Geo-Risk 2023: Advances in Modeling Uncertainty and Variability

Rainfall and water level change are two main factors causing failure of reservoir slopes. Thus, many geotechnical parameters needed for the analysis are highly varied. Spatial random fields-based Bayesian method is proposed, which can systematically assimilate prior knowledge, borehole test data, and long-term monitoring data to obtain posterior distributions. There are three major components of the method. The approach is applied to the Shiliushubao slope of the Three Gorges Reservoir area. Results prove that the updated key geotechnical parameters will quantitatively predict the geohazard of landslide, especially for unsaturated soil slope that suffers an unprecedented heavy rainfall when the reservoir water level is low in the summer. According to the conditions of heavy rainfall and rapid rise and fall of the Yangtze River water level in 2020, the reliability analysis of the old Shiliushubao landslide is carried out in the Three Gorges Reservoir area. The results for the two different conditions both indicate that the safety factor of the slope stability is low, but the reliability index meets the minimum requirement of 2.70 according to the specification. None of the additional reinforcement measures are required.

Two key challenges facing the reliability analysis of slopes considering spatial variability of geotechnical parameters are high dimensionality and computational cost. To this end, this study proposes a slice inverse regression (SIR) based Extreme gradient boosting (XGBoost) method for reliability analysis of slopes considering spatial variability. This paper uses a typical slope as an example to illustrate the proposed method. The results show that the reliability analysis based on SIR and XGBoost can predict the failure probability of a slope with reasonable accuracy and efficiency. The results are compared with those obtained by other methods. The stability and generalization of the limit gradient boosting model with sliced inverse regression in terms of computational efficiency are further illustrated.

This paper investigates the reliability of infinite and two-dimensional slopes in cohesive-frictional soils subjected to pseudo-seismic loadings by the random field approach. For the infinite slope, the focus is on the “worst-case” slope angle, with which the probability of slope failure reaches a maximum. And for the two-dimensional slope, the emphasis is on the “worst-case” spatial correlation length, which results in the maximum probability of slope failure. It is shown that the worst-case slope angle is related to the horizontal seismic coefficient and a nondimensional parameter. The worst-case spatial correlation length is most obvious when the deterministic factor of safety is relatively low and the coefficient of variation of shear strength is relatively high.

With the rapid development of urban rail transit, the shield tunnel in-service is inevitably affected by the surrounding construction. The adjacent construction will cause the stress redistribution of the soil around the tunnel in-service and thus affect the deformation performance of the existing tunnel. This study investigates the effect of ground surface surcharge on the deformational behavior of existing shield tunnel in spatially variable soil. A three-dimensional random field model of soil stiffness parameter is employed in this study. The soil elastic modulus is highlighted and modeled by isotropic random field that is discretized by covariance matrix decomposition. On this basis, the reliability analysis of longitudinal deformation and transverse contraction of shield tunnel is carried out by using the random finite element method (RFEM) and Monte-Carlo (MC) algorithm. The research results reveal the deformation pattern of the tunnel caused by the ground surface surcharge and quantitatively describe the influence of the spatial variability on the deformational performance of existing tunnel. It demonstrates that ignoring spatial variability leads to an underestimation of tunnel convergence, particularly when it is severely disturbed by nearby environments, as the ground surface surcharge in this paper. The work mentioned in this paper provides a theoretical support for the prediction and control of tunnel deformation in engineering practice.

To characterize the joint seismic hazard observed at multiple sites, earthquake simulations are typically performed to capture source and ground motion correlation. A shortcoming of this process is that it is difficult to visualize the influence of different input parameters. In this work, a framework is proposed that utilizes a Bayesian network (BN) to provide a transparent characterization of the joint seismic hazard and dependencies between the input parameters. The framework is intended to be applied to a region such as the Central and Eastern United States, where a grid source characterizes the hazard as opposed to a complex network of faults. Inputs to the BN will be derived from an existing probabilistic seismic hazard analysis, and source and ground motion correlation will be introduced through the BN calculations. The framework is applied to an example scenario and verified with earthquake simulations.

The piping risks of river dikes are discussed in the present study. It is shown how the cone penetration test (CPTU) is used to obtain detailed information on the inside of dikes or underneath them. Since the CPTU makes spatially short-interval tests possible, the spatial variability of the soil properties can be identified. In this study, CPTU results are transformed into permeability based on the CPTU model tests, which have been conducted in the laboratory by using the CPTU mold. The permeability is spatially interpolated by the geostatistical simulation method and then applied to a 3-D finite element seepage analysis. Finally, the locations at high risk for piping inside a river dike in Japan are clarified through the seepage analysis.

In this study, the bivariate random field modelling method considering different dependent structures between soil parameters based on Laplace-transformed Archimedean copulas (LT-ACs) is improved and employed to investigate the soil deformation performance caused by shield tunnelling. Firstly, based on copula theory and the two-step idea, a bivariate joint cumulative distribution function (CDF) is constructed by combining marginal distributions and LT-ACs. The marginal distributions are used to characterize the randomness of a single geotechnical parameter, and the LT-ACs are used to characterize the dependences between geotechnical parameters. Next, to improve the sampling efficiency, the Marshall-Olkin (M-O) algorithm based on the inverse Laplace transform is employed to sample the LT-ACs. Combined with the covariance matrix decomposition method, the improved approach is utilized to generate a bivariate cross-correlated random field. The modelling feasibility and efficiency superiority of the proposed approach is verified through comparative analysis. Finally, the improved cross-correlated random field modelling method is employed to investigate the surface settlement caused by shield tunnel construction. The effects of different LT-ACs of (c, ϕ), (c, E), and (ϕ, E) on the surface deformation of shield tunnel excavation are revealed.

Probabilistic landslide risk assessment provides the quantitative measure of slope safety considering consequences of landslide. It is well known that the slopes are formed of anisotropic and non-homogeneous slope material in natural conditions. However, risk analysis of slope failure taking into account spatial variability of soil parameters is rarely conducted, which is necessary to provide practical estimation of the landslide risk for natural slopes. The spatial variability of slope material can be captured in analysis of slope safety by considering probabilistic techniques using random field theory. Hence, a methodology is proposed for probabilistic assessment of landslide risk considering spatial variability of soil parameters in the present study. The study utilized Monte Carlo simulation method and random field theory. Monte Carlo simulation method is used to determine the failure probability of the slope. Random field theory is utilized to generate random field for soil parameters using local averaging simulation. An example application is demonstrated to validate the proposed methodology. The results of the example application suggest that the spatial variation of soil parameter significantly affects the landslide risk. The determined posterior distribution can be used for design of slope and planning of remedial measures against slope failure.

Reliability-based design (RBD) of slopes is a classic problem in geotechnical engineering. The objective is to find an optimal slope angle that meets the safety requirement for a given target reliability index (or target failure probability). Many probabilistic methods have been adopted in RBD to account for uncertainties involved in slopes, but they are often criticized for the low computational efficiency as numerous deterministic slope stability analyses are inevitably required. Meanwhile, few research studies had focused on the dynamic RBD of slopes when more site exploration data are progressively collected. To address these issues, this paper proposes a framework of the dynamic RBD of slopes. A cohesive slope is investigated as an example to illustrate the proposed method. First, the non-Gaussian random fields of soil shear strength parameters are discretized using the midpoints method based on the prior statistics, and the preliminary reliability-based design of slope angle is carried out using an inverse first-order reliability method (IFORM). Then, the Bayesian Updating with Structural reliability method (BUS) is employed to conduct the probabilistic inverse analyses of soil parameters with more available site-specific data. At last, the updated design of slope angles meeting the target reliability index can be acquired based on the IFORM. The results show that the proposed methodology can obtain a reliable informational design of slope angle with increasing site-specific data and can act as a practical and effective tool for the dynamic RBD of slopes in spatially variable soils.

A probabilistic approach for upper bound bearing capacity evaluation of two-layered soil is demonstrated in the study—a scenario of a sand layer on a top of clay layer is considered (as in the case of a working platform). A kinematical failure mechanism for two-layered soil together with assumption of undrained shear strength spatial variability is used in the study. The considered failure geometry is assumed for plane strain conditions; however, the assumed spatial variability of undrained shear strength is modelled in three dimensions. The discretization of the random field to the random variables is done by using Vanmarcke’s spatial averaging, which does not require the explicit generation of the random field. The developed algorithm is based on the so-called constant covariance matrix approach, which uses one covariance matrix during Monte Carlo simulation and improves numerical efficiency. The proposed approach allows for including a linear trend within the spatially variable layer. This is an important feature because the trend is often observable in the undrained shear strength and impacts the bearing capacity estimates. Finally, the discussion on the result and comparison with those obtained by other methods is provided in the study.

The critical secant gradient function (CSGF) is a spatial function that defines the hydraulic conditions causing the progression of backward erosion piping, a significant internal erosion failure mode for dams and levees. While recent studies have defined the CSGF analytically and have also demonstrated how to measure it in the laboratory, uncertainty in measurements of the CSGF has not yet been quantified. In this study, a preliminary assessment of the uncertainty in measuring the CSGF is developed by analyzing the residual errors between the best estimate of the CSGF for each experiment and the measured values of the secant gradient at specific points. The results indicate that the errors in the best estimate of the measured CSGF are approximately normally distributed with a standard deviation of 7% for the experimental configuration used. Further research is needed to assess if this level of error is acceptable in practice.

Earthen levees are important earthen structures built along waterways for flood protection. Many of the levees have lived out their design life. The reliability of these levees under flooding hazard conditions is critical since the failure can be catastrophic and cause serious damage to the community. The paper aims to present a probabilistic scheme to evaluate the reliability of earthen levees considering the soil spatial variability using the subdomain sampling and finite difference methods. The effect of spatial variability of soil parameters will be explicitly incorporated based on a discretization of the finite difference model and the random field theory. The samples will be generated in a set of subdomains partitioned in the space of uncertain input variables to improve computational efficiency. A case study is utilized to demonstrate the effectiveness of the proposed framework for probabilistic assessment of earthen levees. The effects of different scales of fluctuation and flood water elevations on the reliability of earthen levees are also studied. The results from this paper can provide useful insights for practitioners to evaluate the reliability of the earthen levees and make a risk-informed engineering decision.

Spatial variability characterization of marine geotechnical properties is essential for the design and analysis of offshore wind engineering. To improve the characterization performance, a Bayesian conditional co-simulation method is proposed. The Bayesian theory is firstly used to estimate the cross-variogram model between primary and secondary variables. And then, the conditional co-simulation method is used to simulate marine geotechnical properties at unsampled locations by integrating measurement data on primary and secondary variables. The proposed method is applied to the offshore wind farm in China. The spatial variability model of undrained shear strength is built. The results show that the proposed method can characterize the spatial variability of marine geotechnical properties properly.

Due to their dense sampling interval, cone penetration tests (CPTs) are useful for the purpose of identifying the auto-correlation structure of soil spatial variability. However, only the vertical auto-correlation structure can be effectively identified because CPTs are conventionally conducted in the vertical direction. The identification of the horizontal auto-correlation structure cannot be effectively achieved by conventional CPTs. In the literature, very limited horizontal CPTs were conducted by researchers, but they are seldom conducted in practice probably due to its high cost and technical difficulty. Inclined CPTs are more feasible than horizontal CPTs. The purpose of the current paper is to investigate the possibility of adopting inclined CPTs to identify the horizontal auto-correlation structure of soil variability by numerical examples. A two-dimensional random field is used to generate synthetic CPTs data. The feasibility of identifying the horizontal auto-correlation parameters is then investigated by analyzing the synthetic data from inclined CPTs. The preliminary results obtained by the current paper may be useful for our future work in this line of research.

In engineering practice, cone penetration tests (CPTs) are often used in geotechnical site characterization to assess liquefaction potential of granular soils. It is widely recognized that soil liquefaction assessment results interpreted from a limited number of investigation points may contain multiple sources of uncertainties. Increasing the number of investigation points is a straightforward way to improve the reliability level of interpreted liquefaction assessment results. However, no rational or scientific methods regarding the optimal placement of investigation points is available for probabilistic soil liquefaction assessment. To address this challenge, this paper proposes a CPT-based smart site investigation strategy for probabilistically evaluating soil liquefaction potential in a cross-section with proper consideration of various sources of uncertainties and soil spatial variability.

Evaluation of slope bearing capacity is necessary when foundations of infrastructure are built on the crest of slopes. In practical engineering, bearing capacity and failure modes of slopes against footing loads are highly associated with stratigraphic distribution. In the existing studies regarding the evaluation of slope bearing capacity, stratigraphic boundaries between layers were characterized by deterministic lines according to information from limited boreholes. Such an adoption overlooks local weakness between any two adjacent boreholes and may result in unsafe design. To narrow this gap, based on the Markov random field (MRF) and the yield design theory (YDT), a theoretical framework is developed to evaluate bearing capacity and potential failure modes of slopes considering stratigraphic uncertainty. To quantify stratigraphic uncertainty, the MRF and the discriminant adaptive nearest neighbor-based k-harmonic mean distance (DANN-KHMD) classifier are combined in a Bayesian machine-learning framework to enhance the robustness of uncertainty outcomes by rationally sampling initial stratigraphic realization but also can update model parameters in an unsupervised manner. A YDT-based numerical deterministic model is proposed to analyze slope stability without any step-by-step iterations and any assumptions on failure patterns of slopes. By introducing sampled stratigraphic information into the numerical deterministic model and running the Monte Carlo simulation, the failure probability of slopes against footing loads and the probability of different failure modes are computed. Because the proposed model is much more computationally efficient than those using finite-difference and finite-element deterministic models, the proposed framework has the potential to serve as a practical tool for the evaluation of slope bearing capacity and identification of slope failure modes.

Out of the three sources of model uncertainties (ground, geotechnical, and geologic model uncertainties), geologic model uncertainty was less discussed in geotechnical engineering analyses. In this study, we focused on the effect of geologic model uncertainty, expressed as the joint spacing uncertainty, on the debris accumulation features of a dip slope sliding case. 3D distinct element models were established by incorporating LiDAR digital elevation map and the given joint set distribution. Based on the analysis results, it was found that the crest displacement, run-out distance, and debris coverage width were affected by the variations in dip joint spacing. In contrast, the debris coverage area was affected by the variations in strike joint spacing. Therefore, if the sliding mass run-out risk could threaten the nearby residents or facilities, it is also crucial to consider the joint spacing uncertainty in the corresponding analyses.

Underground geotechnical structures such as tunnels usually go through multiple geological layers. For underground construction purposes, it is necessary to identify the locations of interfaces of various geological layers, such as the interface of different geological formations, or interfaces of rock layers of different weathering grades. Due to the limited site investigation data, it is challenging to infer an individual interface of geological layers, let alone multiple interfaces. This study presents a vector generalized additive model to simultaneously predict multiple geological interfaces, which are treated as correlated response variables in the model. Borehole data in Singapore were used to demonstrate the capacity of the model. The resulting interfaces are compared with those inferred from a generalized additive model, which deals with each geological interface separately. The results show that the vector generalized additive model can capture the correlation of the different geological interfaces and on average has a smaller prediction uncertainty in the geological interfaces than the generalized additive model.

Geo-risk assessment depends on a though and accurate characterization of geotechnical model. However, subsurface lithological variations and inadequate well data produce uncertainties in such models, which often lead to large societal hazards such as collapse of engineered structures, geohazards, etc. Accurate valuation of geotechnical model mainly depends on rock mass quality assessment. Geotechnical parameters such as Young’s modulus are used in the assessments of rock mass strength. However, engineering parameters are conventionally obtained via drilling tests. Borehole methods are pricey, time-taking; require more equipment; provide point-scale data; offer vertical data coverage only at shallow depths; and are barely conducted in the steep topographic terrains. Alternatively, geophysical methods provide rapid, less invasive, more economical, less time-consuming, and more user-friendly way for geotechnical investigation. In this paper, we propose suitable and direct link between geotechnical and geophysical parameters. The proposed approach is more meaningful and reliable to obtain geotechnical parameters using geophysical data of CSAMT method. Our approach provides adaptable formulas to obtain engineering parameters where even though no well data is accessible. Our methodology provides more accurate geotechnical models for thorough geo-risk evaluation at large depths. This research reduces the uncertainty due to structural heterogeneities and inadequate drilling tests, narrows the gap between insufficient geological knowledge and a true geotechnical model, and offers a comprehensive insight into rock mass strength assessment.

Assessing the degree of uncertainty that exists within the conceptual component of an engineering geological model (EGM) is an essential, yet often omitted step in finalizing an EGM as basis for construction of an engineering work. While all EGMs are based on geological concepts and interpretations generally focused towards the engineering purpose of the model, not all models are adequately robust nor properly calibrated or verified. This paper comments on the literature relating to the evaluation of EGM uncertainty in general and proposes a process of self-checking the reliability of the conceptual components of an EGM, specifically targeted at practitioners involved in engineering projects.

A detailed 3D stratigraphic model is essential for designing underground structures such as tunnels, as it can reduce the risk of geotechnical failure. However, traditional methods of subsurface geological investigation, such as drilling and geophysical testing, may not yield sufficient stratigraphic data due to cost or testing limitations, resulting in a high degree of uncertainty in the developed 3D models. Recently, airborne LiDAR technology has provided high-resolution topographic data to help improve the accuracy of geological mapping. Still, reliable procedures to create 3D stratigraphic models have not yet been developed. This paper proposes a methodology for modeling stratigraphic bedding that combines LiDAR surface observation data, LiDAR-derived attitude data, and drilling (borehole) data to create engineering-scale, high-precision 3D stratigraphic models. First, regression analysis for stratigraphic beddings is performed using the LiDAR observation points exposed on the surface. Next, each stratigraphic bedding in 3D space is initially simulated with a multinomial mathematical model and calibrated with LiDAR-derived attitude data. Then, each stratigraphic bedding is further calibrated with the borehole-derived stratification. Finally, all the stratigraphic bedding models are integrated to yield a 3D stratigraphic model. In summary, this paper demonstrates the potential of LiDAR data in developing a reliable 3D stratigraphic model at the engineering application scale.

Generally, the number of boreholes drilled in a project is constrained by the field investigative budget. How to select additional boreholes to increase the reliability of the deduced stratigraphic profile, or to reduce the uncertainty of the deduced stratigraphic profile, is an essential issue. This paper utilizes the stochastic Markov random field (MRF) to study the effect of added boreholes in a synthetic stratigraphic model. The information entropy is employed to quantify the stratigraphic model uncertainty. First, the parametric studies of borehole locations and MRF parameter were conducted. Then, the accuracy of MRF simulation was assessed by comparing the MRF-generated stratigraphic model with the synthetic stratigraphic model. The results show that (1) the average information entropy may be expressed as a quadratic function of the location of an additional borehole; and (2) the average information entropy decreases with the increase in stratigraphic anisotropic ratio and vice versa. Furthermore, the correlations among additional borehole location, stratigraphic anisotropic ratio, and average information entropy were obtained using multivariate regression analysis.

The estimation of column diameter related to the jet grouting systems is a challenging task in jet grouting design. A bunch of influencing factors has a close relationship with a jet grouting column, such as the resistance of surrounding soil, the jet grouting pressure, the number of nozzles, the lifting speed of the rod, etc. Due to the complicated mechanism associated with the jet grouting method, the existing methods cannot predict the column diameter very well. In the present study, a new empirical correlation equation was proposed to estimate the column diameter of jet grouting under the Bayesian framework based on a series of in situ test data from real practice. The selected best model using the Bayesian model selection can capture the characteristics of jet grouting diameter, and the estimated column diameters using the best model have better agreement with the measured data than the semi-theoretical methodology.

Significant advances in numerical techniques to assess static and dynamic liquefaction susceptibility of slopes have occurred over the past few decades. However, an important and often-overlooked uncertainty in such work is the in situ stress state below slopes, which can have a significant effect on the outcome of such analyses. To assess the performance of some common modelling techniques of slopes, the stress states that develop in plane strain hollow cylinder torsional shear tests of a sandy silt gold tailings are compared to model predictions. From this comparison, the uncertainty in such predictions and potential means to refine model calibrations incorporating plane strain test techniques in the future are outlined. Methods to iteratively adjust elasticity and plastic hardening parameters in a critical state model to better reproduce the plane strain calibration test are outlined.

The Loess Plateau is the world’s largest loess accumulation region, where landslides often threaten residents. To reduce the loss caused by loess landslides, numerous approaches have been developed to gain insight into the processes that cause landslide or to identify sensitive areas via landslide susceptibility mapping. None of these approaches, however, can statistically assess the impact of a potential landslide, which is critical for landslide risk management. To address this issue, this study first constructs a loess landslide database by field investigation, from which a multivariate Gaussian distribution model was developed. The model consists of landslides’ data (e.g., height, width, area, and length) transformed using Johnson’s transformation, Box-Cox, and Nataf transformation. Given the height of an unstable slope, the width, length, and area of a potential landslide is then statistically predicted. Database complied in Baoji city, Shaanxi, is used to demonstrate the proposed method. Results show that Johnson’s transformation has satisfactory accuracy and robustness compared with the other two methods.

To perform a geotechnical reliable design, the spatial variability and the uncertainties related to the adopted engineering geological model (EGM) must be taken into account. However, any conceived EGM is characterized by uncertainties covering (1) the bias in the mathematical expression that transforms the measured parameters into design ones; and (2) the uncertainty associated with the variability of the soil and rock parameters in the prediction equations. Hereinafter, the sequential Gaussian co-simulation method (SGCS) has been applied to propagate the uncertainty in the calculation of the undrained shear resistance s_u from measured CPTu profiles (i.e., q_c, f_s, u₂) through a linear model of co-regionalization. The studied area is located in the Po River alluvial plain (Bologna Province, Italy), where the mixture of silts, sands, and clays gets thicknesses of hundreds of meters. These heterogeneous deposits have been mechanically characterized through a 3D EGM to be used in reliability-based designing.

Driven piles can be severely damaged during driving into soil with high boulder content and can potentially lose their structural integrity, resulting in premature pile refusal. This can cause large additional project cost and delays, including an urgency to change the design in progress. Geotechnical uncertainties related to the spatial variability of soil’s boulder content aggravate the complexity of the problem, making it difficult to assess the probability of premature pile refusal due to boulders and to identify the optimal pile design and driving strategy. Existing tools for drivability assessment are mainly deterministic and excessively simplistic, relying on the technical expertise of the personnel involved in the design and execution of the project rather than adopting a systematic treatment of the uncertainties at the specific geological location. A transparent methodology to support the decision-making in pile design is necessary for a cost-effective driving and optimal design solutions. This paper discusses how pile design can be understood from a risk perspective, with specific focus on the assessment of pile drivability. It is found that a new probabilistic approach that provides a correlation between the results from site investigations with the quantities of boulder in the soil layer by inverse analysis can create a solid basis for decision-making in pile design.

The presence of noisy data or outliers in borehole drilling and piezocone penetration test (CPTU) may lead to biased quantification of uncertainties for soil classification and soil property evaluation. Several statistical methods have been proposed in the literature to identify and filter such noisy data; nevertheless, they may not properly interpret the physical meaning of noisy data. This study incorporates a widely used CPTU-based soil classification chart into a coupled Bayesian machine learning method to achieve noise filtering in the integration of borehole and CPTU data. CPTU data are converted to soil behavior types or soil zones based on the soil classification chart and probabilistically related to the authentic soil types by a transition probability matrix under the Bayesian framework. The proposed method is demonstrated by the probabilistic site characterization of the Hong Kong-Zhuhai-Macao Bridge project. Results indicate that noisy data far away from the dominating data set can be properly identified and separated. The proposed model successfully captures the variation of major soil strata revealed by borehole logs and simultaneously identifies the minor variations of significant thin layers recorded by the CPTU data. A sensitivity study indicates that the spatial autocorrelation of soil type should be properly considered in the noise filtering of soil classification.

Spatial uncertainty of soil parameters has a significant impact on the analysis of slope stability. Interval field analysis is emerging as a complementary tool of the conventional random field method that can take spatial uncertainty into account. This approach has not been investigated in slope stability analysis. The present paper proposes a new method, named the interval field limit equilibrium method (IFLEM), for assessing the stability of slope in the presence of the interval field. In this method, the modified exponential function is introduced to characterize the spatial uncertainty of the interval field, and the Karhunen-Loève-like decomposition is employed to generate the interval field. Then, in a single calculation, the deterministic slope stability analyzed by the Morgenstern-Price approach is implemented in order to estimate the safety factor. Subsequently, the upper and lower bounds of the interval of safety factor are efficiently evaluated by a kind of surrogate-assisted global optimization algorithms, such as Bayesian global optimization (BGO) used in this study. Finally, the effectiveness of the proposed method is verified by the numerical example. The results indicate that the proposed method can provide reasonable accuracy and efficiency, which is potentially applicable to a number of geotechnical systems.

Spatial variability of subsurface conditions and uncertainty in implementing methods and models for geotechnical site characterization are critical factors that contribute to financial and safety risks in transportation construction projects. As advanced data-rich techniques and methodologies are developed and implemented for geotechnical site characterization, design, and analysis, new tools are needed to leverage these techniques. A web-based platform will be introduced to provide innovative ways to automate and optimize the process of geotechnical site characterization. Specifically, this platform allows engineers to interactively visualize and efficiently evaluate and interpret statistical features of geotechnical data to facilitate development of design models. This is accomplished by automated evaluating model uncertainty using statistical analysis techniques incorporated into the Federal Highway Administration’s (FHWA’s) Geotechnical Engineering Circular (GEC) No. 5. This web-based platform has been implemented in several large highway and bridge design and construction projects with the Louisiana Department of Transportation and Development (LADOTD). Prototype project case histories will be briefly introduced in the paper. This web-based platform can be extended to incorporate a deep foundation database from LADOTD to eventually facilitate calibrating site-specific resistance factors from the load and resistance factor design (LRFD) methods for deep foundation design.

The pile-founded T-walls play a vital role in flood protection. However, most of the current studies on the stability of pile-founded T-walls are performed using a deterministic approach. However, many uncertainties exist in the soil properties, and neglecting these uncertainties might overestimate the safety of the pile-founded T-walls. This paper presents a comprehensive study on the stability assessment of pile-founded T-wall systems using both deterministic analysis and probabilistic analysis. In the deterministic analysis, a finite difference model is first developed to evaluate the stability of the flood protection system following the traditional procedures, in which the factors of safety under different flooding levels are obtained. In probabilistic analysis, the uncertainties in geotechnical parameters are explicitly considered. In the probabilistic assessment, an MCS-based kriging surrogate model is formulated to predict the stability of the pile-founded T-wall under different flooding hazard levels. The kriging-based surrogate model can approximate the finite difference solutions with its input parameters, which improves the computational efficiency of the probabilistic assessment. A case study of the pile-founded T-wall design resting on layered foundation soils is used to demonstrate the effectiveness of the proposed framework. The results can lead to a critical evaluation of the probability of failure in addition to the factor of safety under different flood water levels, which can provide information for risk-informed decision-making.

This study examines the settlement of a strip footing placed on a two-layered soil profile. The influence of spatial variability of soil parameters on the probability of foundation settlement was studied. To account for soil spatial variability, the influence of reference stiffness modulus and shear strength parameters is separately modelled using isotropic and anisotropic random fields with specified vertical and horizontal scales of fluctuation (SoF). To allow high precision in evaluating these analyses, the random finite element method (RFEM) was used in the study in combination with a hardening soil model. The study proposes a technique that may improve our understanding of the behaviour of soil models more advanced than the Mohr-Coulomb model in probabilistic applications. The proposed approach connects commercial software (ZSoil) with the authors’ own procedures implemented in MATLAB in the framework of the Monte Carlo method to obtain settlement prediction and settlement distributions. The importance of the model parameters was investigated to propose parameters whose spatial variability has a decisive influence on the settlement distributions obtained. Accordingly, the settlement values obtained for the non-random case are shown to be lower than the mean settlement values obtained for the random cases. This shows the importance of using a probabilistic approach. In addition to this, the results of the analysis show that the mean values of the input parameters and the coefficient of variation contribute significantly to the results obtained in the vertical SoF and the horizontal SoF.

Aggregate piers are widely used in ground improvement applications to enhance the stiffness of soft clays and their mechanical properties. The literature includes several studies that are aimed at quantifying the uncertainty in bearing capacity predictions for spread footings that are supported on ground reinforced with aggregate piers. Few researchers, however, targeted the quantification of model uncertainties that are associated with common “settlement-prediction” models for such foundation systems. The objective of this study is to fill this gap by utilizing load-settlement data from full scale load tests for footings on aggregate piers to compare the measured load-settlement response with that predicted using existing analytical methods and numerical tools that are used in practice. The database is also used to quantify the model uncertainty in settlement predictions of available models with particular focus on settlement prediction at the service or design load. The model uncertainty as reflected through the ratio of measured to predicted settlement was found to be relatively high, particularly for the simplistic linear elastic theory-based models (e.g., Priebe). An illustrative reliability-based example is presented to showcase the need for including the effects of model uncertainty in the serviceability-based design of footings on aggregate piers.

The stone column is one of the ground improvement methods that are widely used around the world. This technique is an effective method to improve the weak soil by increasing the bearing capacity of the soil, establishing a drainage path, and reducing the settlement, which can be cost-effective and environmentally friendly. This is an effective technique, since many studies have been conducted on this technique to optimize the performance of the foundation of stone columns. However, there are still deficiencies related to the column-soil system modeling, design procedure, column backfill material types, and loading type (i.e., working or ultimate, static or dynamic). This paper highlights the gaps in the experimental, numerical, and theoretical analysis of the stone column in the published research papers to provide future researchers with information that assigns the risk in designing and constructing this technique. This paper will focus on studies of a single and groups of columns that are installed in different weak soils as end bearing or floating columns while considering all column types. Summaries of the data and findings of the previous studies mentioned in this paper were tabulated to facilitate the accessing of the information by other researchers.

As the offshore industry moves into deeper water, helical piles are emerging as a potential foundation solution option. Numerous researchers have made great efforts to explore the uplift response of helical piles in clay. However, in most previous studies, the wished-in-place assumption was adopted, and the inherent spatial variability of soil strength was also neglected. The present research explores these two effects on the uplift behavior of helical piles through a large deformation random finite element method. A strain-softening soil constitutive model proposed in past literature is employed to model the soil strength remoulding caused by the pile installation and extraction process. The validity of the numerical model used to simulate the installation process and the subsequent uplift process is verified by the installation torque and the uplift capacity, respectively. The spatial variation of soil strength is modeled as a random field, and then a series of Monte Carlo simulations are performed to investigate the installation torque and uplift capacity of the helical piles under different random realizations. The analysis results show that for the helical piles with different penetration depths, the installation effect as well as the random distribution of the soil strength markedly affects the uplift capacity. Moreover, a probabilistic analysis of the uplift capacity is conducted, which might provide a reference for the safety design of the helical pile considering the influence of the installation process.

The influence of spatial variability of the undrained cohesive strength of foundation soils on the bearing capacity of footings is limited in the literature to footings seated directly on the foundation. This is an unlikely arrangement in practice. This paper revisits the footing problem by considering a thin granular layer between a strip footing and soft foundation soil using analytical and stochastic numerical modelling. The case of the clay foundation only and the case of a granular layer over the same clay foundation with random homogenous strength and modulus is shown to be more critical (less safe) than the case with isotropic or anisotropic random spatial variability at practical margins of safety. Margins of safety are expressed as the probability that the bearing capacity from Monte Carlo simulation is less than the factored design deterministic solution for the same mean soil strength, or equivalently by reliability index.

The modified weighted uniform simulation (WUS) method for reliability analysis is applied to the stabilizing pile-reinforced slopes. It has the advantage of simultaneously predicting the probability of failure P_f and capturing the most probable failure points (MPPs), which makes it particularly promising for reliability-based design works with low sampling cost. Based on the illustration of the modified WUS, the effect of sample size on the accuracy of results is reduced by employing weight indices of samples instead of their size. Comparatively, 750 samples are capable of dealing with the stabilizing pile-reinforced slope using WUS, in which Monte Carlo simulation (MCS) needs 20,000 samples to converge. An exhaustive framework is proposed for analyzing the reliability of the slope reinforced with stabilizing piles considering the different pile parameters as well as soil properties based on the modified WUS. The results demonstrated that the stabilizing pile mainly increases slope stability by improving the most probable failure mode. The results will ulteriorly provide a certain reference value for the prevention and control of the stabilizing pile-reinforced slopes.

This paper will demonstrate how to apply the concept of reliability analysis to a very common geotechnical analysis problem, specifically one-dimensional consolidation settlement. As will be described, important contributions of reliability analysis include the ability to assess the relative importance of specific analysis parameters and the consideration of potential epistemic and aleatory uncertainties associated with the analysis parameters. The results can inform the geotechnical engineer regarding site characterization strategies that will explicitly improve the confidence in settlement calculation results. This methodology can readily (and should) be included in geotechnical education and training classes to facilitate adoption of reliability analysis in current curriculum and geotechnical engineering practice.