Stability Analysis of Tailrace Outlet Slope at Right Bank of Kala Hydropower Station

Abstract

The tailrace outlet slope located on the right bank of the Kala hydropower station represents a typical bedding slope characterized by a moderate to large dip angle. The excavation at the toe of the slope create favourable conditions for rock mass deformation and failure. In order to evaluate the slope’s stability, a thorough investigation and analysis of the engineering geological conditions are conducted. Additionally, the stress-strain characteristics resulting from the slope excavation are simulated utilizing the discrete element software 3DEC. Finally, the strength reduction method is used to evaluate the safety factor of the slope. The research results show that the stability of the slope is notably influenced by the presence of medium and large dip structural planes, the cutting excavation at slope toe can lead to deformation and localized block instability. The implementation of the system pre-stressed cables effectively increases the safety factor of the slope and ensures the stability of the tailrace outlet slope. These findings will provide valuable references for the design of similar rock slopes.

1 Introduction

The construction of large-scale hydropower projects in southwestern China has triggered considerable concerns regarding the stability of high and steep rock slopes. In response to this issue [1], Zheng Yingren, Song Shengwu, and Huang Runqiu have conducted a comprehensive study on high rock slope stability and have identified several common failure mechanisms associated with these slopes [2,3,4]. However, it is worth noting that rock slopes exhibit diverse characteristics based on their specific geological environments. In mountainous regions, rock slope deformation and failure caused by excavation is a significant geological challenges. Amongst these challenges, layered rock slopes are highly susceptible to collapse and failure as a result of excavation under the influence of weak structural planes such as joints, bedding planes and faults [5]. Therefore, the stability evaluation of the layered rock slope is particularly important.

The stability analysis of slopes typically utilizes two main methods: the strength reduction method and the limit equilibrium method (LEM) [6]. The LEM has been widely employed in civil projects due to its simplicity and effectiveness in assessing slope stability. However, this method still has certain limitations. For example, it does not take into account the deformation and stress characteristics of rock masses within slopes. To address these limitations, the strength reduction method based on numerical simulation can be employed, which provides a more comprehensive assessment of slope stability [7].

The Kala Hydropower Station, situated in the middle reach of the Yalong River, is the seventh cascaded development station. It serves primarily for power generation, with an installed capacity of 1020 MW. The reservoir maintains a normal water level of 1,987 m and has a storage capacity of 2.4 × 10⁹m³. The right bank is a prototypical bedding slope with a dip angle 55~65°. Due to intricate geological and tectonic processes, various unfavorable geological features are present, including faults (f₁₂₄, f₁₉₈, f₁₉₉, f₂₀₁ et al.), carbonaceous slate interlayer, and other weak geological structural planes within the tailrace outlet slope. Such unfavorable features contribute to the poor stability conditions of the slope, and excavation activities in the lower section of the slope further intensify the likelihood of rock mass deformation and failure [8]. Therefore, it becomes essential to evaluate the stability of the tailrace outlet slope. This study utilizes the strength reduction method to analyze the stability of the tailrace outlet slope at the Kala Hydropower Station. The findings of this analysis can provide valuable insights for the design and construction of the slope.

2 Geological Background

2.1 Engineering Geology

The outlet of the tailrace tunnels is characterized by a natural slope that exhibits significant height and steepness, as well as a complex geological composition. The bedrock in the study area is composed of metamorphic rock belonging to the Zagunao group of Upper Triassic(T3Z2). The exposed rock layers consist mainly of sandy slate, metamorphosed sandstone, marble, and carbonaceous slate structures with interbedded characteristics. The rock mass within the slope generally exhibits weak weathering, and the strongly unloaded rock mass extends horizontally to a depth of approximately 10~20 m, as shown in Fig. 1.

The rock formation within the slope exhibits a dip direction ranging from N55°E to N65°E and a dip angle of 55~65°, while the slope on the right bank follows a dip direction of N50°E to N60°E with a slope angle ranging from 30° to 45°. Within the slope, numerous faults have developed, with those striking NW to NWW being the most prominent and extensive, including f₁₂₄, f₁₉₈, f₁₉₉, f₂₀₁ and others. Additionally, two primary sets of joints can be observed: the first set features orientations ranging from N65°E to N75°E with a southeast inclination angle of 85° to 90°, while the second set exhibits orientations from N30°W to N35°W with a southwest inclination angle of 25° to 30°.

Fig. 1.

The geological profile of the tailrace outlet slope.

2.2 Design of the Tailrace Outlet Slope

The tailrace outlet slope consists of two main parts: the cut slope and the natural slope. The cut slope has a maximum height of 112.5 m, extending from an elevation of 2015 m to 1902.5 m, as shown in Fig. 2(a). To ensure stability, different slope ratios are adopted. For elevations above 1950 m, a slope ratio of 1:0.5 is used. From 1950 m to 1930 m, a slope ratio of 1:0.3 is applied. Below 1930 m, the slope ratio becomes vertical. Additionally, benches, each 3 m wide, are established every 20 m in the cut slope. The natural slope above the cut slope has a height exceeding 500 m.

To safeguard and reinforce the slope, a designed protection and reinforcement scheme comprising three key elements is implemented, as illustrated in Fig. 2(b). Firstly, a layer of 15 cm of shotcrete is uniformly applied to all newly excavated surfaces. Secondly, rock bolts are placed at 2-m intervals to provide shallow support, with the length of the bolts ranging from 6 to 9 m. And thirdly, pre-stressed cables are employed to control slope deformation and ensure overall stability. These cables are designed with a capacity of 2000 kN, with lengths ranging from 40 to 50 m, and spacing set at 4 m × 4 m.

Fig. 2.

The excavation plane view and support scheme of the tailrace outlet slope.

3 Numerical Models and Boundary Conditions

3.1 The Discrete Element Model

Based on the actual construction sequence, a simulation of the construction process is carried out using the 3DEC software, as shown in Fig. 3. The model is designed with dimensions of 660 m in the X direction, perpendicular to the slope strike, 300 m in the Y direction, and a vertical direction height of 650 m. Normal displacement constraints are applied on boundaries of left, right, frontal, and back, the bottom boundary is limited by a fixed constraint, and the top boundary is free.

Fig. 3.

Numerical calculation model.

3.2 Calculation Parameters

Joint elements are utilized to simulate the geological structural planes, such as the carbonaceous slate interlayer J_C7, joints J₄₇, J₄₈, J₁₁₉, and faults f₁₈₉, f₁₉₈, f₁₉₉ et al. The constitutive model employed for these structural planes follows a linear Coulomb shear-strength criterion, which sets limits on the shear force acting at each interface node. The rock mass is considered as an elastic-plastic material, employing a Mohr-Coulomb model.

Accurate estimation of the mechanical parameters of both the rock mass and structural features is very important for the stability analysis of the slope. In this study, the rock mass of the tailrace outlet slope is classified into four grades based on weathering characteristics, as depicted in Fig. 4. The strength parameters of the rock mass and faults are determined through in-situ testing and similar construction experience, which are listed in Table 1 and Table 2 [9].

Fig. 4.

Classification of rock mass.

Table 1. Mechanical parameters for the rock mass.

Table 2. Mechanical parameters for structural planes.

4 Analysis Results

4.1 The Deformation Characteristics Resulting from Excavation

The construction process, including excavation and the installation of reinforcements, is accurately simulated based on the actual work carried out on the slope. Fig shows the comparison of deformation characteristics after excavation under the conditions of no support and applied support. As shown in the Fig. 5, the deformation of the rock mass is primarily controlled by weak structural planes. With the cutting excavation at slope toe, the fault f₁₉₈ will be exposed on the excavation face, and the rock mass on both sides of the fault has obvious discontinuous deformation.

Fig. 5.

The deformation Characteristics after excavation.

From Fig. 5(a), there is an unstable block, the bottom slip plane is fault f₁₉₈, the rear edge is fault f₁₉₉, and the upstream and downstream side boundaries are joint J₄₇ and J₄₈ respectively. Without considering any support measures, this block presents significant risks of instability and failure, thereby compromising construction safety. However, by implementing the reinforcement measures depicted in Fig. 2(b), the shear deformation along the fault f₁₉₈ is effectively controlled, and the maximum deformation induced by excavation is generally within 10 mm.

4.2 Slope Stability Analysis

The strength reduction method [10] is used to analyze the stability of the slope after reinforcement with pre-stressed cables:

$$ \left. {\begin{array}{*{20}c} {c_{t} = c/F_{t} } \\ {\varphi_{t} = \tan^{ - 1} (\tan \varphi /F_{t} )} \\ \end{array} } \right\} $$

(1)

where Ft is strength reduction factor.

The strength reduction method employed in this study involves adjusting the shear strength of the structural plane by modifying the reduction factor Ft. Subsequently, a stability analysis of the slope is conducted using the Discrete Element Method. The reduction factor serves as the safety factor when the slope reaches a critical failure state. In this paper, the critical failure state is determined based on the plastic yielding zone connection criterion and the displacement mutation criterion [11].

Figure 6 shows the deformation velocity of the slope under critical instability, its show that the deformation velocity of the huge potential block composed of structural planes f₁₉₈, J₄₇ and J₄₈ is significantly higher than that of other parts. To analyze the stability of this block, three observation points (P1, P2, and P3) are set along its boundaries. Figure 7 presents the relationship curves between the displacements of the observation points and the strength reduction factor. Notably, the displacement of P2 experiences a sharp increase when the strength reduction factor exceeds 1.25. Therefore, according to the displacement mutation criterion, the safety factor of the block composed of structural planes f₁₉₈, J₄₇ and J₄₈ can be defined as 1.25.

Fig. 6.

The deformation velocity of the slope under critical instability.

Fig. 7.

Relation curve of displacements of the observation points and strength reduction factors.

Figure 8 shows the development of the plastic yielding zone on the structural planes throughout the process of strength reduction. Examination of the Fig. 8 reveals that plastic yielding failure initially occurs on the structural planes near the rear edge of the block. As the reduction factor increases, the plastic yielding zone gradually extends towards the front edge of the block. At a strength reduction factor of 1.30, the plastic zone on the bottom slip plane f₁₉₈ becomes fully connected. Therefore, based on the criterion of plastic yielding zone connection, the reduction factor of 1.25 from the previous calculation step is defined as the safety factor for the block.

Fig. 8.

The development of the plastic yield zone (shown in blue) on the structural planes with the strength reduction factors.

4.3 Stability Evaluation and Guiding to Construction

The stress-strain characteristics of slope excavation indicate that cutting the slope toe will cause sliding failure along fault f₁₉₈ without any support. However, implementing pre-stressed cable support can significantly enhance the stability of the slope and effectively restrict shear displacement within weak structural planes. With the installation of this support system, the safety factor of the tailrace outlet slope reaches 1.25, thereby satisfying the minimum safety factor requirement specified in the code [12]. Therefore, the current reinforcement scheme can be considered rational and dependable. Nevertheless, it is crucial to maintain a vigilant monitoring of geological conditions throughout the slope excavation process and carefully assess their potential impacts on slope stability.

5 Conclusions

This study aims to investigate and analyze the deformation characteristics and stability of a complex bedding slope located at the outlet of the tailrace tunnels in the Kala Hydropower Station. The following conclusions can be drawn:

• (1) The overall stability of the tailrace outlet slope mainly depends on the huge potential block formed by structural planes f₁₉₈, J₄₇ and J₄₈. The excavation of the slope toe has resulted in the removal of the rocks that previously acted as a stabilizing factor, leading to a significant deterioration in slope stability.

• (2) On the basis of ensuring the safety of the supporting structure itself, the pre-stressed anchor cables can effectively restrict the shear deformation of the block along the fault f198, thereby improving the overall stability of the slope.

• (3) The stability of the slope is assessed using the strength reduction method, with a comparison made between the calculation results obtained from two failure criteria: the plastic yielding zone connection criterion and the displacement mutation criterion. The results indicate that the safety factor of the huge block reinforcement by pre-stressed anchor cables is 1.25, and the stability of the block meets the requirements of the code, which can ensure the safety of the slope.