Three-Dimensional Numerical Analysis and Engineering Evaluation of Stilling Basin and Foundation Bedrock of Kala Hydropower Station, China

Kala reservoir is a large hydropower station, which will be built on the Yalong River in Sichuan Province, China. The topography and geomorphology at the project area of the hydropower station are characterized by high mountains and a deep V-shaped valley, where the engineering geological conditions are complex. The stilling basin of the Kala reservoir is planned to be built on a weak rock mass called a sericitized slate. Therefore, the safety of stilling basin structure has an important impact on the regular operation of the Kala hydropower station. To evaluate the working state of the stilling basin structure, a three-dimensional numerical model was built, including the valley, mountains and stilling basin structure. FLAC3D (A three-dimensional finite-difference simulation software) was used to simulate engineering and mechanical responses of the stilling basin structure and the foundation rock mass under various working conditions. Based on the simulation results, the structural layout of stilling basin and the rationality of sericitized slate treatment measurements were verified. It was determined that the engineering properties of the sericitized slate would generally meet the engineering requirements. However, considering that the characteristics of sericitized slate are easy to weaken with water, it was suggested to carry out necessary foundation improvement for sericitized slate to strengthen its engineering mechanical properties.


INTRODUCTION
Many hydropower stations have been built in the deep V-shaped river valleys in Southwest China [1,2]. These hydropower projects are built on complex geological environments [3]. Weak and bad geological strata often appear in key hydraulic structures such as dam foundations, underground powerhouses, or hydraulic tunnels [4][5][6][7]. The complex geological environments cause engineering problems for constructing hydropower projects in this region. These engineering problems related to weak rock masses include but are not limited to an insufficient foundation bearing capacity, excavation-reduced relaxation, expansion of plastic zones, large time-dependent deformations. These problems should be evaluated and predicted in the engineering design stage to put forward practical support and reinforcement measures.
In rock engineering, the size of damage or plastic zone are traditionally used to conduct the engineering evaluation of weak rocks [8,9]. In the field tests, it can be determined by measuring the variations of a sound wave with depth in rock drilling [7,12], the size of rock damage or plastic zones can be conventional determined. The borehole acoustic testing method has high accuracy and important engineering practical value. It has been widely used in a large number of hydropower projects in China [7,10,11].
When there is a lack of field-measured acoustic data, the numerical simulation method becomes an inevitable choice. This method can qualitatively determine the range of damage or plastic zones under varieties of working conditions, which provides an important reference in the pre-feasibility design stage of a project. Numerical simulation technology has also been widely used in the design of hydropower projects in China. A large number of successful application cases have been achieved [8,12].
For a shallow excavation of rock foundation, excavation activities generally produce small disturbances in the rock mass, which cause limited releases or changes of in-situ stress states. Therefore, the foundation bearing capacity can also be used to evaluate the stability of bedrock. This method is to judge whether the foundation pressure on the bedrock exceeds the standard value of the foundation bearing capacity. Although this method is simple, it has good practicability and is widely used [13,14].
At present, the Kala hydropower station to be built on the Yalong River in Sichuan Province has encountered the problem of adverse geological conditions. The dam site of Kala hydropower station is located in a section of deep V-shaped valley. Part of the foundation bearing stratum of the stilling basin is a weak sericitized slate, which is characterised by broken rock mass structure, poor rock mass quality, low strength and easy deformation. It can be predicted that the sericitized slate as the bedrock will show complex inelastic and time-dependent deformation, which will have a potentially adverse impact on the stability of stilling basin structure. Therefore, safety evaluation for stilling basin structure and bedrock rock mass is of great engineering value for the design and construction of the project.
By analysing the engineering geological conditions, this study established a three-dimensional numerical model of the valley, mountains and stilling basin structure of the Kala reservoir. Then, the three-dimensional finite difference method (FLAC3D7.0) was used to analyze the engineering and mechanical responses of the stilling basin structure and bedrocks under various working conditions. Based on the numerical modelling results, the stabilities of stilling basin and sericitized slate was evaluated by using plastic zone, bearing capacity and point safety factor. This study has a certain reference value for the design and construction of hydropower projects under similar topographic and geological conditions.

Topography and Geomorphology
The topography of the dam site of the Kala hydropower station is a typical deep V-shaped river valley. On the slope of the left bank, rock masses are exposed and partially covered with quaternary diluvium. On the lower part of the right bank slope, the terrain is steep and the bedrock is exposed. While the upper part is covered with quaternary colluvium and diluvium, with relatively gentle terrain.

Engineering Geological Conditions
(1) Stratum and lithology Sandy slate, metamorphic sandstone, carbonaceous slate and marble are exposed at the dam site. These rocks belong to the Zagunao Formation (T 3 Z 2-1∼2-17 ) of the Upper Triassic of Mesozoic. The rock stratum on the right bank is along [7,12]. The stratum is characterized by a monoclinal structure. The strike of the rock stratum is consistent with the river flow direction, generally inclined to the left bank. The rock stratum is in the reverse slope direction on the left bank.
(2) Geology structure At the dam site, various structural discontinuities, such as faults, interlayer compression zones and joint fissures are developed. According to scale, they can be divided into class II, III, and IV structural interfaces. Among them, the geological conditions downstream of the dam are the worst, where stilling basin structures are planned to build. Under the stilling basin structure, there is a weak sericitized slate, which might adversely affect the construction of the stilling basin.
(3) Characteristics of sericitized slate According to the engineering survey, the sericitized slate is located in elevation (EL.) 8.60-923.83 m and is distributed in a bladder shape. It is mostly in interbedded or interlayer contact with the surrounding hard rock strata. On the whole, the sericitized slate is exposed at a lower elevation near the river downstream. Sericitized slate is a kind of weak rock mass characterised by broken structure, poor quality, low strength, and easy deformation. A mesh generation software named Griddle was selected to establish a high-quality grid numerical model. Many practices show that Griddle has strong mesh generation performance in geotechnical simulations. In this study, the eight-node hexahedron element was mainly used in Griddle to mesh the geological model. Four-node tetrahedral elements were used for transition in some parts that are difficult to have meshed with hexahedral elements. Figure 1A shows the numerical model established using Griddle. It has 1156977 solid elements and 577128 nodes. Because of the cross-cutting of strata and faults, the numerical model has 73 element groups. Different colours distinguish these groups. Sericitized slate is a bad geological material encountered in the Kala hydropower project, which would cause potential adverse effects on the construction of stilling basin. Figure 2A shows the spatial relationship between the stilling basin and the sericitized slate. It can be seen that a sericitized slate is located inside the mountain on the left bank. According to the engineering design, a part of sericitized slate will be excavated and exposed as the foundation and slope rock mass, which will contact the bottom plate and sidewall on the left side of the stilling basin. Sericitized slate can be divided into three layers. Among them, the material parameters of the sericitized slate in the second and third layers are similar, so no more detailed stratification is required in this study. Figure 2B shows the three-dimensional numerical model of the hydraulic structure of the stilling basin. The stilling basin structure has 5 structural joints along the river and 6 structural joints across the river. These structural joints are about 2 cm wide and the concrete blocks on both sides are separated from each other. Thus, in the numerical model, interface elements are adopted to simulate the mechanical behaviours of the structural joints, as shown in Figure 2C.

Geological Modeling and Material Parameters
In FLAC3D7.0, the interface element is generally used in contact analysis. The interface element has four mechanical parameters. They are normal stiffness K n , shear stiffness K s , cohesion c and friction coefficient μ. In this numerical investigation, K n 2.8 × 10 11 N/m and K s 2.8 × 10 11 N/m are adopted. Considering that the width of these structural joints is 2 mm, it is reasonable to think that the interface elements have no cohesion and friction effects. Thus, c 0 and μ 0 are adopted in this study.
In this study, the model shown in Figure 1A was imported into FLAC3D7.0 for conducting numerical simulations. FLAC3D7.0 is a finite difference software, which has been developed by Itasca for numerical simulation of geotechnical engineering. In this software, the tensile stress is specified as positive. Therefore, in its calculation results, minor principal stress is equivalent to major principal stress in rock mechanics and engineering. In the numerical model shown in Figure 1A, there are 13 materials involved. Their material parameters are shown in Table 1, which are input into FLAC3D7.0.

Modelling Loads and Boundary Conditions
The following four kinds of loads are taken into account in the numerical analysis.
(1) Deadweight load, which is applied on the model by inputting the values of material density and gravity acceleration (9.81 kg · m/s 2 ). (2) Hydrodynamic pressure load, which is applied to the surface of the base plate and sidewall of the stilling basin.  and applied to the element nodes at the bottom floor and sidewall of the stilling basin. (4) Seismic load. It is applied using the pseudo-static method to the effects of an earthquake. According to this method, the model density of some materials is increased by 15%.
The boundary condition of the model is set to constrain the normal displacement at the bottom and the four vertical boundaries of the model.

Working Conditions
During the operation of the hydropower station, the bottom plate of the stilling basin is subjected to various upward and downward loads. Therefore, according to the operation and service conditions of stilling basin, the load combination is divided into forward and reverse load combinations. All forward loads (downward loads) are considered as the maximum value, while reverse loads (upward loads) are not considered or considered as the minimum value. The most adverse combination of upward and downward loads should be considered to ensure the safe operation.
In this study, considering the combination modes of different loads, the engineering mechanical responses of stilling basin structures and bedrocks under 4 working conditions are simulated and analysed, which are presented in Table 2. Concerning the application of load, some special notes should be described as follows: (

MODELLING RESULTS AND ANALYSIS
In this study, a series of simulations were carried out. Limited to the length of the paper, only some calculation results are selected for display and analysis below. However, some other valuable simulation results will also be discussed and analyzed in the text descriptions or tables. Figure 3 shows the simulation results under working condition No.1 (frequent flood). It can be seen from Figures 3A,B that under the condition of the frequent flood, the maximum tensile major principal stress is about 32.68kPa. The maximum tensile minor principal stress is about 2.706MPa, which appears on the stilling basin structure. Figure 3F shows that under the working condition of the frequent flood, the maximum deformation of the project area is    1.20-1.34 mm. The direction of maximum displacement is from the right bank towards the left bank. It is found that the deformation of the left bank in this area is larger than that of the same position on the right bank. Through analysis, it is considered that the deformation of the stilling basin dam in this area is mainly affected by the backfill gravel behind the sidewall and the foundation bedrock of the sericitized slate. The deformation modelling results of stilling basin structure are summarised in Table 3 Under normal operation + earthquake working condition, the maximum deformation of stilling basin is ahout 3.02 mm. Its direction is mainly across the river from the left bank to the right bank. The maximum deformation occurs at the top of the sidewall of stilling basin (Dam 0 + 85-215 m, EL. 1935 m) on the left bank. It can be seen that earthquake significantly impacts the deformation of stilling basin structure, which can produce opposite deformation different from other working conditions. Figures 7A,B show the major principal stress distribution in the stilling basin structure under the check flood working condition. It can be seen that most volumes of the stilling basin are in the compressive stress state. At the dam crest and at the top of stilling basin sidewalls on both banks, the major principal stress is in the tensile state, within a value range of 0-0.35 MPa.  conditions. It can be seen that more than 2/3 elements of the stilling basin are in the compressive states. And less than 1/3 volume is in the tensile state. The calculation results of other working conditions are similar to those under check flood working conditions. At the transverse structural joint (Dam 0 + 135-165 m, EL.1,885-1,900 m) in contact with sericitized slate on the back of the stilling basin sidewall on the left bank, there are local concentrations of tensile and compressive stresses. In this region, tensile minor principal stresses and principal compressive stresses can be as high as 3.029 and 4.160 MPa, respectively. Sericitized slate at the transverse structural joint also affects this region's uneven and uncoordinated deformation.

Modelling Results of the Stilling Basin
The concrete structure is easy to be damaged under the condition of tensile stress, so it is necessary to pay special attention to the state of tensile stress. Table 4 summarises the numerical simulation results of major principal tensile stresses in the stilling basin under 4 working conditions. It can be seen that the concrete of stilling basin structure bears a certain degree of tensile stress, but the value of tensile stress is small, within a range of about 0.028-0.057 MPa. This level of tensile stress will not cause harm to the concrete structure. By extracting the values of these tensile stresses, it is found that they are local tensile stresses, which mainly appear in the transverse structural joints of the sidewall on the left bank (Dam 0 + 181 m, EL. 1878 m), with an area of less than 1 m 2 .

ENGINEERING EVALUATION ON SERICITIZED SLATE Three Engineering Evaluation Methods
In this study, the engineering properties of sericitized slate at the foundation of stilling basin was evaluated in three ways: (1) The standard value of foundation bearing capacity is used for evaluation. When the normal stress applied to the sericitized slate is less than its standard value of foundation bearing capacity, it is considered that the sericitized slate can support the foundation of the stilling basin. (2) The plastic zone is used for evaluation. When the plastic zone appears in the elements of the sericitized slate, it is considered that the sericitized slate encounters plastic deformation and needs to be strengthened. (3) The point safety factor is used for the evaluation of strength reserve. When the point safety factor of the sericitized slate is equal to 1.0, it is regarded that the sericitized slate reaches the plastic yield state and does not have enough strength reserve. Reinforcement is needed. When the point safety factor is greater than 1.0, the sericitized slate is in an elastic state. The larger the point safety factor, the higher the strength reserve. The point safety factor method and related theories will be introduced below. Frontiers in Physics | www.frontiersin.org January 2022 | Volume 9 | Article 807506 8

Point Safety Factor Method and Related Theories
In geotechnical engineering, using the idea of limit equilibrium, the point safety factor of geomaterials can be defined. Based on the Mohr-Coulomb strength criterion, the distance between the stress state of a point and the strength envelope can be determined, as shown in Figure 8. The calculation formula of the point safety factor under compressive stress state can be defined as follows:   However, the stresses in geomaterials are not always in the compressive state. When the stress state of a point is in tension, the tensile strength criterion should be adopted. In this case, the point safety factor is defined as follows:

Engineering Evaluation and Analysis
(1) Evaluating foundation bearing capacity Take the characteristic value (400 kPa) of the foundation bearing capacity of sericitized slate (Layer 2 and 3) as the standard. After excavation, the exposed area of the sericitized slate, contacting to the Frontiers in Physics | www.frontiersin.org January 2022 | Volume 9 | Article 807506 10 foundation of stilling basin, is shown in Figure 9. It can be seen that, under normal operation + earthquake working condition, in most areas, the vertical normal stress Szz on the top surface of sericitized slate is less than 400 kPa. Only in the small areas along the edges, the vertical normal stress Szz is greater than 400 kPa. Therefore, it can be regarded that the foundation bearing capacity of sericitized slate meets the engineering requirements. Similar research conclusions can also be obtained by analyzing the calculation results of other working conditions.
(2) Evaluating plastic zones The calculation results show that, under 3 working conditions of the frequent flood, energy dissipation design flood and check flood, the sericitized slate is in the elastic state and has no plastic zone. Under the working condition of normal operation + earthquake, as shown in Figure 10 (3) Evaluating point safety factor Figure 11 shows the calculated values of the point safety factor in the sericitized slate under 4 working conditions. It is found that the point safety factor in the sericitized slate changes with working conditions. In general, the point safety factors in the most areas of the sericitized slate are greater than 3.5, indicating   Frontiers in Physics | www.frontiersin.org January 2022 | Volume 9 | Article 807506 that these areas have high strength reserves and are not easy to be damaged. Only in the local area near the sidewall of the stilling basin (roughly the same as the plastic zone), the value of the point safety factor is close to 1.0, indicating that the strength reserve in these areas is insufficient.

CONCLUSIONS AND ENGINEERING SUGGESTIONS
In this study, a three-dimensional finite-difference numerical model was built based on the layout of the stilling basin and the geological conditions of the Kala hydropower station. By carrying out a series of numerical simulations under 4 working conditions, the following conclusions can be summarised: 1. Under 4 working conditions, the bank slopes and stilling basin are mainly in the compressive stress states. The tensile minor principal stresses are in a range of 2.317-3.321 MPa. However, the range of tensile major principal stresses is 0.118-0.133 MPa. In addition, it can be seen that there is a certain degree of tensile stresses in the shallow layers of the slopes on both banks, which are about 0-0.4 MPa. The maximum displacements are from the right bank towards the left bank. Under the normal operation + earthquake working condition, the maximum displacement of stilling basin is 3.02 mm, with its direction towards the right bank.  this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
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