This study proposes a High-order Shape Functions-Based Karhunen-Lo & egrave;ve (HSFKL) method to efficiently and accurately simulate irregular, multi-dimensional geotechnical random fields. Unlike conventional KL expansions relying on global polynomials, HSFKL employs high-order shape functions as localised basis functions, naturally adapting to complex and irregular geometries, reducing expansion dimensionality, and facilitating subsequent reliability analysis. By combining Lagrange interpolation with Gauss quadrature and tensor-product techniques, the method converts multi-dimensional integral eigenvalue problems into tractable local element matrix operations, significantly improving computational efficiency. Numerical results indicate that the combination of Legendre shape functions and Serendipity elements is optimal, achieving a 23.2% reduction in expansion terms, a 44.0% decrease in computation time, and up to an 88.5% reduction in discretization error compared with other approaches. Large-scale 3D slope simulations confirm that discretization accuracy critically dictates failure probabilities and mechanisms. To balance precision with computational cost, a 1% covariance error threshold is recommended. Overall, HSFKL establishes a robust and scalable framework, enabling dimensionally efficient reliability analysis for geotechnical systems with significant spatial variability and complex geometries.

In the Karhunen–Loève (KL) series expansion framework for random field discretization, computational errors in common KL methods (e.g., the orthogonal series expansion (OSE) and Jacobi–Legendre–Galerkin (JLG) methods) arise not only from the truncation error due to the number of retained terms (M), but also from eigensolution accuracy related to the number of Gauss integration points (N1D GP) and basis function terms (N1D). The OSE method with a full tensor-product construction and the JLG method with total-order truncation were employed for separable and nonseparable autocorrelation functions, respectively, thereby revealing the decoupled effects of the number of N1D GP and the number of N1D on the eigenvalues and eigenfunctions. The results indicate that the global covariance error may not fully capture local reconstruction errors within the physical domain. For N1D ≥ M + 2, N1D GP primarily influences eigenvalues (λ), while N1D dictates fluctuations in eigenfunctions (f(x)). Accordingly, parameter selection criteria are established for one-dimensional and multi-dimensional random fields, respectively. Engineering case studies indicate that eigensolution accuracy affects the range of variation in load-settlement curves for shallow foundations and that the tilting failure mode of a pile group is particularly sensitive to it. Insufficient accuracy of the eigensolution causes drifts at the most unfavorable failure points and shifts in parameter sensitivity rankings within pile group systems. Furthermore, the convergence pattern of eigensolution errors directly maps onto the convergence behavior of the reliability assessment for pile group systems. This research provides a vital theoretical basis and accuracy parameter selection benchmarks for geotechnical reliability analysis within the KL framework.

Fluctuations in reservoir water levels induce cyclic loading, which alters the mechanical properties of slip zone soils and consequently triggers the step-like deformation of landslides. This study focuses on slip zone soils from the No. 3 branch tunnel of the Huangtupo landslide in the Three Gorges Reservoir Area (TGRA), China. Stress-controlled cyclic triaxial tests were conducted to investigate the cyclic weakening behavior, while strain-controlled cyclic triaxial tests, scanning electron microscopy, and numerical simulations were employed to elucidate the underlying mechanisms. The results showed that cyclic loading slightly reduced the shear strength of slip zone soil specimens under constant consolidation pressure, deformation increased with cyclic amplitude, and cumulative axial strain increased rapidly and then stabilized. The dynamic shear modulus (G) initially decreased sharply, followed by a slight increase or stable fluctuation within a certain range. The damping ratio (D) first decreased and then gradually fluctuated within a stable range. The failure strain range of the slip zone soils was determined to be 3.5%–7.8% of cumulative axial strain. In stress-controlled cyclic tests, the increase in G and the stage-wise changes in stiffness and energy dissipation were caused by structural changes in the soil. The cyclic weakening behavior is divided into three stages: initial pore pressure buildup and structural weakening, structural degradation associated with pore development and particle contact transformation, and re-hardening induced by pore filling. These findings provide a theoretical basis for understanding the staged deformation characteristics and time-dependent effects of reservoir-related landslides in the TGRA.

Pile groups with members of different lengths can mitigate differential settlement among foundation piles, prevent basin settlement, and ensure consistent reliability indicators across individual piles. This paper presents an approach for analyzing the reliability of pile groups with dissimilar pile lengths in spatially variable expansive soils under rainfall. The variation of soil matric suction with depth under rainfall infiltration conditions was analyzed by numerical simulation software. The Karhunen-Lo & egrave;ve (KL) expansion method is used to discretize random fields. The pile-pile and pile-soil interactions in a pile group with dissimilar pile lengths, and the influence of the reduction of matric suction on the ultimate bearing capacity of the piles are analyzed using the modified load transfer method (LTM). The first-order reliability method (FORM) is employed to solve the reliability indices of each pile in a pile group, and the sequential component method (SCM) is adopted to estimate the reliability index of the pile group. Parametric studies show that increasing rainfall intensity and duration reduce the reliability indices of both individual piles and the pile group.

Pile foundations serve as fundamental structural elements in geotechnical engineering. Accurate prediction of pile bearing capacity is crucial for structural safety and design efficiency in foundation engineering. This study presents a probabilistic framework for evaluating eight bearing capacity prediction methods, incorporating uncertainty quantification through statistical analysis of model factors and resistance factors within the Load and Resistance Factor Design paradigm. The investigated methods encompass five traditional methods (Analytical Formula Method, Empirical Parameter Method, Cone Penetration Test, Load Transfer Method, and Numerical Simulation Method) and three machine learning (ML) methods (Long Short-Term Memory (LSTM), Convolutional Neural Network, and Temporal Convolutional Network). A comprehensive database comprising 474 static load test results from vertically loaded piles in Anhui, China was established to facilitate robust method evaluation. The assessment incorporates six complementary performance metrics: coefficient of determination between predicted and measured bearing capacities; coefficient of variation, 20% accuracy level, inter-percentile range of cumulative distribution functions, and 95% confidence intervals of model factors; and efficiency ratios. The results indicate that the LSTM outperforms all other methods in predictive accuracy. Furthermore, ML approaches consistently surpass traditional methods across all evaluation metrics. These findings reveal data-driven techniques' potential to improve pile capacity prediction reliability amidst geotechnical uncertainties.

In geotechnical engineering, precise probabilistic assessment of slope stability is crucial for risk management and the safe operation of engineering projects. To perform probabilistic assessments of slopes accurately and efficiently, six machine learning (ML) algorithms, including Logistic Regression (LR), Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF), Extremely Randomized Tree (ERT), and Gradient Boosting Tree (GBT), are adopted to establish surrogate models for the relationship between a slope's safety factor and soil's shear parameters. Latin Hypercube Sampling (LHS) is employed to generate training samples for constructing surrogate models using ML algorithms. Adaptive Synthetic Sampling (ADASYN) is used to balance the number of samples of failure and safety classes by generating synthetic samples for the failure sample set, and a Genetic algorithm (GA) is used to optimize the hyper-parameters of ML and ADASYN algorithms to improve the accuracy of the surrogate models. Two criteria are proposed to measure the accuracy of surrogate models built using ML with Genetic-ADASYN algorithms, and a formula is presented to estimate the optimal number of samples for the training set. Based on the surrogate models, reliability indices and failure probabilities of slopes can be readily estimated using the Monte Carlo Simulation Method (MCSM). Case studies of five slopes with different complexities are adopted to illustrate the proposed method for the probabilistic analysis of slope stability and to compare the accuracy of surrogate models built using different ML algorithms. Results show that the Genetic-ADASYN algorithm can significantly improve the accuracy of surrogate models built using ML algorithms, and among the six ML algorithms, GBT is the best ML algorithm due to its generalizability and accuracy in slope stability prediction problems. The research findings can provide a reference for risk assessment of slope engineering and help to improve the accuracy and efficiency of probabilistic slope stability analysis.

Soil has spatial variability, which means that soil properties at two spatial points are correlated but different. Reliability analysis and risk evaluation of vertically loaded pile in spatially variable soils is important for both the safety evaluation and optimal design of the pile. In this study, the conditional random field theory is adopted to simulate the random fields of soil parameters, and the Karhunen-Lo & egrave;ve (KL) expansion method is employed to discrete the random fields. Based on the formulas of unconditional Karhunen-Lo & egrave;ve (UKL) expansion method, calculation process and formulas of two conditional KL expansion methods (CKL1 and CKL2) are derived. A hybrid method, FORM-CKL-LTM, is proposed to carry out reliability analysis for pile's stability. In FORM-CKL-LTM, the first-order reliability method (FORM) is used to calculate the reliability index of the pile, the conditional Karhunen-Lo & egrave;ve (CKL) is adopted to discrete random fields of soil parameters, and the load transfer method (LTM) is employed to calculate the ultimate bearing capacity of the pile. By applying FORM-CKL-LTM to a case study of a vertically loaded pile, features of the CKL1, CKL2, and FORM-CKL-LTM are illustrated. The two CKLs can make full use of the measured soil properties at different observation points near the pile. CKL1 and CKL2 are superior to UKL because the first two methods can constrain the fluctuation of the discrete values of random field near each observation point, and CKL1 is better than CKL2 because CKL1 can force the fluctuation of random field to be zero at the observation points. The reliability index of the pile depends on the locations and number of observation points. Optimal design of geotechnical investigation points is necessary for the safe evaluation and economical design of piles in spatially variable soils.

To obtain the reliability index or failure probability of a slope, several values of limit state function (LSF) need to be computed. For complex slopes, the LSF of slope stability analysis is usually an implicit function, which is hard to calculate. This study proposes an improved response surface method (RSM) where only one response surface function (RSF) is generated. The Least squares support vector regression (LSSVR), Radial basis function neural network (RBFNN), and Gaussian process regression (GPR) are used as the RSF of the actual LSF, and a method for locating the sampling centre for generating random samples using Latin Hypercube Sampling is presented. Benefiting from the improved sampling method and the flexibility and global fitting properties of the LSSVR, RBFNN, and GPR, the RSF needs to be generated only once and it can simulate the actual LSF very well even for highly nonlinear LSF. Based on the RSF using LSSVR, RBFNN, or GPR, the Monte Carlo simulation method (MCSM) is adopted to perform reliability analysis to assure the accuracy of reliability index. The excellent performance of the proposed RSM is verified by four examples, including a problem with highly nonlinear LSF and three slope examples with increasing complexities.

As a complement to the longitudinal wave-based method, the flexural wave-based method has been used to evaluate the pile integrity. This paper reveals dispersion and attenuation characteristics of F-(flexural) waves in piles and emphasizes the importance of capturing the axial velocity response for evaluating the pile integrity. The characteristics of F-wave propagation in piles and the transient dynamic response at the pile-top in the time domain are investigated to provide guidance for pile integrity testing. The pile is simplified as an elastic TM (Timoshenko) beam and the surrounding soil is simplified as a Winkler foundation. The dispersion and attenuation relations of the first propagating F-wave in the free and embedded piles are analyzed. The transient axial and lateral velocity responses of intact and defective (necking, bulging and mud clamping) piles in the time domain are obtained using the FDM (finite difference method) when the pile is subjected to a transient lateral excitation afterwards. The effects of pile and soil properties on the transient F-wave propagation and the dynamic response of the pile-top are investigated through a comprehensive parametric study. The finite difference solution based on the pile-soil model established in this paper is validated through comparisons with the 3D finite difference solution and experimental results. It is found that the stiffness of the surrounding soil has a great influence on the dispersion and attenuation characteristics of low-frequency F-wave. Shorter pulse durations or larger pile diameters can result in stronger reflections at the pile-tip; however, they can also enhance the thickness-shear mode and lead to the appearance of high-frequency interference. Reflections from the pile-tip or defects are more pronounced in axial velocity than in lateral velocity, so it is recommended that axial velocity should be collected in addition to lateral velocity during pile testing using the F-wave-based method. A method for eliminating the high-frequency interference using the difference between axial velocity responses on both sides of the pile-top is proposed, based on 3D simulation results. The TM model cannot adequately characterize the 3D effects of F-wave propagation in piles.

System reliability analysis of pile group in spatially variable unsaturated expansive soil has been a long-standing challenge due to multiple and complex influencing factors. This study proposes a system reliability analysis framework for vertically loaded two adjacent piles in a pile group. Multiple failure modes are considered including the compressive or pullout failure and the failure of excessive differential displacement. The Karhunen-Loe`ve expansion method is used to establish the spatial variability of soil properties. The load transfer method for pile group is used to investigate the load-displacement response considering the effects of infiltration and swelling of soil. The component reliability analysis of each failure mode is calculated by the first-order reliability method, and the sequential compounding method is utilized to combine all failure modes into a system and to calculate the system reliability index. The proposed framework can easily evaluate the sensitivity indices of the component and system reliability index with respect to soil properties. The accuracy and computational efficiency of the proposed framework are verified by a case study, and the effects of rainfall infiltration, autocorrelation distances, vertical load, and pile spacing on the component and system reliability index and the controlling limit state are investigated.

Reliability analysis of pile groups is a hot issue in geotechnical engineering. Pile groups with dissimilar pile lengths can be adopted to alleviate the differential settlement among foundation piles and to ensure the consistency of reliability index of each foundation pile. This paper presents an approach for analyzing the reliability of pile groups with dissimilar pile lengths subjected to vertical loads in spatially variable expansive soils under rainfall. The variation of soil's matric suction with depth under rainfall infiltration is clarified using analytical formula. The Karhunen-Loeve (KL) expansion method is used to discretize random fields. The pile-pile and pile-soil interactions in a pile group with dissimilar pile lengths, and the influence of the reduction of matric suction on the ultimate bearing capacity of the piles are analyzed using the modified load transfer method (LTM). The first-order reliability method (FORM) is employed to solve the reliability indices of each pile in a pile group, and the sequential component method (SCM) is adopted to estimate the reliability index of the pile group. A framework is proposed for the reliability analysis of pile groups in spatially variable unsaturated expansive soil under rainfall. Furthermore, a parameter study is carried out to assess the influence of rainfall intensity and duration on the reliability indices of pile groups.

Exceeding the maximum allowable differential settlement is a common engineering accident in the pile group projects. Spatial variability of soil has a great influence on the differential settlement of pile group. This paper presents a reliability analysis methodology for the vertically loaded two–pile group embedding in the horizontal and vertical spatially variable soil, where the load transfer method (LTM) for pile group is utilized to investigate the load–displacement response considering the pile–pile interaction and the non-linear relationship of the pile–soil interface; the Karhunen–Loève (KL) expansion method is used to simulate the spatial variability in the horizontal and vertical directions of soil parameters; and the first–order reliability method (FORM) is adopted to perform reliability analysis. Proposed method considers the compressive failure limit state and the differential settlement failure limit state of two piles, and it is applied to a two–pile group case to verify the accuracy and high efficiency. Effects of the pile length, the maximum allowable settlement of two piles, the maximum allowable differential settlement, and the horizontal and vertical autocorrelation distance (ACD) on the reliability index are analyzed, and the controlling limit states (CLSs) of the two–pile group under different calculation conditions are discussed.

Accurate assessment of pile group's performance in spatially variable unsaturated expansive soil has long been a challenge in geotechnical engineering. This paper presents a methodology to perform reliability analysis for vertically loaded pile group, where the modified load transfer method (LTM) is utilised to investigate the load-displacement response considering the pile-pile interaction and the non-linear relationship of the pile-soil interface under the influence of matric suction reduction and the swelling of expansive soil; the Karhunen-Loeve (KL) expansion method is adopted to simulate the spatial variability of soil parameters; the first-order reliability method (FORM) is utilised to perform reliability analysis of each pile in the pile group; and the reliability analysis of pile group is then performed using the sequential compounding method (SCM) by considering the pile group as a parallel system. By applying the proposed methodology to a 3 x 3 pile group under different vertical loads and infiltration times, the relative magnitudes of reliability indices for different piles in the pile group and the pile group system under two failure modes of uplifting and sinking are identified. The effects of soil's spatial variability and pile spacing on the reliability of pile group are also analysed.

Soil has spatial variability, which means that soil properties at different locations are different but correlated. To represent the spatial variability of soil surrounding a pile, the random field method (RFM) is usually adopted to discretize a random field into a number of random variables. Then, the first-order reliability analysis method (FORM) is modified and employed to perform reliability analysis, and the load-transfer method (LTM) is adopted to compute the bearing capacity of the pile. To reduce the computation cost of the reliability analysis and random field simulation, a FORM-LTM-variance reduction method (VRM) method is proposed to conduct reliability analysis for single pile in spatially variable soil, in which VRM is adopted to transfer a random field into a random variable over a characteristic length. By comparing the reliability indices using FORM-LTM-RFM and FORM-LTM-VRM, analytical formulas of the characteristic lengths under different pile lengths, coefficients of variation (COVs), and autocorrelation distances (ACDs) are computed. Benefitting from the computation accuracy and efficiency of the FORM-LTM-VRM with analytical formulas of characteristic length, resistance factors in LRFD for the reliability-based design of single pile in spatially variable soil can be easily computed for different safety levels. The accuracy and efficiency of the FORM-LTM-VRM with analytical formulas of characteristic length are demonstrated by a case study of a vertically loaded pile.

To improve the computational efficiency and accuracy is a constant pursuit for evaluating the stability of geotechnical structures built in spatially variable soils. This study proposes an important-region-based Karhunen - Lo & egrave;ve expansion and first-order reliability method (KL-FORM-IR method) to perform reliability analysis for shallow foundation resting on spatially variable soil. The KL-FORM-IR method further improves the computational efficiency by ignoring the variability of the soil parameters outside the important region. An identification method for locating the important region of shallow foundation is first proposed, and the effect of the scale factor (Kf), autocorrelation distance of soil properties, and foundation width (B) on the identification of important regions are investigated. For the purpose of validation, the proposed KL-FORM-IR method compared with the KL-FORM and KL-MCSM by performing reliability analyses based on the same numerical model. Conclusively, the KL-FORM-IR method can improve the computational efficiency and it contributes a new approach to the reliability analysis of shallow foundation resting on a spatially variable soil.

In the random field model's consideration of the spatial variability of soil, soil properties at different locations play different roles in the reliability analysis of the foundation. Investigating the importance distribution of the random field through reliability sensitivity analysis (RSA) is beneficial for understanding how the random field affects the reliability of the foundation. However, many existing RSA methods for the random field model are deficient in terms of efficiency, accuracy, and applicability under complex engineering conditions. Consequently, this study proposes an efficient RSA method for the random field model based on the Karhunen-Loeve (KL) expansion method and the first-order reliability method (FORM) to identify the important random field domain in foundation engineering. In the proposed method, the mean reliability sensitivity index (MRSI) is extended to a random field model of continuous form to characterize the importance distribution of the random field. The MRSI is analytically derived based on the results of the KL expansion method and the FORM without additional limit state function (LSF) calculations. Subsequently, the important random field domain, in which the variation of the mean of the soil property contributes significantly to the reliability index, is identified based on the MRSI. Last, two foundation engineering examples that consider the cross-correlated random fields of cohesion and friction angle, including strip footing on single-layer soil and pile in multiple-layer soil, were used to verify the proposed method. The results showed that an important random field domain with a small area dominates the variation of the reliability index of a foundation, and important random field domain area increases with autocorrelation distance (ACD). This innovative identification method holds great engineering significance, because it allows geotechnical practitioners to gain a comprehensive understanding of the failure modes and foundation treatment areas of foundations in spatially varying soil. In the random field model's consideration of the spatial variability of soil, soil properties at different locations play different roles in the reliability analysis of the foundation. Investigating the importance distribution of the random field through RSA is beneficial for understanding how the random field affects the reliability of the foundation. However, many existing RSA methods for the random field model are deficient in terms of efficiency, accuracy, and applicability under complex engineering conditions. Consequently, this study proposes an efficient RSA method for the random field model to identify the important random field domain, in which the variation of the mean of the soil property contributes significantly to the reliability index. Two foundation engineering examples that consider the cross-correlated random fields of cohesion and friction angle, including strip footing on single-layer soil and pile in multiple-layer soil, were used to verify the proposed method. The results showed that the innovative identification will allow geotechnical practitioners to gain a comprehensive understanding of the failure modes and foundation treatment areas of foundations in spatially varying soil.

[目的/意义]现有科研机构绩效评价体系较为复杂不宜广泛应用,因此有必要建立一套科学且简单易操作的科研机构绩效综合评价体系.[方法/过程]从创新环境、创新投入、创新产出和创新收益入手,构建科研机构创新绩效评价指标体系,数据均来源于公开统计报表制度,具有权威性和可获得性.通过因子分析方法对数据进行处理,得出三大公共因子,最后利用 DEA模型计算综合效率,通过两种方法相结合的方式对20家科研机构的科技创新效率进行评价.[局限]由于报表制度的限制,部分不符合条件的科研机构并未在系统中,导致这部分单位无法参与评价.[结果/结论]研究得出安徽省科研机构的创新能力评价结果分为两类,一类是传统科研机构创新能力两级分化明显,另一类是新型研发机构创新势头突飞猛进.建议对于传统科研机构,加大投入保障,促进转型升级,培育引进高端人才;对于新型研发机构,深化对科研机构"放管服"改革,促进成果转化效率.下一步随着政策的调整和考核方向的变化,继续对指标体系进行优化调整.

为研究土体空间变异性对基桩承载特性和可靠度的影响,建立了空间变异土体中竖向基桩的数值计算模型,采用KL 一阶可靠性方法进行了基桩在承载能力极限状态下的可靠度分析,验证了根据全局方差相对误差确定级数最优展开项数的合理性,分析了土体不排水抗剪强度Su与弹性模量E的空间变异性对竖向基桩可靠指标的影响规律.结果表明:在数值模拟中应考虑桩土接触面黏聚力强度随着Su随机场离散值的变化而变化;E的空间变异性影响基桩抗力与桩顶位移曲线的形状,但不影响基桩极限承载力及可靠指标的大小;可靠指标随着Su的变异系数及竖直自相关距离的增加而减小;在相同的离散精度条件下,单指数型与平方指数型自相关函数对基桩可靠指标的影响很小,但后者的计算量明显小于前者.

In the past few decades, solidification/stabilization (S/S) technology has been put forward for the purpose of improving soil strength and inhibiting contaminant migration in the remediation of heavy metal-contaminated sites. Cement, lime, and fly ash are among the most common and effective binders to treat contaminated soils. During S/S processing, the main interactions that are responsible for improving the soil’s behaviors can be summarized as gelification, self-hardening, and aggregation. Currently, precipitation, incorporation, and substitution have been commonly accepted as the predominant immobilization mechanisms for heavy metal ions and have been directly verified by some micro-testing techniques. While replacement of Ca2+/Si4+ in the cementitious products and physical encapsulation remain controversial, which is proposed dependent on the indirect results. Lead and zinc can retard both the initial and final setting times of cement hydration, while chromium can accelerate the initial cement hydration. Though cadmium can shorten the initial setting time, further cement hydration will be inhibited. While for mercury, the interference impact is closely associated with its adapted anion. It should be pointed out that obtaining a better understanding of the remediation mechanism involved in S/S processing will contribute to facilitating technical improvement, further extension, and application.

Probabilistic analysis has been widely used to assess the inherent uncertainty of variables in laterally loaded pile systems, but the calculation is still difficult and time-consuming. The present study presents an efficient probabilistic analysis framework for a laterally loaded pile system. The performance of the system is defined as the lateral deflection at the pile head and maximum bending moment of the pile shaft, corresponding to two failure modes. Within this framework, the spatial variability of the soil and the correlation between failure modes are considered by the random field theory and the First-Order Reliability Method, respectively. Moreover, the Sequential Compounding Method is used as an efficient tool to determine the system reliability indexes. The framework is confirmed by comparing the reliability indexes of failure modes and systems with those of the Monte Carlo Simulation Method. Furthermore, a parametric analysis and system sensitivity analysis are performed. The results show that the auto-correlation distance, allowable lateral displacement at the pile head, and allowable bending moment of the pile shaft have a great influence on reliability indexes of failure modes and system, and the major parameter of soil in affecting pile is the elastic modulus compared with the undrained shear strength.