Expected Effectiveness Evaluation and Optimization Methods of Slope Site Investigation Program
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摘要: 目前的勘探方案预期效果评价指标常未能反映物理过程且参数较难确定.此外，勘探方案优化框架中的勘探点布置策略往往依赖位置关系并需事先确定勘探范围.为解决上述问题，以不排水抗剪强度参数为例，提出并采用安全系数的均方根误差折减率期望（expected reduction rate of the root mean square error，ERRS）量化因融合参考勘探数据而导致的安全系数评估结果向参考安全系数集中效果的期望提升程度，并将其作为勘探方案预期效果评价的指标.此外，结合该指标和贪心算法构建了以优化勘探位置和数量为目的的勘探方案优化框架.ERRS指标计算过程采用乔列斯基分解中点法和改进贝叶斯更新方法离散参数完全及条件随机场实现，并基于多重二阶响应面代理模型替代确定性空间变异边坡稳定性分析，有效提高指标计算精度和效率.不排水饱和黏土边坡案例显示：提出的ERRS指标能够在无需确定复杂参数的情况下，获得与其他指标接近的评价结果；所构建的勘探方案优化框架能够在不事先确定勘探范围的情况下，得到指定勘探数量下更优的勘探点布置，进而获得更节省成本且预期效果较好的勘探方案.提出的指标和优化框架可为实际边坡工程场地勘探方案评价及优化设计提供参考.Abstract: Current evaluation indicators for depicting the expected effectiveness of exploration program often fail to reflect physical process, and the involved parameters are difficult to determine. Besides, the exploration layout strategies in existing optimization frameworks usually rely on the positional relationship, and require determination of the investigation range in advance. To solve the above problems, taking the undrained shear strength parameter as an example, in this paper it proposes and employs the expected reduction rate of the root mean square error (ERRS) to quantify the expected degree of improvement in the concentration effect of factor of safety assessment results towards the reference factor of safety due to the incorporation of reference exploration data, which serves as an indicator to evaluate the expected effectiveness of exploration program. Additionally, a framework for optimizing exploration program is constructed using this indicator in conjunction with a greedy algorithm, aimed at optimizing the locations and number of exploration points. The ERRS indicator calculation process employs the Cholesky decomposition-based midpoint method and the improved Bayesian updating method to discretize both unconditional and conditional random fields. The multiple second-order response surface is used as a surrogate model to replace the deterministic slope stability analysis of spatially variable slopes, significantly enhancing the precision and efficiency of the indicator calculation. Example of undrained saturated clay slope shows: the proposed ERRS indicator can achieve evaluation results close to other indicators without the need to determine complex parameters; the constructed exploration program optimization framework can provide an improved arrangement of exploration points under a specified number of explorations, resulting in more cost-effective and better-performing exploration program without the need to predefine the exploration range. The proposed indicator and optimization framework can serve as a reference for evaluating and optimally designing exploration program in practical slope engineering projects.
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图 2 勘探方案评价流程及ERRS计算框架
Fig. 2. Evaluation process of investigation program and ERRS calculation framework
图 5 不排水抗剪强度均值场和先验随机场的一次典型实现
a. 不排水抗剪强度均值场; b. 典型先验随机场实现
Fig. 5. Mean field and one typical implementation of prior random field of undrained shear strength
图 6 边坡安全系数随潜在滑动面数量的变化
Fig. 6. Variation of the factor of slope safety with the number of potential slip surfaces
图 7 不同方法计算的边坡安全系数的比较
Fig. 7. Comparison of the factors of safety calculated by different methods
图 8 两个典型的等距布置勘探方案
a. 勘探方案①; b. 勘探方案②
Fig. 8. Two typical equidistant arrangement investigation programs
图 9 安全系数先验均值随先验随机场实现数量的变化
Fig. 9. Variation of the prior mean of factor of safety with the number of prior random field implementations
图 10 ERRS随参考随机场实现数量的变化
Fig. 10. The variation of ERRS with the number of reference random field implementations
图 11 不同勘探方案的后验随机场实现均方根误差云图
a. 勘探方案①; b. 勘探方案②
Fig. 11. RMSE cloud map of posterior random field implementation for different investigation programs
图 12 不同方法计算的后验安全系数比较
Fig. 12. Comparison of posterior factor of safety calculated by different methods
图 13 不同评价指标随单个勘探点勘探位置的变化
Fig. 13. The variation of different evaluation indicators with investigation position of single investigation point
图 14 ERRS随不同因素的变化
a. 随第k个勘探位置Lk; b. 随勘探数量
Fig. 14. The variation of ERRS with different factors
图 16 不同勘探数量下的最佳勘探点布置(小范围等距框架)
a. 勘探数量为1; b. 勘探数量为2; c. 勘探数量为3; d. 勘探数量为4
Fig. 16. Optimal investigation point layout for different numbers of investigation point quantities (small-range equidistant framework)
图 17 不同勘探数量下的最佳勘探点布置(大范围等距框架)
a. 勘探数量为1; b. 勘探数量为2; c. 勘探数量为3; d. 勘探数量为4
Fig. 17. Optimal investigation point layout for different numbers of investigation point quantities (large-range equidistant framework)
图 18 不同优化框架下ERRS随勘探数量的变化
Fig. 18. The variation of ERRS with investigation point quantity for different optimization frameworks
表 1 随机场模型参数取值
Table 1. Parameter values of random field model
参数 模型 参数取值 土体重度γ 常量 20 kN/m3 地面土体不排水抗剪强度su0 常量 14.669 kPa 趋势分量b 常量 0.3 随机波动分量
w(x, z)二维平稳高斯随机场 均值：0
标准差：0.24
水平波动范围：38 m
垂直波动范围：3.8 m
自相关函数类型：指数型
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