Study on Deformation Characteristics of Gate Dam and Earth-Rock Dam System on Deep Overburden

1. Introduction

As China’s western hydropower development strategy continues to deepen, the deep overburden foundation conditions at dam sites are unavoidable [1], while river areas also typically feature low head and high flow characteristics. The gate dam and earth-rock dam system offers advantages such as minimal ecological impact, short construction periods, and strong terrain adaptability, making it the preferred dam type for such sites. Several regional key projects, including Duobu, Futang, Shawan, and Yingliangbao, have been constructed, playing an important and positive role in regional power generation, irrigation, ecological protection, and navigation. However, there is limited research on the three-dimensional deformation characteristics of the entire gate dam and earth-rock dam system, making it difficult to accurately assess and quantitatively evaluate the safety status of the structure during construction and operation. Therefore, studying the deformation characteristics of the hybrid dam system and exploring the mechanisms of deformation interaction between structures is of great significance for dam management decision-making.

To this end, relevant scholars have conducted a series of studies targeting different engineering issues. For example, Xu Jiaqi and He Yunlong [2] used Goodman contact surface elements to study the dynamic response process at the joint between the gate dam and core wall dam of the Guanyin Rock Hydropower Station; Kong Ke et al. [3] took the Tongzilin Hydropower Station as a case study to investigate the influence of the joint form at the end of the frame-type underground continuous wall on its stress deformation; Jiang Yunlong et al. [4] investigated the stress-strain characteristics of the dam section at Dagu Tan; Wang Dengyin et al. [5] used a three-dimensional finite element model to analyze the static stress-strain characteristics of the dam at Danba; Duan Bin et al. [6] employed three-dimensional finite element calculations to assess the effectiveness of reinforcement schemes for the dam foundation at Danba and summarized the advantages of different reinforcement options; Ren Wei et al. [7] addressed the key issues in settlement control for the Duobu Dam, proposing reasonable standards for uneven settlement, settlement control, and differentiated foundation treatment technologies. Overall, the aforementioned research findings provide important reference value for accurately understanding the deformation characteristics of weir dams. However, due to the limitations of conventional modeling and analysis methods in terms of precision analysis [8], it is challenging to simultaneously consider important components such as earth-rock dams, gravity retaining walls, spillway weir dams, cutoff walls, underground continuous walls, and unevenly distributed overburden layers within a hydropower plant hub. Therefore, the aforementioned studies primarily focus on local structural analysis and simplified models, focusing on the mechanical response of isolated components, which makes it difficult to reasonably reflect the deformation interactions between components within the system.

Given this, this paper takes a certain ongoing mixed dam project as its background and employs self-developed refined modeling and analysis methods to conduct a three-dimensional deformation characteristic study of the gate dam and earth-rock dam system, exploring the deformation patterns and distribution characteristics of different components, which can provide reference basis for improving and optimizing dam design schemes.

2. Cross-Scale Refinement Analysis Method

2.1. Octree grid Discretization Algorithm

The octree is a hierarchical tree-like data structure used for dividing three-dimensional space, suitable for mesh partitioning in three-dimensional space [9]. The basic principle of octree grid partitioning is to recursively divide the root cell into eight interconnected subcells according to a 2:1 balanced division principle, continuing until all grid cells meet the size criteria and the division stops. The advantages of the octree grid discretization algorithm include the ability to perform cross-scale grid partitioning, rapid unit size scaling, good mechanical matrix properties of the grid, high grid quality, and simple algorithm construction [10,11]. Figure 1(a) shows the schematic structure of an octree grid discretization with a partitioning level of 3.

2.2. SBFEM Analysis Method

The octree discretization algorithm specifies that the size of adjacent cells varies by a factor of $2^n$, resulting in cubic cells and polyhedral cells with hanging edge nodes after discretization (with a total number of cell nodes greater than 8 and a number of faces greater than 6), as shown in Figure 1(b). Cubic cells can be solved using FEM, but the number of nodes in polyhedral cells is not fixed, making it difficult to calculate using conventional FEM.

Wolf and Song [12] proposed the Scale-Boundary Finite Element Method (SBFEM) based on a semi-analytical numerical solution method. This method combines the advantages of the finite element method and the boundary element method, offering a simple data structure, ease of constructing polyhedra, and convenient program implementation. It has been proven by the authors et al. [8,13,14,15] to be an effective method for solving cross-scale grid computations. SBFEM has been applied to various fields, including elastic-plastic analysis [12,13]; crack analysis [16,17]; free vibration analysis [18]; and soil-structure interaction [19,20]. For the convenience of readers in better understanding the work presented in this paper, detailed derivations can be found in References [14,21].

3. Numerical Model of Gate Dam and Earth-Rock Dam

3.1. Geometric Model

The project is a hybrid hydraulic engineering project consisting of a concrete gate dam and a concrete face rockfill dam. Its main components include the gate dam section, cutoff wall, underground continuous wall, gravity retaining wall, and rockfill dam section with a concrete face, and it contains multiple layers of covering soil. The project is characterized by numerous irregular structures, intersecting components, and complex connections, posing a serious challenge to conventional modeling methods and requiring extensive simplification in the analysis. Based on the design parameters, this paper uses efficient BIM (Building Information Modeling) technology to establish a geometric entity model of the entire dam system, accurately reflecting the spatial characteristics of the terrain and key components, as shown in Figure 2.

3.2. Grid Discretization

Using the refined modeling method developed by the authors, efficient cross-scale discretization of the geometric model was achieved. Local grid refinement was performed on key components in dam design, such as gates, cut-off walls, gravity walls, and panels, resulting in a total of 778,195 elements, 842,876 nodes, and over 2.5 million degrees of freedom, thereby enhancing the reliability of the analysis results. The three-dimensional grid used in this discretization is shown in Figure 3.

3.3. Grid Discretization

Concrete structures are modeled using a linear elastic model, while soil is modeled using an improved generalized plasticity model developed by the authors. Parameters are calibrated based on relevant experimental results (see Table 1), where $G_0$ is the elastic shear modulus; $K_0$ is the elastic bulk modulus; $M_g$ is the slope of the critical state line in the $p^{\text{'}}-q$ plane; ${\alpha }_g$ is the material constant; $H_0$ is the plastic modulus coefficient; $H_{U0}$ is the initial unloading modulus; $M_f$, ${\alpha }_f$, $m_s$, $m_v$, $m_l$, $m_u$, $r_d$, ${\gamma }_{DM}$, ${\gamma }_u$, ${\beta }_0$, ${\beta }_1$ are model parameters. $m_v$ and $m_s$ can be determined based on the initial slope of the stress-strain relationship curve under different confining pressures; $m_l$ and $m_u$ are determined by fitting the stress-strain relationship curves under different confining pressures; $r_d$ is determined based on cyclic loading tests [22]. The soil-structure interface adopts a state-dependent generalized plastic contact model [23].The aforementioned constitutive models have been integrated into the research team’s self-developed high-performance geotechnical engineering analysis software system GEODYNA8.0. The software integration results have been applied to seismic analysis of several world-class high dams in China [24,25,26,27,28].

4. Calculation Results and Analysis

4.1. Dam Deformation

Figure 4 shows the vertical deformation patterns of three representative cross-sections of the mixed dam system, which exhibit two main characteristics: (1) The maximum vertical settlement of the earth-rock dam section is approximately 0.32 m, while that of the gate dam section is approximately 0.23 m. The deformation difference between the two dam sections is approximately 28.1%. This is because the earth-rock dam has a larger volume, resulting in greater soil deformation caused by its construction compared to the gate dam section. (2) The dam exhibits significant non-uniform settlement deformation along the dam axis, primarily due to the uneven spatial distribution of soil layers. The gate dam section has relatively fewer weak soil layers at the lower section, while the earth-rock dam section has a more extensive distribution of weak soil layers. Additionally, the larger volume of the earth-rock dam section results in relatively greater soil deformation.

4.2. Joint Displacement in the Gate Dam Section

Figure 5 shows the location of the indirect joints between the gate piers in the gate dam section and the deformation patterns of each joint after impoundment. It can be observed that: Joints ① and ⑦ exhibit significant lateral displacement along the river axis; The vertical displacement and opening displacement of joints ①, ②, and ③ on the left bank are relatively large, primarily due to the thickness of the overlying soil layer at the base of the left bank gate piers increasing gradually along the dam axis, resulting in slight differences in vertical settlement between the gate piers. Additionally, joint ⑦ also exhibits significant vertical displacement, primarily due to the greater vertical deformation of the panel dam section compared to the gate dam section, which causes joint displacement deformation. Overall, the deformation of the joints in all directions is relatively small and remains within the design allowable range.

4.3. Stress and Deformation of the Cutoff Wall

Figure 6 shows the distribution pattern of deformation in the cutoff wall after impoundment. Due to the uplift effect of bedrock on both banks, the vertical direction is subjected to the gravitational force of the upper gravity retaining wall and the dam body load. The maximum vertical settlement of the cutoff wall occurs in the middle of the river valley, reaching 0.07 m. Due to the influence of vertical settlement deformation, the walls on both banks tend to deform toward the middle of the river valley, with the maximum deformation along the dam axis on the right bank being 0.02 m. Figure 7 shows the stress distribution characteristics of the cutoff wall, with the maximum compressive stress of 9.0 MPa primarily occurring in two regions: ① the lower part of the gravity retaining wall, due to vertical settlement of the cutoff wall causing compressive stress along the dam axis and in the river direction. ② The bottom of the right bank cutoff wall, primarily due to the strong supporting effect of the bedrock on both banks of the cutoff wall, causing mismatched deformation between the wall bodies and the surrounding soil layers, resulting in significant stress concentration at the wall base. Similarly, this uneven settlement deformation pattern also causes a large tensile stress zone at the top of the right bank wall, with a maximum tensile stress of 2.6 MPa, which can be addressed through reinforcement measures such as adding reinforcing bars.

4.4. Stress and Deformation of Underground Continuous Walls

Figure 8 shows the spatial distribution of deformation patterns for gravity retaining walls. Due to the uneven spatial distribution of loads on the upper part of the underground continuous wall ①, the wall exhibits a spatial distribution characterized by greater deformation on the downstream side and the left bank. Similarly, since the loads in the earth-rock dam section are primarily concentrated at the top of the upstream side of the underground continuous wall ②, the upstream side of the wall experiences greater deformation, accompanied by clockwise rotation along the river direction. Figure 9 and Figure 10 illustrate the stress distribution characteristics of the wall under the aforementioned deformation mode. For the underground continuous wall ①, first, since the upstream side deformation is smaller than the downstream side deformation, the wall bottom exhibits bending deformation in the XOY plane, resulting in tensile stress along the river direction; Secondly, due to the rigid contact between the top and the gravity retaining wall, the upstream side of the wall tends to bend along the XOY plane under this deformation pattern, resulting in significant tensile stress at the top of the wall, with a maximum of 5.0 MPa, primarily caused by vertical stress. Similarly, for the underground continuous wall ②, due to uneven vertical settlement, the upstream side of the wall bottom exhibits bending deformation in the XOY plane, resulting in tensile stress of 3.0 MPa, primarily caused by river-parallel stress.

5. Conclusions

Taking a certain construction project as a background, based on independently developed cross-scale detailed modeling and analysis methods, and combined with a generalized plasticity model of soil, we took the lead in conducting a comprehensive three-dimensional stress-deformation characteristic analysis of the gate dam and earth-rock dam system on deep overburden. The results show that:

• Due to uneven distribution of dam body loads and soil layers, the spatial unevenness of deformation in the mixed dam system is quite obvious. This is the main reason why the displacement of the indirect joints between the gate piers in the gate dam section is large on both sides of the dam, but small in the middle section.
• The vertical cutoff wall in the middle of the river valley is subjected to the gravitational force of the upper gravity retaining wall and the load of the dam body, while the embedded sections on both sides are constrained by the rock foundation. This results in uneven settlement deformation, with greater deformation in the middle and lesser deformation on both sides. This causes a certain amount of tensile stress at the top of the cutoff wall on the right bank, which can be reinforced by measures such as reinforcement.
• The spatial non-uniformity of deformation in the underground continuous wall is quite pronounced. In the region where the maximum vertical deformation occurs, the bottom of the wall exhibits significant tensile stress, primarily caused by in-line stress. Additionally, due to the rigid contact between the top of the wall and the gravity retaining wall, deformation of the underground continuous wall along the in-line direction is restricted. Consequently, a certain range of tensile stress appears at the top of the wall on the side with the smallest vertical deformation, primarily caused by vertical stress.

The author will further investigate the dynamic response characteristics of the gate dam and earth-rock dam system and explore the impact of liquefaction of weak soil layers on the superstructure. Additionally, by combining a concrete plastic damage model and a generalized plastic constitutive model of soil, the author will elucidate the failure evolution patterns of concrete structures such as cutoff walls and gate dams, providing theoretical references for seismic safety assessments of engineering structures.