A Non-intrusive Stochastic Method For Slope Reliability In Hydroelectricity Engineering

A large number of hydropower projects in southwestern China have been built, under construction and planning, in which the height of most of slopes is up to hundreds of even over one thousand meters. Engineered slope failures will endanger the engineering safety, and result in enormous casualties and huge economic losses. Thus, the stability of high-steep slopes has a very important effect on the safety of the dam-reservoir system. Although the causes for the occurrence of slope failures are very complicated, they are always closely related with the uncertainties in geological conditions, boundary conditions, loads, performance degradation of anchorage and drainage systems, etc. The spatial variability of rock and soil properties, which is one of the main sources of uncertainties in slope engineering, and performance degradation of anchorage system for in-service slopes are the main reasons for causing slope failure. However, the discretization of anisotropic cross-correlated non-Gaussian random fields for characterizing the spatial variability of rock and soil properties has not been sufficiently investigated. The reliability problems of heterogeneous multi-layered soil slopes with a consideration of multiple spatially correlated soil properties are not well addressed. The existing commercial finite element software packages cannot be utilized adequately in slope reliability analysis. The time-dependent reliability problems of anchored rock slopes considering corrosion effects of pre-stressed rock bolts and cables have not been studied extensively. Few attempts have been made to study reliability problems of complex three-dimensional rock slopes in practice. To address the above five key scientific issues, extensive studies are performed in this thesis. The implementation details and some conclusions are summarized as follows:(1) The non-intrusive stochastic analysis theory for slope reliability is developedThe Karhunen-Loeve expansion method and extended Cholesky decomposition technique for the discretization of anisotropic cross-correlated non-Gaussian random fields are developed. A stochastic response surface method for slope reliability analysis involving cross-correlated non-normals is proposed. The closed-form expressions for fourth to sixth order Hermite polynomial chaos expansions involving any number of random variables are derived. The polynomial chaos expansion method based on the linearly independent probabilistic collocation method and Latin hypercube sampling method is proposed. The analytical expressions for statistical moments of output responses and Sobol’s indices of random variables and spatially varying variables are formulated, respectively. The research outcomes enrich non-intrusive reliability analysis theory in slope engineering.(2) A non-intrusive stochastic finite element method for slope reliability analysis considering spatial variability of soil properties is proposedThe flowchart of finite element analysis of slope stability based on ABAQUS and GEOSTUDIO software packages using a batch mode is illustrated. The reliability problems of a saturated clay slope and an unsaturated soil slope considering multiple spatially correlated soil properties are studied, respectively. There exists a critical coefficient of variation for slope reliability analysis considering spatially varying undrained shear strength parameter, which depends on the value of factor of safety. The proposed method does not require the user to modify existing deterministic finite element codes. By this means, the complex deterministic finite element analysis of slope stability is deliberately decoupled from reliability analysis. The proposed method improves the computational efficiency significantly in comparison with the direct Monte-Carlo simulation and properly evaluates the slope reliability at low probability levels (i.e., pf<0.001) with the consideration of spatial variability of soil properties.(3) A multiple second-order response surface method for efficient parametric sensitivity analysis considering effect of autocorrelation functions (ACFs) is proposedThe scales of fluctuation, autocorrelation distances, coefficients of variation, and cross-correlation coefficients of soil shear strength parameters are systematically summarized, which lays the groundwork for characterizing the spatial variability of soil properties. The effects of five theoretical ACFs (i.e., single exponential, squared exponential, second-order Markov, cosine exponential and binary noise ACFs) on the slope reliability are explored. Among the selected five ACFs, the failure probability associated with the commonly-used single exponential ACF is underestimated. The difference in the failure probabilities using the other four ACFs is generally minimal. It will lead to an overestimation of slope reliability level and unconservative slope designs if the single exponential ACF is used for modeling the spatial correlation of soil properties. In addition, the difference in the failure probabilities associated with the five ACFs depends on the scales of fluctuation and the coefficients of variation of shear strength parameters, the cross-correlation coefficients between shear strength parameters. In general, the ACFs have a more significant effect on the reliability of a heterogeneous slope than that of a homogeneous slope.(4) A multiple stochastic response surface method for system reliability analysis of slopes considering spatial variability of soil properties is proposed A new approach for the identification of representative slip surfaces considering the spatial variability of soil properties is developed. The system reliability problem of multi-layered soil slopes considering the spatial variability of soil properties is studied. The capacity and validity of single-response surface method for slope system reliability analysis in spatially variable soils based on finite element analysis of slope stability are addressed. The effects of spatial variability, variability of shear strength parameters and cross-correlation between shear strength parameters on the system reliability of slopes are explored from a system analysis point of view. The effect of the number of representative slip surfaces on the system failure probability is dominated by that of the failure probability of each representative slip surface. The variability of shear strength parameters and the cross-correlation between shear strength parameters affect the number of representative slip surfaces, the failure probability of a given slip surface and the system failure probability in a consistent manner. The multiple stochastic response surface method can effectively overcome the complexities associated with system reliability analysis of slopes considering the spatial variability of soil properties, while the single-response surface method associated with finite element analysis of slope stability cannot accurately evaluate the system reliability of slopes with spatially correlated soil properties.(5) The time-variant system reliability and serviceability reliability of anchored rock slopes incorporating rock bolt corrosion effect are exploredThe time-dependent models for tension force at the free length and shear resistance at the bolt-grout interface of fixed length of the rock bolt are established, respectively. The applicability of corrosion rate model for the rock bolt is validated by the corrosion experimental data. The time-variant system reliability of anchored rock slope stability considering rock bolt corrosion effect has been clarified. An efficient approach for determining the maximum allowable deformation of slopes is suggested. The time-variant serviceability reliability of anchored rock slopes has been preliminarily elucidated. In the early service period of the anchored rock slope, the corrosion of rock bolts has a slight influence on the anchored force and failure probability of slope. In contrast, the effect of corrosion on the anchored force and failure probability of slope becomes more significant in the later service period. In addition, an approximate linear relationship exists between the logarithm of the failure probability for slope deformation, log(pf), and the maximum allowable deformation of the slope, and this linear relationship becomes more obvious as the failure probability of slope decreases. (6) A non-intrusive stochastic finite difference method for reliability analysis of complex three-dimensional slope stability is proposedThe abutment slope at the left bank of Jinping I Hydropower Station is taken as a typical case, the effects of slope excavation during construction, reinforcement measures such as pre-stress cables and anti-shear concrete plugs on the slope deformation, stability and reliability are investigated in detail, respectively. The proposed non-intrusive stochastic finite difference method can improve the computational efficiency greatly and provide an effective tool for solving reliability problems of complex three-dimensional slopes in hydroelectricity engineering. The parametric sensitivity analysis results demonstrate that the slope stability mainly depends on the shear strength of rock masses of sliding resistance when the rock masses above the elevation of1810m are excavated, while the slope stability is significantly affected by the shear strength of the sliding surfaces of the deformed and cracked rock mass when the rock masses below the elevation of1810m are excavated. The shear-resistant concrete plugs play a more important role in controlling the slope deformation and improving the slope reliability than the pre-stressed cables. Additionally, the excavation disturbance during the construction period also affects the slope reliability significantly.