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.

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.

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.

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.

Reliability analysis of geo-structures using random field method is getting more and more attention due to soil's spatial variability. KL-FORM is a computationally efficient and accurate method for the reliability analysis of soil slope with spatial variability. A major concern of the KL-FORM is the determination of the number of KL expansion terms, which controls both the computation cost and accuracy of reliability analysis. The proper number of KL expansion terms can be selected by comparing the discretization error of the random field with a predefined allowable discretization error. To guide the selection of allowable discretization error of soil slope, a thorough analysis of the relationship among the allowable discretization error, size of the random field, auto-correlation distance, and reliability index of soil slopes with spatial variability is carried out, and a criterion for determining the proper allowable discretization error is proposed.

Soil-water characteristic curve (SWCC) is an important curve in unsaturated soil mechanics. A SWCC can be obtained by curve fitting for a group of data points of suctions and water contents. The lower and the higher part of suction can be measured by the osmotic method and the filter paper method, respectively. Based on the results of a lot of laboratory tests of suctions and water contents of clay, four combinations of data points measured from the osmotic method and the filter paper method are employed to perform the curve fitting for SWCC. Results show that the statistics of SWCC parameters can be accurately obtained by curve fitting all data points of the osmotic method plus only one data point with high suction of the filter paper method. This finding can save a lot of laboratory effort for the measurement of SWCC of unsaturated soils.

At present, the reliability analysis and design method of vertically loaded piles embedded in spatially variable soils is difficult to be applied in practical engineering due to the huge computation effort required. To improve computational efficiency, this paper proposes a new method called the FORM-KL-LTM, which integrates the advantages of the first-order reliability method (FORM), the Karhunen-Loeve (KL) expansion method, and the load transfer method (LTM). The main framework of the FORM-KL-LTM is the FORM, which is used to perform reliability analysis for the pile. The KL expansion method is adopted to carry out random discretization to generate the discrete soil parameters required by each iterative computation of the reliability index using the FORM, and the LTM is employed to evaluate the nonlinear load-settlement behavior of the pile head and to compute the values of limit state functions required by the FORM. The proposed method is computationally efficient because the number of random variables is controlled by the limit number of KL expansion terms. Based on the FORM-KL-LTM, a reliability sensitivity analysis method is proposed, which can compute the sensitivity index for measuring the relative sensitivity of the reliability index with respect to soil properties. Furthermore, a procedure for the reliability-based design (RBD) of piles embedded in spatially variable soils is established for the design of pile geometry, and a design ratio is defined to select the controlling limit state in the RBD of pile for both the ultimate limit state and the serviceable limit state. The procedure, accuracy, and efficiency of the proposed methods are demonstrated by providing an example of the reliability analysis and design of a vertically load pile in spatially variable soils.

&+)',+#'&= A424=C H40AB C74 45542CB >5 B?0C80; E0A8018;8CH >5 B>8; ?A>?4AC84B >= C74 A4;8018;8CH >5 ?8;4B 0A4 64CC8=6 <>A4 0=3 <>A4 0CC4=C8>= 4=4A0;;H B?0C80; E0A8018;8CH 20= 14 34B2A8143 1H C74 A0=3>< 584;3 F7827 8B 2>>B43 >5 8=58=8C4 2>AA4;0C43 A0=3>< E0A801;4B )> 2>=B834A C74 B?0C80; E0A8018;8CH >5 B>8; ?A>?4AC84B 38B2A4C8=6 0 2>=C8=D>DB A0=3>< 584;3 8=C> 0 58=8C4 =D<14A >5 A0=3><

Geomaterial has spatial variability, which can be described by the random field theory. A powerful tool for realizing random fields is the Karhunen–Loève series expansion (K–L expansion) where the number of random variables depends on the number of K–L expansion terms rather than on the number of grids of geo-structure model. However, the K–L expansion requires the solution of an integral eigenvalue problem whose analytical form exists only in the special case. Hence, the Galerkin method is usually employed to calculate the approximate solution, which especially for multi-dimensional random field inevitably causes the huge computational cost of multi-fold integrals and the approximate error of the solution. For quickly and accurately simulating the random field with fewer random variables, a Jacobi–Lagrange–Galerkin (JLG) method is proposed where the huge amounts of multi-fold integrals are transformed into simple matrix multiplications which are implemented quickly in a MATLAB environment. Furthermore, the discretization error and its influence factors are discussed to determine the parameters of the JLG method, and the procedure of the JLG method is proposed. Finally, a two-dimensional shallow foundation and a three-dimensional slope are employed to demonstrate computational efficiency, accuracy, and applicability of the JLG method.

To analyze the influences of parameter uncertainty on system reliability, a system reliability sensitivity analysis method based on the sequential compounding method (SCMSA) is proposed. The SCMSA makes use of the principle of SCM combination element, and further calculates the equivalent correlation coefficient between the two components and other remaining components in the system on the basis of calculating the reliability and sensitivity of a simple system with two components in parallel or in series, so as to achieve the purpose of combining the two components and simplifying the complex system. The advantage of SCMSA is that it integrates the calculation of the relative sensitivity index into the system reliability analysis, so that the sensitivity analysis can be calculated together as a byproduct of the reliability analysis, and this method can be applied to the system reliability sensitivity analysis of the relative non-normal variables. Finally, a simple numerical example is used to illustrate the calculation process, calculation accuracy and calculation advantage of SCMSA, and it is applied to the sensitivity analysis of a system reliability of semi-gravity retaining wall, indicating that the SCMSA can provide a theoretical basis for the risk analysis and prevention of geotechnical engineering.

Most of the pile's vertical static load tests in construction sites are the proof load tests, which is difficult to accurately estimate the ultimate bearing capacity and analyze the reliability of piles. Therefore, a reliability analysis method based on the proof load-settlement (Q-s) data is proposed in this study. In this proposed method, a simple ultimate limit state function based on the hyperbolic model is established, where the random variables of reliability analysis include the model factor of the ultimate bearing capacity and the fitting parameters of the hyperbolic model. The model factor M = R-uR / R-uP is calculated based on the available destructive Q-s data, where the real value of the ultimate bearing capacity (R-uR) is obtained by the complete destructive Q-s data; the predicted value of the ultimate bearing capacity (R-uP) is obtained by the proof Q-s data, a part of the available destructive Q-s data, that before the predetermined load determined by the pile test report. The results demonstrate that the proposed method can easy and effectively perform the reliability analysis based on the proof Q-s data.

Spatial variability is an inherent uncertainty of soil properties. Current reliability analyses generally incorporate random field theory and Monte Carlo simulation (MCS) when dealing with spatial variability, in which the computational efficiency is a significant challenge. This paper proposes a KL-FORM algorithm to improve the computational efficiency. In the proposed KL-FORM, Karhunen-Loeve (KL) expansion is used for discretizing random fields, and first-order reliability method (FORM) is employed for reliability analysis. The KL expansion and FORM can be used in conjunction, through adopting independent standard normal variables in the discretization of KL expansion as the basic variables in the FORM. To illustrate the effectiveness of this KL-FORM, it is applied to a case study of a strip footing in spatially variable unsaturated soil under rainfall, in which the bearing capacity of the footing is computed by numerical simulation. This case study shows that the KL-FORM is accurate and efficient. The parametric analyses suggest that ignoring the spatial variability of the soil may lead to an underestimation of the reliability index of the footing.

The soil-water characteristic curve (SWCC) is an important curve describing the relationship between the suction of unsaturated soils and the saturation or water content, and is an important basis for analyzing the strength, deformation and seepage of unsaturated soils. It is very time-consuming to measure soil suction directly or indirectly indoors. In order to quickly and accurately obtain the SWCC of unsaturated soils, an improved method for predicting SWCC based on the pore size distribution (PSD) of soils is proposed. This method uses the mercury intrusion porosimetry (MIP) to measure the PSD of soils, and the filter paper method is used to measure a suction value of soil samples and its corresponding saturation. Then according to the test results at this point, the pore volume of soils measured by the MIP tests is corrected, and the pore volume after correction is used to calculate the saturation of soils under different suction conditions. This method can overcome the problem of small pore volume measured by the MIP tests. The comparative analysis of the predicted and measured SWCCs before and after the correction of 9 groups of soil samples shows that the proposed method can predict the SWCC of unsaturated soils more accurately. On this basis, the fitting parameters of SWCC and their probability statistical characteristics of multiple groups of soils can be obtained conveniently and quickly.

The spatial variability is an inherent attribute of soil properties. To consider the influences of spatial variability of soils on the reliability of geotechnical engineering, a KL-FORM and a KL-RSM are proposed, in which the Karhunen-Loeve expansion method is used for the discretization of random field, and the first-order reliability method (FORM) or response surface method is adopted for the reliability analysis based on the results of KL expansion. By considering the coefficients of the KL series expansion as the basic variables in the reliability analysis, the KL expansion method and the FORM or RSM can be combined together. An iterative method is proposed for determining the number of KL expansion terms, and flow charts of the KL expansion and the KL-FORM are presented. The proposed KL-FORM and KL-RSM are demonstrated by two case studies: a shallow foundation in a spatially variable unsaturated soil, and an undrained saturated clay slope with spatial variability. The case studies show that the KL-FORM and the KL-RSM are computationally accurate and efficient. Under the requirements of a certain discrete error, the number of KL expansion items and the reliability index decrease with the increase of autocorrelation distance.

随着建筑业的飞速发展和建筑功能要求的提高,建筑能耗在社会总体能耗中所占的比例越来越大.建筑能耗占国民经济总能耗的1/3,我国居住面积占总建筑面积的65%左右,居住建筑的节能是建筑节能的核心.文章分析了建筑与节能的关系,并对节能现状进行总结,提出了居住建筑节能设计在技术方面的问题和解决措施,为未来新建筑节能提供依据.

本文深入探讨了给排水施工常见的问题及对策。