考虑材料空间变异性的胶凝砂砾石坝地震响应分析

Seismic response analysis of hardfill dams considering material spatial variability

  • 摘要: 胶凝砂砾石材料的离析现象导致其材料参数具有较强的空间变异性。为研究材料参数空间变异性对胶凝砂砾石坝地震响应的影响,首先采用Cholesky分解法和拉丁超立方抽样方法生成材料参数的随机场;然后考虑材料参数自相关距离的影响,基于中心点离散法将随机场参数赋值给Oyuk坝有限元模型;最后通过对比随机场模型和确定参数模型的计算结果,揭示材料参数空间变异性对大坝地震响应的影响。研究结果表明,当考虑材料参数空间变异性时,胶凝砂砾石坝的地震响应呈现出正态分布规律。材料参数空间变异性对胶凝砂砾石坝应力响应的影响较为显著,而对位移响应和加速度响应的影响相对较小。随着变异系数的增大,大坝地震响应的概率密度曲线形状呈现出变低和变宽的趋势。确定参数模型得到的响应结果在随机场响应区间的位置存在差异,例如确定参数模型的加速度峰值响应在约2/3坝高以下位于响应区间的上限附近,而在约2/3坝高以上逐渐移动至响应区间的中间部位。受鞭梢效应影响,随机场模型计算得到加速度峰值标准差在坝体下部较低,在坝体上部迅速增大至较高水平。随机场模型计算得到的第一主应力峰值在坝踵附近表现为受拉,其建基面受拉区的分布范围约为确定参数模型的68.9%~114.4%。

     

    Abstract: Segregation in hardfill materials leads to significant spatial variability in material parameters. To assess the influence of spatial variability of material parameters on the seismic response of hardfill dams, this paper used the random field method. A Gaussian autocorrelation function was used to describe the spatial correlation of the material parameters. Spatially correlated random variables were generated using Cholesky decomposition combined with Latin hypercube sampling, and were subsequently assigned to finite elements through the central-point discretization method. Considering the non-negativity of material parameters, the random field parameters were assumed to follow a lognormal distribution, and three coefficients of variation for the elastic modulus—I(cov) = 0.1, 0.2, and 0.3—were considered. The horizontal and vertical autocorrelation distances were taken as 10 m and 2 m, respectively. The representative 100 m-high Oyuk Dam in Turkey was selected for seismic response analysis. Based on a sample-size convergence analysis, 300 random-field realizations were used for each I(cov) in the statistical analysis. For I(cov) = 0.2, the peak acceleration, relative displacement, and principal stress responses are distributed within certain ranges and approximately follow normal distributions. The coefficients of variation of the peak horizontal acceleration at the dam crest and the peak major principal stress at the dam heel are 0.009 and 0.090, respectively, indicating that the spatial variability of material parameters has a markedly greater effect on the variability in principal stress than on that of displacement and acceleration. As I(cov) increases, the probability density curves of the seismic responses become progressively lower and broader. The mean horizontal relative displacements at the dam crest are 2.56, 2.59, and 2.64 cm for I(cov) = 0.1, 0.2, and 0.3, respectively, showing a gradual increase with I(cov). In contrast, the mean peak major principal stresses at the dam heel are 1.99, 1.96, and 1.94 MPa, while the mean peak minor principal stresses at the dam toe are 4.43, 4.38, and 4.30 MPa, respectively, showing a gradual decrease with I(cov). For I(cov) = 0.1, the probabilities that the horizontal relative displacement at the dam crest, the peak major principal stress at the dam heel, and the peak minor principal stress at the dam toe obtained from the random-field model exceed the corresponding results from the deterministic parameter model are 75.63%, 45.42%, and 46.99%, respectively. Regarding the spatial distribution of the seismic response, the peak horizontal accelerations along the dam centerline, predicted by both the random-field and deterministic-parameter models, generally increase with dam height. Below about two-thirds of the dam height, the deterministic results generally lie near the upper bound of the random results; above this elevation, they gradually shift toward the center of the random-result range. The standard deviation of the peak horizontal acceleration obtained from the random-field model remains relatively low below half of the dam height. It increases rapidly above this elevation due to the whipping effect. Along the dam-foundation interface, the peak major principal stress distributions obtained from the random-field and deterministic-parameter models exhibit generally consistent trends. The maximum tensile stress occurs near the dam heel, whereas the central portion of the interface is in compression. The deterministic parameter model gives a tensile-zone length of 36.7 m along the dam-foundation interface. When material spatial variability is considered, the tensile-zone length ranges from 25.3 to 42.0 m, corresponding to approximately 68.9%–114.4% of the deterministic result. In addition, the standard deviation of the peak major principal stress at the dam heel is 0.31 MPa, which is markedly larger than that at other locations along the dam-foundation interface. The results show that parameter spatial variability has a non-negligible influence on the statistical characteristics and spatial distribution of the seismic response of hardfill dams.

     

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