle mortar simulated concrete mainly consists of cement, sand, gypsum, mineral oil, water, and baryte sand. Through extensive material mix proportion experiments, the effects of each component on the physical properties of the simulated concrete were thoroughly studied. As shown in Figure 2a, increasing the water content in the mix results in a decrease in both the tensile and compressive strength of the material. The primary role of water in the mix is to react with the cement, forming a gel that binds the aggregates together. However, excess water makes the material more difficult to shape, extends the curing period, and leaves more residual water after hydration. As this residual water evaporates, more pores are created, which directly reduces the material’s strength. In Figure 2b, increasing the proportion of mineral oil (while keeping other mix components unchanged) significantly reduces the compressive strength of the material. Mineral oil prevents cement hydration by coating cement particles, thereby reducing material bonding strength and achieving low-strength simulation. As shown in Figure 2c, increasing the gypsum content in the mix does not significantly increase material strength. The addition of gypsum improves material brittleness, simulating the tensile strength of dam full-graded concrete (which is much lower than its compressive strength), leading to brittle cracking and failure under strong seismic loading. Generally, increasing gypsum content has little effect on both tensile and compressive strength of the material. Considering that the addition of gypsum and mineral oil reduces the mass density of the material, part of the sand was replaced with baryte sand (specific gravity = 4000 kg/m³) to increase the mass of the aggregate while maintaining its volume, thereby improving the overall mass density of the material.

In line with the mechanical performance requirements for the dam model material, a large number of mix designs were tested to cast the simulated concrete and evaluate its mechanical properties. The final mix ratio for the novel microparticle mortar simulated concrete was determined to be 1:2:0.4:0.64:0.48:3.3 for cement, sand, gypsum, mineral oil, water, and baryte sand, respectively. The resulting simulated concrete material had a dynamic elastic modulus of 440 MPa and a mass density of 2230 kg/m³. For prototype dam concrete, the dynamic elastic modulus was 33 GPa, mass density was 2400 kg/m³, and Poisson’s ratio was 0.167. Based on these values, the geometric scale for the dam model test was determined as $C_L$ = 1:70, density scale $C_{\rho }$ = 1.08, elastic modulus scale $C_E$ = 1:75, frequency scale $C_f$ = 0.12, and acceleration scale $C_a$ = 0.99. Below are the test results for the compressive strength, tensile strength, and dynamic elastic moduli of specimens, which were cast simultaneously with the dam model.

2.2. Model Material Testing

2.2.1. Compressive Strength of Model Material

Compressive specimens of the model material were cubic blocks with a side length of 70.7 mm. After casting, the specimens were demolded after 7 days and cured for 7, 14, and 21 days, respectively, before conducting axial compressive strength tests.

Under axial compression, the cubic specimens experienced maximum stress on the surface at a 45° angle to the axial direction. The failure surface exhibited a typical “X”-shaped pattern, as shown in Figure 3.

Through multiple sets of cubic compressive tests, the variation in the compressive strength of the simulated concrete with age was determined, as shown in Figure 4. The average compressive strengths of the simulated concrete at 7, 14, and 21 days were 0.10 MPa, 0.15 MPa, and 0.18 MPa, respectively. Statistical analysis of the data showed that the coefficients of variation for the strengths at these ages were 10.00%, 14.19%, and 4.28%, respectively, all controlled within 20%. This indicates that the specimens made in this experiment have good uniformity, and the test data are reliable. Given the significant impact of age on concrete strength, it is crucial to strictly control the curing time and testing window for the simulated concrete prior to the shaking table test. Additionally, Figure 5 shows the normalized compressive stress-strain curve of the simulated concrete, which closely matches the stress-strain curve of conventional concrete [32,33], confirming the similarity in the material’s constitutive relationship.

2.2.2. Tensile Strength of Model Material

Axial tensile specimens were cast using the model material and subjected to axial tensile testing, as shown in Figure 6a. Tensile specimen failure primarily occurred at the central section (smaller cross-sectional area), which was the tensile weak zone. The fracture surface was relatively smooth, as shown in Figure 6b.

Based on multiple sets of axial tensile tests, the measured data for the axial tensile strength of the simulated concrete were obtained (Figure 7). The results show that the average axial tensile strength of the simulated concrete at 7 days and 21 days were 0.007 MPa and 0.027 MPa, respectively. Further analysis of the data’s dispersion revealed that the coefficients of variation for the two sets of data were 19.87% and 5.80%, both of which are within the acceptable range of 20%. This fully demonstrates the good homogeneity of the specimens and the reliability of the experimental data.

2.2.3. Dynamic Elastic Modulus of Model Material

The dynamic elastic modulus of the model material is generally determined using the cantilever beam method. Based on the differential equation of free vibration for cantilever beams, the first-order natural frequency is expressed as:

$${\omega }_1={\left(1.875104\right)}^2\sqrt{{\displaystyle \frac{EI}{\rho A{l}^4}}}$$

(1)

To test the dynamic elastic modulus of the simulated concrete material, several cantilever beam specimens were cast with cross-sectional dimensions of 70.7 mm × 70.7 mm and a height of 600 mm. As shown in Figure 8, a steel base plate was fixed to the ground, and the cantilever beam specimens were bonded to the surface of the steel plate. After the adhesive had fully cured, a small triaxial accelerometer was fixed at the top of the specimen. The top of the specimen was struck on its orthogonal side with a rubber hammer. The first-order natural frequency was obtained by analyzing the acceleration response, and the dynamic elastic modulus was calculated using Equation (1).

The variation in the dynamic elastic modulus of the simulated concrete with age is shown in Figure 9. The dynamic elastic modulus of the simulated concrete at 7 days, 14 days, 17 days, and 21 days was 109 MPa, 294 MPa, 348 MPa, and 440 MPa, respectively. Concrete age has a significant effect on the dynamic elastic modulus; therefore, attention should be given to the curing and age of the simulated concrete before conducting shaking table tests.

3. Dynamic Model Test Design

In this experiment, a dam model was cast using specially designed molds. The thickness of the dam body was 0.34 m, and steel reinforcement was welded onto the model’s steel base plate to enhance the connection between the dam body and the base plate, ensuring effective transmission of shaking table excitation to the dam body. A water tank of appropriate size was designed to simulate the dynamic effect of reservoir water on the dam, as shown in Figure 10. The detailed geometric dimensions of the model dam are shown in Figure 11.

To observe the dynamic response behavior of the gravity dam model from cracking to instability, accelerometers (Hebei MT Microsystems Co., Ltd., Shijiazhuang, Hebei, China), strain gauges (Chengdu Electrical Measurement and Sensing Technology Co., Ltd., Chengdu, Sichuan, China), and hydrodynamic pressure sensors (Shaanxi Dechen Electronic Technology Co., Ltd., Xi’an, Shaanxi, China) were evenly distributed on the dam body. Figure 12 shows the layout of accelerometers, strain gauges, and hydrodynamic pressure sensors on the upstream face of the dam, while Figure 13 shows the layout of accelerometers and strain gauges on the downstream face. In the figures, “A” denotes accelerometer locations, “S” denotes strain gauge locations, and “P” denotes hydrodynamic pressure sensor locations. The elevation of each measurement point is also indicated. To analyze the relationship between the dam’s acceleration response and hydrodynamic pressure, accelerometers and hydrodynamic pressure sensors on the upstream face were arranged at the same elevation. Additionally, an accelerometer was placed on the steel base plate to monitor the input seismic motion during the test.

The peak ground acceleration (PGA) of the prototype gravity dam’s design seismic motion is 0.15 g. Based on the engineering design seismic response spectrum, artificial seismic waves were generated as seismic input in the river direction, as shown in Figure 14. During the experiment, the artificial seismic waves in Figure 14 were compressed according to the frequency scale and amplified according to the excitation acceleration.

The experimental conditions are listed in

Table 1. Experimental Conditions.

Condition	Input Waveform	Amplitude	Duration	Water Level	Explanation
1	White Noise	0.075 g	80 s	Empty Reservoir	Elastic Stage Test under Empty Reservoir Condition
2	Artificial Wave	0.15 g	Artificial Seismic Wave
3	White Noise	0.075 g	80 s
4	White Noise	0.075 g	80 s	Full Reservoir	Damage Accumulation Stage Test under Full Reservoir Condition
5	Artificial Wave	0.15 g	Artificial Seismic Wave
6	Artificial Wave	0.20 g
7	White Noise	0.075 g	80 s
8	Artificial Wave	0.30 g	Artificial Seismic Wave
9	White Noise	0.075 g	80 s
10	Artificial Wave	0.60 g	Artificial Seismic Wave		Failure Stage Test under Full Reservoir Condition
11	White Noise	0.075 g	80 s
12	Artificial Wave	0.70 g	Artificial Seismic Wave
13	White Noise	0.075 g	80 s

, which include tests during the elastic stage, damage accumulation stage, and failure stage. First, artificial seismic waves corresponding to the design seismic level (peak ground acceleration of 0.15 g) were input under both empty and full reservoir conditions. Subsequently, under normal water level conditions, an overload excitation test was conducted. In this phase, only the amplitude of the seismic motion was adjusted while keeping the time history waveform unchanged. In each experimental stage, white noise sweeping was performed to identify structural stiffness degradation (i.e., damage level), which is a key method for analyzing the dam’s failure process.

4. Model Test Results and Analysis

4.1. Frequency

Table 2. Comparison of Numerical Model and Experimental Measured Frequencies.

Condition		Measured Value (Hz)	Calculated Value (Hz)	Error (%)	Experimental Model Scaled to Prototype (Hz)	Numerical Prototype (Hz)	Error (%)
Empty Reservoir	Condition 1	31.91	31.98	0.22	3.80	3.81	0.26
Full Reservoir	Condition 4	26.81	26.08	2.72	3.19	2.94 [a] 3.11 [b]	7.84 [a] 2.51 [b]

^[a] In the numerical calculation, the mass density of water is 1000 kg/m³ and the bulk modulus is 2.07 GPa. ^[b] In the numerical calculation, the material parameters of water are scaled based on the density scale and elastic modulus scale: the mass density is 1076 kg/m³ and the bulk modulus is 155.25 GPa.

shows the comparison of fundamental frequencies between experimental and numerical simulation results under both empty and full reservoir conditions. Under empty reservoir conditions, the deviation between the experimentally measured fundamental frequency and the numerical model is only 0.22%, and when scaled to the prototype, the deviation from the numerical prototype is 0.26%. Under full reservoir conditions, both the experimentally measured frequency and the numerical model frequency show a consistent decrease compared to the empty reservoir fundamental frequency. When the water material parameters strictly follow similarity scale requirements, the error between the numerical prototype and the experimentally measured result after scaling is 2.51%, while the error between the numerical model and the experimentally measured result is 2.72%. The nearly identical errors indicate that this scaling method and boundary condition design can accurately replicate the dynamic characteristics of dam-reservoir coupling. This result fully validates the reliability of the mechanical parameters of the novel simulated concrete material and supports the rationality of the physical model boundary condition setup.

Figure 15 shows the fundamental frequency and damping ratio of the dam body at each test stage, identified using the Enhanced Frequency Domain Decomposition (EFDD) method. Regarding the effect of reservoir water, the fundamental frequency under full reservoir conditions decreases by 16% compared to empty reservoir conditions. This significant difference aligns with the findings in existing literature [15,23], confirming the impact of reservoir water on the dam’s vibrational characteristics. Regarding damage evolution, as the seismic excitation amplitude increases, the dam’s fundamental frequency decreases from 31.91 Hz to 21.15 Hz, clearly reflecting the process of cracks evolving from “microscopic initiation” to “macroscopic penetration.” After inputting seismic waves with peak ground accelerations of 0.15 g, 0.2 g, and 0.3 g, the dam’s fundamental frequency slightly decreases and the damping ratio increases slightly, indicating the initiation of microcracks inside the dam. After inputting a 0.6 g seismic wave, the dam’s fundamental frequency significantly decreases, and the damping ratio increases notably, indicating material damage and crack propagation. After the input of a 0.7 g seismic wave, the fundamental frequency drops to its lowest value of 21.15 Hz, and the damping ratio increases to 16.15%, with through-cracks forming at the dam top, indicating complete dam failure. Thus, analyzing the attenuation process of the dam’s fundamental frequency effectively reflects the nonlinear characteristics of damage accumulation in the dam.

4.2. Acceleration

When a 0.15 g seismic wave is input, the acceleration distribution curves along the elevation under both empty and full reservoir conditions are consistent between the experimental results and numerical simulations, as shown in Figure 16. This indicates that, at this stage, the stress in the dam body is within the material’s elastic range, satisfying the requirements of the design seismic loading. It can be observed that at 1/5 of the dam’s height from the crest, the amplification factor exhibits a significant change. This is the combined result of the typical whip effect in gravity dams and the stiffness inhomogeneity caused by the abrupt change in the dam’s cross-section. The errors between the numerical simulations and experimental results at the dam crest are 14.39% (empty reservoir) and 19.60% (full reservoir), which are within a reasonable range of agreement.

Figure 17 shows the distribution of acceleration amplification factors along the dam height under different conditions. Under full reservoir conditions, the overall acceleration amplification factor of the dam is lower than that under empty reservoir conditions due to the hydrodynamic effect of the reservoir water. As the seismic excitation amplitude increases, the material at the dam top gradually enters the nonlinear stage, leading to a continuous decrease in the amplification factor. After overloading to 0.60 g, significant damage occurs in the dam. When the loading increases to 0.70 g, the acceleration amplification factor at the dam crest increases instead of decreasing. This suggests the formation of through cracks at the top, and the motion of the fractured block changes from elastic deformation to rigid body oscillation, significantly amplifying the acceleration response. Analysis of the acceleration time history at the dam crest for each condition (Figure 18) shows that as the seismic excitation amplitude increases, the acceleration amplitude at the dam crest increases monotonically, with the waveform remaining consistent in most conditions. Only in Condition 12 (corresponding to the instability and failure stage) does the dam top portion completely detach, causing low-frequency oscillations during the seismic excitation. This results in a significant difference in the acceleration time history waveform compared to other conditions.

4.3. Stress

Measured strain data were converted into stress values using the material’s elastic modulus, and the stress results from both the numerical model and the experimental model under design seismic loading were compared, as shown in Figure 19. The distribution trends of tensile and compressive stresses on the dam’s upstream face under both empty and full reservoir conditions were consistent with the numerical simulation results. Both models showed a tensile stress peak near an elevation of 1000 mm, with lower tensile stresses at the dam crest (1250 mm) and the dam heel (50 mm). This indicates that the middle and upper parts of the dam are the primary stress concentration zones. Notably, the stress deviation at the 50 mm elevation of the dam heel was as large as 50%. This discrepancy is primarily due to the development of local microcracks at the dam heel in the physical model, which led to stress release. In contrast, in the numerical simulation, stress singularities or corner effects often occur at geometric discontinuities, resulting in high local stress values. Therefore, the model test results more accurately reflect the real stress and damage characteristics of concrete dams in practical engineering.

Due to the low tensile strength of the dam material, tensile failure is the primary mode of dam failure under seismic loading. Figure 20 shows the dam damage and crack locations after the completion of the experiment. Measurements indicate that the elevations of the two cracks on the dam’s upstream face are 980 mm and 1120 mm, while the crack on the downstream face occurs at an elevation of 1160 mm. These cracks are located in the region of geometric discontinuity in the model dam, which is the seismic weak zone of the dam. The results of this experiment are consistent with the findings of previous studies [14,16,18,20,24].

By comparing the locations of the strain measurement points with the crack positions, it can be seen that the strain gauge at measurement point S2 is located between the two cracks on the upstream face, closer to the lower crack, resulting in the highest measured strain. The strain gauge at measurement point S8 is positioned near the upper part of the crack on the downstream face, and its strain value is smaller than that of S2. Figure 21 and Figure 22 show the stress time histories at measurement points S2 and S8 under different conditions. For comparison, the stress time history at measurement point S6 near the dam heel is also provided, as shown in Figure 23. As can be seen, under the 0.15 g seismic loading, the dam structure remains in the elastic stage, stable, and no significant deformation occurs. As the seismic excitation amplitude gradually increases, the dam begins to experience damage. When the excitation amplitude reaches 0.6 g, the dam stiffness rapidly decreases, and macroscopic cracks appear both below and above the S2 measurement point on the upstream face, extending toward the downstream face. When the excitation amplitude reaches 0.7 g, the cracks penetrate the dam body, and the blocks at the dam crest experience low-frequency oscillations under seismic loading. At this point, the stress time history waveforms at measurement points S2 and S8 contain more low-frequency components compared to other conditions. Notably, because the strain gauges at S2 and S8 are located near the cracks on the upstream and downstream faces, the measured strain responses under 0.6 g and 0.7 g seismic excitation are influenced by microcracks near the macroscopic cracks in the dam body, resulting in larger strain responses. The calculated stress values do not reflect the actual stress response of the dam.

4.4. Hydrodynamic Pressure

Westergaard [34], based on the assumption of a rigid dam body and compressible water, studied the hydrodynamic pressure on a vertical dam face under horizontal seismic loading and provided a simplified calculation formula:

$$P_{\max }={\displaystyle \frac{7}{8}}\alpha \sqrt{H_{0}h}$$

(2)

In the equation, $P_{\max }$ represents the maximum hydrodynamic pressure; $h$ represents the water depth at the calculation point; $H_0$ represents the reservoir water depth; $\alpha$ represents the maximum seismic acceleration coefficient.

Standards [14,15] use the added mass method to calculate the impact of hydrodynamic pressure on a gravity dam. The formula for calculating the mass added to the dam body is as follows:

$$m_a={\displaystyle \frac{7}{8}}{\rho }_w\sqrt{H_{0}h}$$

(3)

In the Equation, $m_a$ represents the added mass per unit area; $h$ represents the water depth at the calculation point. This method effectively replaces hydrodynamic pressure with the inertial force generated by the added dynamic water mass under inertial action.

In this study, two models were used to calculate the distribution of hydrodynamic pressure (as shown in Figure 24): one based on the peak ground acceleration measured from the model’s steel base plate, which was substituted into Equation (2) to obtain the “rigid dam hydrodynamic pressure”; and the other based on the measured accelerations at various points on the dam’s upstream face, combined with the added mass Formula (3), to obtain the “elastic dam hydrodynamic pressure.” A comparative analysis showed that the experimentally measured results lie between the two model results, indicating that these models represent the lower and upper bounds of hydrodynamic pressure, respectively. Specifically, the rigid dam model underestimates the hydrodynamic pressure because it ignores the dynamic amplification effect caused by dam deformation, resulting in smaller values. On the other hand, the elastic dam model tends to overestimate the hydrodynamic pressure due to the overestimation of the water’s inertial effects, leading to larger values. Notably, existing studies [24] often observe that “the rigid dam hydrodynamic pressure is higher at the dam heel than the measured experimental value,” whereas in this study, the measured hydrodynamic pressure at the dam heel is slightly higher than the rigid dam hydrodynamic pressure. This discrepancy may be attributed to differences in the boundary conditions of different model tests: in this experiment, a steel base plate was used, which has a weak effect on wave absorption at the reservoir bottom. Additionally, the contact stiffness between the dam model and the base plate may vary across different studies, affecting the response characteristics of the dam heel hydrodynamic pressure.

In Figure 24, the elastic dam hydrodynamic pressure calculation results show good consistency with the fluid-structure coupled numerical simulation results. The distribution trends of hydrodynamic pressure along the dam height are in close agreement, verifying the effectiveness of the elastic dam hydrodynamic pressure calculation method. This method can serve as an efficient tool for the rapid analysis of hydrodynamic pressure in elastic dams in engineering practice.

Figure 25 shows the variation in hydrodynamic pressure with elevation under different conditions. It can be seen that under all conditions, hydrodynamic pressure consistently increases with water depth, following a similar distribution pattern. The peak hydrodynamic pressure occurs near the dam heel, which corresponds to the deepest area of the reservoir at normal water levels in the prototype. In Condition 5, the hydrodynamic pressure at the dam heel is approximately 1.55 kPa, while in Condition 12, it increases to 8.64 kPa—an increase of 457%. The hydrodynamic pressure at the dam crest in Condition 5 is about 1.04 kPa, and in Condition 12, it rises to 3.07 kPa—an increase of 195%. Hydrodynamic pressure near the dam heel increases linearly with PGA, while the growth rate at the dam crest is significantly lower than at the heel. This indicates that the impact of the reservoir on the dam bottom is more pronounced under strong seismic loading.

5. Conclusions

This study focuses on the core requirements of dam shaking table model testing. A novel microparticle mortar simulated concrete was developed, and a gravity dam-reservoir shaking table model test was designed and conducted. By comparing the experimental results with numerical simulations, the study clearly defines the dam’s dynamic response and damage evolution mechanisms. The main conclusions are as follows:

• The mechanical properties of the novel simulated concrete developed in this study are highly consistent with those of prototype concrete. The material features a low elastic modulus, high mass density, and compatibility with direct water contact. Moreover, it is free of heavy metals, environmentally friendly, and non-toxic, avoiding the pollution and disposal issues associated with traditional materials. Through numerous mix proportion experiments, the influence of various components on the material’s compressive strength, tensile strength, and dynamic elastic modulus was studied, enabling precise control of the key mechanical properties of the simulated concrete.
• The gravity dam-reservoir model designed with a 1:70 geometric scale showed only a 0.22% error in the elastic stage under empty reservoir conditions when compared with the numerical solution, and a 0.26% error when scaled to the prototype. Under full reservoir conditions, the errors between the numerical prototype’s water material parameters (after scaling based on similarity relationships) and the model’s errors were nearly identical, confirming the rationality of the model’s boundary conditions and the reliability of the model material’s mechanical parameters. White noise sweep tests showed that the dam’s fundamental frequency decreased from 31.91 Hz to 21.15 Hz, corresponding to the damage evolution process from micro-initiation and macro-expansion to complete instability.
• Under the design seismic motion (PGA = 0.15 g), the dam remained in the elastic stage under both empty and full reservoir conditions. The distributions of acceleration and stress along the dam height were consistent with the numerical simulation results, meeting the design requirements. Under overload conditions, the amplification factor at the dam crest gradually decreased as damage accumulated. When the PGA increased to 0.70 g, cracks at the dam neck caused the dam crest block to detach, generating a rigid body motion effect that led to an increase in the amplification factor instead of a decrease. The dam neck, where tensile stress was concentrated, became the seismic weak zone. Its tensile strain peak showed the most significant increase as the PGA grew, marking the core area where damage initiation and expansion occurred.
• Hydrodynamic pressure increases with water depth. The hydrodynamic pressure near the dam heel increases linearly with PGA. Due to the more pronounced impact of the reservoir on the dam bottom under strong seismic loading, the growth rate of hydrodynamic pressure at the dam crest is significantly lower than that at the dam heel. A comparative analysis shows that the experimentally measured values lie between the hydrodynamic pressure of a rigid dam (lower bound) and that of an elastic dam (upper bound), which objectively reflects the real fluid-structure coupling effect under the interaction of structural deformation and water motion. The hydrodynamic pressures for rigid and elastic dams form an envelope zone, establishing a numerical range for pressure response. This provides important reference data for seismic evaluation in practical engineering.

The novel microparticle mortar simulated concrete and the associated testing methods developed in this study provide a comprehensive and reliable technical support system for dam shaking table model tests. This system can be widely applied to the seismic performance evaluation and design optimization of similar hydraulic engineering projects. Future research will expand to include the dynamic interaction between complex foundations and dams, as well as response analysis under extreme seismic conditions, in order to obtain more engineering-relevant experimental data.