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Soil constitutive model parameters can be identified from triaxial test data. The identification is frequently performed by fitting a constitutive model to triaxial test data from a purely statistical or probabilistic perspective based on an assumption that measurements are independent. This ignores the sequential attribute of triaxial test data and is, hence, not realistic. In this paper, a probabilistic state space model (SSM) is proposed for undrained triaxial test data analysis, with which the sequential data attribute is explicitly considered and a constitutive model (physics) is linked to the SSM model (statistics) in a natural way. Then, constitutive model parameters can be rigorously learned under a Bayesian framework based on the SSM without artificially augmenting them into hidden variables of SSM. Without loss of generality, the modified Cam Clay (MCC) model is taken as an example to develop the SSM and to demonstrate the proposed Bayesian framework, which is illustrated using simulated and real-life data. Results from the proposed Bayesian framework based on the SSM include not only the best estimates of MCC model parameters but also their posterior distributions for quantifying the identification uncertainty, based on which the identifiability of MCC model parameters is discussed and highlighted.

Various uncertainties arising during acquisition process of geoscience data may result in anomalous data instances (i.e., outliers) that do not conform with the expected pattern of regular data instances. With sparse multivariate data obtained from geotechnical site investigation, it is impossible to identify outliers with certainty due to the distortion of statistics of geotechnical parameters caused by outliers and their associated statistical uncertainty resulted from data sparsity. This paper develops a probabilistic outlier detection method for sparse multivariate data obtained from geotechnical site investigation. The proposed approach quantifies the outlying probability of each data instance based on Mahalanobis distance and determines outliers as those data instances with outlying probabilities greater than 0.5. It tackles the distortion issue of statistics estimated from the dataset with outliers by a re-sampling technique and accounts, rationally, for the statistical uncertainty by Bayesian machine learning. Moreover, the proposed approach also suggests an exclusive method to determine outlying components of each outlier. The proposed approach is illustrated and verified using simulated and real-life dataset. It showed that the proposed approach properly identifies outliers among sparse multivariate data and their corresponding outlying components in a probabilistic manner. It can significantly reduce the masking effect (i.e., missing some actual outliers due to the distortion of statistics by the outliers and statistical uncertainty). It also found that outliers among sparse multivariate data instances affect significantly the construction of multivariate distribution of geotechnical parameters for uncertainty quantification. This emphasizes the necessity of data cleaning process (e.g., outlier detection) for uncertainty quantification based on geoscience data.

Soil spatial variability is difficult to evaluate due to insufficient test data. An alternative option is estimation by indirect methods such as inverse analysis. In this paper, two examples are presented to demonstrate the capability and accuracy of the probabilistic estimation method to characterize soil spatial variability with displacement responses. The first example is a soil slope subject to a surcharge load, in which the spatially varied field of the elastic modulus is estimated with displacements. The results show that estimations based on horizontal displacements were more accurate than those based on vertical displacements. The accuracy of the estimated field was substantially reduced by increasing variance of elastic modulus. However, the estimation was generally acceptable as the error was not more than 10%, even for the high variance case (COVE=1.5). The accuracy of estimation was also affected by the type of covariance function and the correlation length. When the correlation length decreased, the accuracy of estimation was reduced. The second example is a validation of laboratory model tests where a horizontal load was applied on a layered ground. The estimated thicknesses of soil layers were close to those in the real situation, which demonstrates the capacity of the estimation method.

When geotechnical properties show a trend with spatial coordinates, estimation of a variogram model is a challenging task. In the previous studies, the trend-removal method based on ordinary least-...

Background Dendrobii Officinalis Caulis (DC) is a well-known tonic herbal medicine worldwide and has favorable immunomodulatory activity. Various material specifications of DC are available in herbal markets, and DC is ingested by different edible methods. However, whether these specifications and edible methods are suitable or not remains unknown. Methods In this study, we evaluated the suitability of four material specifications (fresh stem, dried stem, fengdou and powder) and three edible methods (making tea, soup and medicinal liquor) based on holistic polysaccharide marker (HPM), the major polysaccharide components in DC. First, the HPMs were extracted from the four specifications of DC by the three edible methods in different conditions. Second, qualitative and quantitative characterization of the extracted HPMs was performed using high performance gel permeation chromatography (HPGPC). Third, immunomodulatory activities of the extracted HPMs were evaluated in vivo. Results The results showed that the HPMs were found to be quantitatively different from various specification of DC and edible methods. In vivo analysis indicated that the HPMs exerted positive effects on innate immune responses by increment in proliferation of splenocytes, secretion of IL-2 and cytotoxicity activity of NK cells. Moreover, the dosage amount of HPM should be defined as a certain range, but not the larger the better, for exerting strong immunological activities. Conclusion According to the both chemical and biological results, fengdou by boiling with water for 4 h is the most recommended specification and edible method for DC.

It is not uncommon to encounter engineering structures that can be modeled as series systems with a large, even unlimited, number of correlated components (e.g., component number greater th...

Significant commitment of cost, man power, and time are often required for characterizing particle morphology of granular materials based on X-ray micro-computed tomography (μCT) scanning and image processing. As a result, only a small portion of particles can be scanned, leading to uncertainty in characterizing realistic particle shape. This paper develops a probabilistic method to characterize and simulate sand particle shape based on Sphere Harmonic (SH) analysis, where Nataf transformation is used to construct the joint probability distribution of SH shape descriptors and to generate their random samples for reconstructing virtual particles. The proposed approach was applied to characterizing and simulating particle shapes of Leighton Buzzard sand (LBS), and these simulated particles were used as clump templates for discrete element method to account for effect of realistic particle shape. It was shown that the proposed approach properly characterizes and simulates the particle shape of LBS in a probabilistic manner.

The spatial variability of geomaterials affects the failure mechanism and reliability of geotechnical structures significantly, and can be modeled rigorously as a three-dimensional (3-D) random field. However, the simulation of multivariate, large-scale and high-resolution 3-D random fields is a challenging task due to extraordinary demands in computational resources. This paper proposes a stepwise covariance matrix decomposition method (CMD) with the aid of separable correlation functions, in which the 3-D random field is generated sequentially along each single dimension with small one-dimensional correlation matrices. The method not only inherits the simplicity of the widely-used general CMD, but also significantly reduces the computational time and required memory space. It only takes a few seconds to construct large-scale and high-resolution 3-D random fields, with the requirement on memory space reduced by more than ten orders of magnitude. The maximum random field resolution is significantly improved from approximately 21 × 21 × 41 using the general CMD to over 501 × 501 × 1001 using the stepwise CMD, which suffices in most engineering applications. The stepwise CMD facilitates 3-D spatial variability modeling in probabilistic site characterization and routine geotechnical reliability analysis.

Quantitative risk assessment of slope failure provides valuable information for slope reinforcement design and risk mitigation. Most of previous studies assessed the slope failure risk based on the critical slip surface with the minimum factor of safety. In general, the critical slip surface is unknown prior to the slope stability analysis and can vary with the underground soil profile. It was, however, observed in slope stability analyses that a slope may, simultaneously, fail along multiple slip surfaces. How to effectively incorporate multiple failure slip surfaces (MFSS) into slope failure risk assessment remains an open question. This paper develops a new method that provides an overview of the failure probability of soil masses at different locations on a slope, which is referred to as the area failure probability chart (AFPC) in this paper. Based on the AFPC, a general slope failure risk assessment framework is proposed to incorporate MFSS into slope failure risk assessment. The proposed approach is illustrated through a slope example. It is found that AFPC shows results of slope reliability analysis in a straightforward and visible way, which enhances the risk perception and communication for geotechnical practitioners, and ignoring MFSS leads to underestimation of slope failure risk.

It is common to encounter a diversity of design scenarios with different values and statistics of loads and/or geotechnical parameters in design practice of engineering geology and geotechnical engineering. Maintaining a uniform level of reliability close to the target reliability under various design scenarios is a key goal of geotechnical reliability-based design (RBD), which is a fundamental challenge for semi-probabilistic RBD methods because a wide range of design scenarios can be involved in geotechnical design practice. This paper develops an efficient RBD updating approach under a full probabilistic design framework, which combines direct Monte Carlo simulation (MCS) with a sample reweighting technique to efficiently obtain final designs under different design scenarios by a single simulation run, avoiding repeatedly performing direct MCS for different design scenarios. This leads to considerable computational saving, particularly as the number of design scenarios concerned is large. The proposed approach is illustrated through a pad foundation design example and a rock slope design example. Results show that the proposed approach properly calculates failure probabilities of different possible designs under different design scenarios by a single run of direct MCS, provided that sufficient failure samples are generated in the direct MCS run to cover failure regions of different design scenarios, which are used to determine the updated final designs. Reliability of the final designs obtained from the proposed approach for various design scenarios is generally uniform and is close to the target reliability level prescribed for the design purpose. Moreover, the proposed approach is able to link site investigation efforts to design saving in an efficient and straightforward manner. It also provides insights into the sensitivity of the final design to uncertain parameters involved in design.

Determining soil–water characteristic curve (SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and time-consuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points (e.g., volumetric water content vs. matric suction) on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty (or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge (e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation (MCMCS), specifically Metropolis-Hastings (M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database (UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner. Keywords: Soil–water characteristic curve, Bayesian approach, Unsaturated soils, Degrees-of-belief, UNSODA

Determining the sensitivity of monitoring variables is essential to field monitoring design for effectively monitoring the safety and reliability levels of geotechnical structures in uncertain environment. Reliability sensitivity analysis of monitoring variables provides a rational approach for identifying sensitive monitoring variables and is capable of accounting for geotechnical uncertainties. It, however, can be computationally expensive, especially when sophisticated numerical models (e.g., finite difference model, FDM) are involved and repeated simulation runs are required. This paper proposes a reliability sensitivity analysis method that leverages on the robustness of direct Monte Carlo simulation (MCS) and the Bayesian Updating with Structural Reliability Methods. The proposed approach allows performing the reliability sensitivity analysis of a monitoring variable by a single run of direct MCS, avoiding repeated simulation runs for different possible observational values of a given monitoring variable. Illustrative examples demonstrate the capability of the proposed approach in identifying the most sensitive monitoring variables among candidates. It is possible to achieve a significant reduction in the number of evaluations of numerical models for reliability sensitivity analysis of monitoring variables using the proposed approach.

Mohr-Coulomb shear strength parameters (i.e. cohesion c and friction angle ϕ) have been widely applied to analyses and designs of rock engineering (such as tunnels, underground caverns, and rock slopes), and they are statistically correlated. Such a correlation plays a vital role in the reliability and risk assessment of rock engineering, and is often quantified by their correlation coefficient ρc,ϕ. Observations on ρc,ϕ for intact rocks and rock masses are, however, conflicted, indicating that the ρc,ϕ is negative for intact rocks while positive for rock masses. Reasons for such a confliction are unrevealed, posing difficulties in determining a proper ρc,ϕ value for reliability and risk assessment of rock engineering. This study revisits the statistical correlation between c and ϕ of rock masses based on Hoek-Brown (H-B) failure criterion and triaxial test data of intact rocks. The rock masses, whose c and ϕ are derived from H-B failure criterion using triaxial test data of intact rocks, are referred to as “H-B rock masses”. Various uncertainties affecting ρc,ϕ of H-B rock masses are first identified, and their effects on ρc,ϕ are systematically explored. It is shown that the positive correlation between c and ϕ of H-B rock masses is attributed to the simultaneous decrease in c and ϕ with the decrease of Geological Strength Index of rock masses and the increase in lumped uncertainty in triaxial test data of intact rocks. Nevertheless, the negative correlation between c and ϕ of intact rocks is due to the decomposition of a certain shear strength of intact rocks into cohesion and friction parts. The increase in one part leads to the decrease in the other part so as to obtain the same shear strength of a given type of intact rock. The generalized H-B failure criterion allows exploring the correlation between c and ϕ of intact rocks and rock masses under a unified framework.

This paper develops a Bayesian approach for model comparison and characterization of the bivariate distribution of c′ and ϕ′ using limited site-specific data. The copula approach is presented to model the bivariate distribution of c′ and ϕ′. The Bayesian model comparison method is developed to select the most probable bivariate distribution model of c′ and ϕ′. The most probable model is used to characterize the joint probability density function (PDF) of c′ and ϕ′ under the Bayesian framework. The developed approach is illustrated and validated using real data of c′ and ϕ′ for clays from the core wall of Xiaolangdi rockfill dam in China.

Many experimental results have presented that soil deformation and strength properties for the same type of soil samples are with a certain variability at the same density and stress states, and even at the identical laboratory conditions. Micro mechanical interpretations of this phenomenon are the random spatial arrangement of constituent particles and heterogeneity of particle geometry and mechanical properties. This paper mainly focuses on the influence of the latter, which is still an open issue for the community of granular materials, by the random discrete element method. The random field model is firstly incorporated into the discrete element method to characterize the heterogeneity of equivalent particle properties for a simple linear rolling resistance contact model. Two RFM parameters named coefficient of variation and scale of fluctuation are adopted to represent the variability and spatial correlation pattern of particle properties, respectively. Monte Carlo simulations are then performed by repeatedly conducting DEM simulations of drained triaxial compression tests on a series of dense heterogeneous specimens. The macroscopic soil deformation and strength parameters are analyzed statistically. The contact network characteristics of three representative heterogeneous specimens are discussed and compared with those of the homogenous specimen to explore the underlying microscopic mechanisms. Moreover, the variability of soil properties due to the random spatial arrangement of constituent particles is compared with that due to the heterogeneity of particle properties. The study helps to provide more insights into the cross-scale understanding of the variability of sandy soil properties in the laboratory.

Slopes are frequently stabilized by reinforcement measures in geological and geotechnical engineering. Effectiveness of reinforcement measures is vital to slope failure risk mitigation, but it is affected by geological and geotechnical uncertainties arising from loads, geological formations and geotechnical properties. In face with these uncertainties, slope reinforcement measures are often monitored at site, and monitoring variables that are sensitive to the safety and reliability of the reinforced slope stability shall be carefully selected during monitoring design, which highly depends on engineering experience and judgments (i.e., prior knowledge). How to exercise the prior knowledge in a quantitative and transparent way in geotechnical monitoring design remains unexplored. This can be accomplished using reliability-based monitoring sensitivity analysis, which requires significant computational costs due to repeated inverse analyses and reliability analyses given different possible values of monitoring variables. This paper develops an efficient reliability-based monitoring sensitivity analysis framework based on BUS (i.e., Bayesian updating with structural reliability methods) with Subset Simulation methods. The proposed approach is illustrated using a real reinforced slope example. Results show that it quantifies reliability sensitivity of different monitoring variables (e.g., displacements at different locations on slope surface) in a cost-effective manner based on prior knowledge. Such reliability sensitivity information facilitates decision-making in selecting sensitive monitoring variables during the monitoring design of reinforced slopes.

This study proposes an efficient full probabilistic design method using an advanced Monte Carlo simulation (MCS) algorithm, so-called generalized Subset Simulation (GSS), for which a concept of design response vector is proposed. The proposed design response vector contains responses of all possible designs and is used to, simultaneously, explore failure domains of different designs. With the design response vector, the proposed approach determines feasible design domains of different geotechnical limit states by a single GSS run. The GSS run can be terminated as the target reliability level (or other user-defined reliability levels) is reached to avoid completely exploring the whole design space. This provides significant computational savings, particularly as the design space is relatively large and the target reliability level is relatively high. The proposed approach is illustrated using a drilled shaft design example. Results show that it provides an efficient and robust vehicle to determine the feasible design domains for full probabilistic design compared with direct MCS and original Subset Simulation-based approaches. Moreover, based on failure samples generated by GSS, the design point is, approximately, determined and can be used to back-calculate case-dependent resistance (or deformation) factors, which links MCS-based full probabilistic design to semi-probabilistic design.

Geological uncertainty is often ignored in slope reliability analysis, even though the inherent variability of soil parameters is considered. This paper aims to propose a method for slope reliability analysis by considering both the inherent variability of soil parameters and geological uncertainty. A coupled Markov chain (CMC) model is used to simulate the geological uncertainty. An implementation procedure for slope reliability considering the aforementioned two types of uncertainty is provided. A slope reliability problem is analyzed to validate the proposed method with the borehole data from Perth, Australia. Different borehole layout schemes are designed to reflect the effect of both number and location of boreholes on slope reliability. Moreover, which type of uncertainty mentioned above has a greater impact on slope reliability is explored. The results indicate that the proposed method can effectively evaluate the slope reliability considering these two types of uncertainty. If only the inherent variability is considered, the accuracy of reliability analysis mainly depends on the used geological profiles. Borehole layout scheme has a significant effect on slope reliability. Both probability of failure ( P f ) and mean of factor of safety (FS) of slope do not monotonously vary with an increasing number of boreholes. The boreholes designed in the critical influence zone can provide more information to improve the accuracy of slope reliability. The coefficients of variation (COVs) of shear strength parameters and the discrepancy among the means of shear strengths for different soils play different and major role between the two types of uncertainty in the reliability analysis of soil slope.

This paper aims to investigate the impact of sample size on geotechnical probabilistic model identification. First, the copula approach is presented to model the bivariate distribution of geotechnical parameters. Thereafter, the AIC scores are adopted to identify the best-fit marginal distribution and copula. Second, the variation of AIC scores because of small sample size is investigated using simulated data. Finally, the impact of the variation of AIC scores on identification of the best-fit marginal distribution and copula is examined. The minimum sample sizes for geotechnical data are also suggested to obtain a correct identification of the probabilistic models. The results indicate that the AIC scores estimated from a small sample exhibit large variation. The variation of the AIC scores has a significant impact on probabilistic model identification. The marginal distributions and copulas have a low percentage of correct identification when sample size is small. The percentages of correct identification for the marginal distributions and copulas increase with increasing sample size. The correlation coefficient between geotechnical parameters has a much larger impact on probabilistic model identification than the COV of geotechnical parameters. The suggested minimum sample sizes for geotechnical data are useful for guiding practical geotechnical site investigation.

Slope failure mechanisms (e.g., why and where slope failure occurs) are usually unknown prior to slope stability analysis. Several possible failure scenarios (e.g., slope sliding along different slip surfaces) can be assumed, leading to a number of scenario failure events of slope stability. How to account rationally for various scenario failure events in slope stability reliability analysis and how to identify key failure events that have significant contributions to slope failure are critical questions in slope engineering. In this study, these questions are resolved by developing an efficient computer-based simulation method for slope system reliability analysis. The proposed approach decomposes a slope system failure event into a series of scenario failure events representing possible failure scenarios and calculates their occurrence probabilities by a single run of an advanced Monte Carlo simulation (MCS) method, called generalized Subset Simulation (GSS). Using GSS results, representative failure events (RFEs) that are considered relatively independent are identified from scenario failure events using probabilistic network evaluation technique. Their relative contributions are assessed quantitatively, based on which key failure events are determined. The proposed approach is illustrated using a soil slope example and a rock slope example. It is shown that the proposed approach provides proper estimates of occurrence probabilities of slope system failure event and scenario failure events by a single GSS run, which avoids repeatedly performing simulations for each failure event. Compared with direct MCS, the proposed approach significantly improves computational efficiency, particularly for failure events with small failure probabilities. Key failure events of slope stability are determined among scenario failure events in a cost-effective manner. Such information is valuable in making slope design decisions and remedial measures.

Particle shape affects the mechanical properties of sands, but the underlying micro-mechanisms are not yet explored, at least partially, due to difficulties in accessing the particle scale information in the laboratory. This study aims to fill this gap through DEM by proposing a general framework for DEM simulation considering realistic particle shape and grading characteristics. Within the proposed framework, the irregular sand particle is approximated by 3D clump, and numerical triaxial drained compression tests are conducted for five granular assemblies of different overall regularity. The simulated critical state friction angles of these five assemblies are consistent with those predicted by an empirical formula proposed in the literature. The simulation results demonstrate that decreasing of overall regularity enhances the interlock effect between particles, making the assembly a higher stiffness and shear strength. Moreover, among different fabric anisotropies, the anisotropies of contact normal and normal contact force fabrics contribute to about 80% of the critical shear strength regardless of the overall regularity. With the decreasing of the overall regularity, the contribution of the anisotropy of contact normal fabric increases while that of normal contact force fabric decreases. The overall regularity mainly affects the anisotropies of contact normal and shear contact force fabrics.

Response surface methods are widely used in slope reliability analysis due to the high efficiency. However, they are often criticized of the curse of high dimensionality, problem-dependent accuracy, and mechanism-free interpretation. To address these issues, this study proposes a response surface-guided adaptive slope reliability analysis method for slopes in spatially varying soils. A sparse quadratic polynomial is initialized using a two-fold dimensionality reduction technique. The response surface-based preliminary slope reliability analysis is successfully corrected to an unbiased, finite element-based target slope reliability analysis, during which the response surface updates iteratively with an increasing high accuracy from special emphasis nearby the failure domain. Two spatially varying soil slopes are investigated. Results indicate that the proposed method can provide an efficient and unbiased estimation of finite element-based target slope failure probability with a low variability, develop a more accurate and problem-oriented response surface model for slope reliability analysis, and explore failure mechanisms of slope stability in spatially varying soils. Its performance is insensitive to the accuracy of initial response surface. Additionally, it prominently outperforms both response surface and finite element-based subset simulations, regardless of high-dimensional or low-failure-probability problems. These advantages significantly enhance the application of response surface on practical slope reliability analysis.

A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.

This paper aims to propose an auxiliary random finite element method (ARFEM) for efficient three-dimensional (3-D) slope reliability analysis and risk assessment considering spatial variability of soil properties. The ARFEM mainly consists of two steps: (1) preliminary analysis using a relatively coarse finite-element model and Subset Simulation, and (2) target analysis using a detailed finite-element model and response conditioning method. The 3-D spatial variability of soil properties is explicitly modeled using the expansion optimal linear estimation approach. A 3-D soil slope example is presented to demonstrate the validity of ARFEM. Finally, a sensitivity study is carried out to explore the effect of horizontal spatial variability. The results indicate that the proposed ARFEM not only provides reasonably accurate estimates of slope failure probability and risk, but also significantly reduces the computational effort at small probability levels. 3-D slope probabilistic analysis (including both 3-D slope stability analysis and 3-D spatial variability modeling) can reflect slope failure mechanism more realistically in terms of the shape, location and length of slip surface. Horizontal spatial variability can significantly influence the failure mode, reliability and risk of 3-D slopes, especially for long slopes with relatively strong horizontal spatial variability. These effects can be properly incorporated into 3-D slope reliability analysis and risk assessment using ARFEM.

Determination of site-specific values of geotechnical parameters (e.g., undrained shear strength, Su) is a key step in geotechnical analyses and designs at a particular site. This, however, has been a challenging task in geotechnical practice because of various uncertainties in geotechnical parameters and the fact that the number of test data obtained during geotechnical site investigation at a site is often too sparse to accurately estimate statistics of the geotechnical parameters. These issues can be rationally addressed under a Bayesian framework. This study proposes a Bayesian sequential updating (BSU) approach for probabilistic characterization of geotechnical parameters based on multi-source information, including the information available prior to the project, referred to as prior knowledge in Bayesian framework, and results of different types of tests that might be performed at different locations in a soil layer within a specific site. In this paper, the proposed BSU approach is formulated for probabilistic characterization of Su of clay using over-consolidation ratio (OCR), standard penetration test (SPT) data, and cone penetration test (CPT) data. OCR, SPT, and CPT data are sequentially incorporated into the Bayesian framework to update statistics (e.g., mean, standard deviation, and probability density function) of the Su profile. Equations are derived from the proposed approach and are illustrated using real OCR, SPT and CPT data. The proposed BSU approach is shown to perform satisfactorily and provide insights into evolution of the statistics of geotechnical parameters as more results of different testing procedures are used. Such insights allow geotechnical practitioners to inspect the quality of information from different testing procedures (including test results and transformation models adopted to interpret them) and to identify the most informative test procedure.

Inherent spatial variability (ISV) of design soil properties (e.g., effective friction angle φ ′) can be incorporated into probability-based geotechnical analyses and designs using random field models. Defining a random field model includes determination of random field parameters (i.e., mean μ , standard deviation σ , and scale of fluctuation λ ) and the correlation function that specifies the spatial correlation of the concerned design soil property (e.g., φ ′) at different locations. This is, however, a challenging task at a given site due to a lack of direct test data of design soil properties and various uncertainties (e.g., transformation uncertainty) arising during site investigation. This paper develops Bayesian approaches for probabilistic characterization of the ISV of φ ′ using indirect test data (i.e., cone penetration test (CPT) data) and prior knowledge, which identify random field parameters of φ ′ through Markov Chain Monte Carlo Simulation (MCMCS) and, simultaneously, make use of Gaussian copula to select the most probable correlation function M ⁎ among a pool of candidate correlation functions based on MCMCS samples. The proposed Bayesian approaches account, rationally and transparently, for the transformation uncertainty associated with the transformation model between φ ′ and CPT data. The proposed approaches are illustrated and validated using real-life and simulated CPT data. Results show that the proposed approaches properly identify the random field model (including μ , σ , λ , and M ⁎ ) of φ ′ using project-specific CPT data, and the random field parameters of φ ′ depend on the correlation function used to interpret CPT data. In addition, the suitability of MCMCS in Bayesian probabilistic characterization of soil properties is highlighted, particularly for the cases with a limited number of test data.

An efficient analytical method for quantifying the correlation between performance functions of different slope failure modes in spatially variable soils is proposed, and its performance in slope system reliability analysis is investigated. First, a new correlation coefficient (NCC) is proposed to evaluate the correlation among slope failure modes considering spatial variability. For comparison and verification, the simulation-based correlation coefficient (SCC) is also presented. Second, appying these two types of correlation coefficients, the effects of soil spatial variability on the representative slip surfaces (RSSs) and the system probability of slope failure are investigated using different system reliability methods, including a probabilistic network evaluation technique, a risk aggregation approach, and a bimodal bounds method. A single-layered cohesive slope is investigated to illustrate the validity of the proposed NCC. The results indicate that the proposed NCC can efficiently and accurately quantify the correlation among slope failure modes considering soil spatial variability. The number of RSSs indicated by the NCC is in good agreement with the number obtained using the SCC. The system failure probabilities of slope stability obtained with the SCC and the NCC using a risk aggregation approach are generally comparable. Also, the system reliability bounds of slope stability obtained using the NCC are relatively close together and comparable to those obtained using the SCC. Thus, the NCC shows good performance when evaluating the correlation among slope failure modes, and was effectively applied to analyze a single-layered cohesive slope considering soil spatial variability.

Effects of different initial conditions of pore water pressure distribution on slope stability are investigated based on rainfall data in the Three Gorges Reservoir Area. A method to incorporate the initial condition of pore water pressure distribution into the slope stability analysis is suggested. Then, sandy and clayey slopes are taken as examples to investigate the effect of antecedent rainfall on slope stability. Results indicate that the influence of antecedent rainfall on the slope stability increases as the saturated permeability coefficient of the soil decreases.

The reliability-based robust geotechnical design (RGD) approach provides an effective tool to deal with the uncertainty in the estimated statistics of geotechnical parameters in a reliability-based design. However, the existing reliability-based RGD approach is not straightforward to apply as it involves multiple concepts. In this paper, the applicability of the existing reliability-based RGD approach is improved by utilizing Monte Carlo simulation (MCS). Here, an MCS-based weighted technique is used to evaluate the failure probability of a geotechnical system. With the aid of this weighted technique, the variation in the failure probability, caused by the uncertainty in the estimated statistics of geotechnical parameters, is computed using MCS. To further improve the efficiency of the RGD method, a series of single-objective optimizations are used in lieu of a multi-objective optimization in the robust design optimization process. The proposed MCS-based RGD approach is illustrated through an example of rock slope design. Compared with the existing reliability-based RGD approach, the MCS-based RGD approach is not only more intuitive and easier to follow, but also more computationally efficient.

Geological uncertainty appears in the form of one soil layer embedded in another or the inclusion of pockets of different soil type within a more uniform soil mass. An efficient coupled Markov chain (CMC) model has been proposed to simulate geological uncertainty in the past. This model, however, cannot be directly applied to geotechnical engineering. The primary problem lies in the estimation of horizontal transition probability matrix (HTPM), one key input of the CMC model. The HTPM is difficult to estimate due to the wide spacing between boreholes in the horizontal direction. Hence, a practical method for estimating the HTPM is proposed based on borehole data. The effectiveness of this method can be evaluated using the following approach. Several virtual borehole outcomes are simulated using artificial HTPM. The HTPM estimated from the virtual boreholes is compared with the artificial HTPM. Boreholes collected from Perth, Australian are adopted to illustrate the proposed method for HTPM estimation. The results show that the estimated HTPM agrees well with the artificial HTPM if the artificial (real) HTPM or vertical transition probability matrix (VTPM) is strongly diagonally dominant (diagonal element is larger than the sum of off-diagonal elements). The estimated HTPM is not sensitive to the borehole layout scheme as the diagonal dominancy of the HTPM is strong.

In site investigation, the amount of observation data obtained for geotechnical property characterisation is often too sparse to obtain meaningful statistics and probability distributions of geotechnical properties. To address this problem, a Bayesian equivalent sample method was recently developed. This paper aims to generalize the Bayesian equivalent sample method to various geotechnical properties, when measured by different direct or indirect test procedures, and to implement the generalized method in Excel by developing an Excel VBA program called Bayesian Equivalent Sample Toolkit (BEST). The BEST program makes it possible for practitioners to apply the Bayesian equivalent sample method without being compromised by sophisticated algorithms in probability, statistics and simulation. The program is demonstrated and validated through examples of soil and rock property characterisations.

Limit equilibrium methods (LEMs) and finite element methods (FEMs) of slope stability analysis can be used in computer-based probabilistic simulation approaches (e.g., direct Monte Carlo Simulation (MCS) and Subset Simulation (SS)) to evaluate the slope failure probability (Pf). For a given slope problem, the computational effort for the LEM is generally much less than that required for the FEM, but the FEM tends to give a more realistic prediction of slope failure mechanism and its associated factor of safety. To make use of the advantages of both the LEM (e.g., computationally more efficient) and FEM (e.g., theoretically more realistic and rigorous in terms of slope failure mechanisms), a new probabilistic simulation method is developed in the paper. The proposed approach combines both a simple LEM (i.e., Ordinary Method of Slices considering a limited number of potential slip surfaces) and FEM with the response conditioning method to efficiently calculate Pf of slope stability and to give an estimate of Pf consistent with that obtained from directly performing MCS and SS based on the FEM. It is illustrated through two soil slope examples. Results show that the proposed approach calculates the Pf properly at small probability levels (e.g., Pf < 0.001). More importantly, it significantly reduces the number of finite element analyses needed in the calculation, and therefore improves the computational efficiency at small probability levels that are of great interest in slope design practice. In addition, the proposed approach opens up the possibility that makes use of the information obtained using a simple model (e.g., LEM) to guide the reliability analysis based on a relatively sophisticated model (e.g., FEM).

This paper aims to develop an efficient geotechnical reliability-based design (RBD) approach using Monte Carlo simulation (MCS). The proposed approach combines a recently developed MCS-based RBD approach, namely expanded RBD approach, with an advanced MCS method called “Subset Simulation (SS)” to improve the computation efficiency at small probability levels that are often concerned in geotechnical design practice. To facilitate the integration of SS and expanded RBD, a generalized surrogate response f is proposed to define the driving variable, which is a key parameter in SS, for expanded RBD of geotechnical structures (e.g., soil retaining structures and foundations). With the aid of the proposed surrogate response, failure probabilities of all the possible designs in a prescribed design space are calculated from a single run of SS. Equations are derived for integration of the surrogate response-aided SS and expanded RBD, and are illustrated using an embedded sheet pile wall design example and two drilled shaft design examples. Results show that the proposed approach provides reasonable estimates of failure probabilities of different designs using a single run of the surrogate response-aided SS, and significantly improves the computational efficiency at small probabilities levels in comparison with direct MCS-based expanded RBD. The surrogate response-aided SS is able to, simultaneously, approach the failure domains of all the possible designs in the design space by a single run of simulation and to generate more complete design information, which subsequently yields feasible designs with a wide range of combinations of design parameters. This is mainly attributed to the strong correlation between the surrogate response and target response (e.g., factor of safety) of different designs concerned in geotechnical RBD.