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Despite the clearly stated procedures in current standards, and contrary to its name, nonstandard execution of the standard penetration test (SPT) has been common. The use of different equipment and procedures produces significantly different SPT blow counts. To minimize the effects of these differences, correction factors are applied. Two of these corrections factors, namely hammer energy efficiency ratio (CE) and rod length (CR) corrections, are the scope of this research study. With the intent of quantifying the effects of variabilities and reducing the uncertainties, SPT hammer efficiency measurements were compiled from available literature. Additionally, new hammer energy measurements were performed in the field, controlling the variables of the problem. The resulting database is used to probabilistically develop a set of new CE and CR recommendations. The recommended mean energy ratios for safety hammer and automatic hammers are estimated as 67%±11% and 78%±12% , respectively, which are higher than typically assumed values in engineering practice. The recommended rod length correction values at shallow depths, proven to be also a function of SPT blowcounts, N (SPT-N) values, are higher than typically used values. This suggests less pronounced rod length effects. Additionally, a modified procedure to assess the stress-wave energy at anvil and above the SPT sampler elevations is introduced. [ABSTRACT FROM AUTHOR]

A methodology for cost-effective design of jet grouted water-sealing bottom plugs is presented in this paper. These massive barriers, made of partially overlapping jet grouted columns, are required to ensure temporary waterproofing to excavation areas and adequate uplift resistance against water loads. Therefore, the proposed calculation procedure simultaneously focuses on the structural performance and continuity of the plug. The design may be optimized by considering the possibility of reducing column length, performing injections only in the lower part of the plug, and leaving the upper part of the plug untreated. The reduction in column length may then result in a very slender slab, and a structural check has to be performed to avoid tension fracturing or overall structural collapse. Additionally, in spite of strict controls, jet grouted columns are never perfectly cylindrical or exactly aligned along their prescribed position, and thus the plug may present imperfections. Statistical evaluation of defects with experimental data from different field trials and their simulation with the Monte Carlo method shows that the imperfections are less relevant for the structural performance of the plug, but must be carefully taken into account in the analysis of seepage. Imperfections have been thus introduced in the structural analysis by means of partial factors evaluated from probabilistic analysis. The latter calculation provides a rule to control the effects of incomplete watertightness of the plug. The introduced relations are expressed with design charts. [ABSTRACT FROM AUTHOR]

A probabilistic cone penetration test (CPT) based liquefaction triggering procedure for cohesionless soils is derived using a maximum likelihood method with an updated case history database. The liquefaction analysis framework includes revised relationships for the magnitude scaling factor (MSF) and for estimating fines contents from CPT data when laboratory test data are not available. The updated case history database and methodology for developing the liquefaction correlation are described. Measurement and estimation uncertainties, the potential effects of false positives and false negatives in the case history database, and the effects of the choice-based sampling bias in the case history database are accounted for. Sensitivity analyses showed that the position of the most likely triggering curve and the magnitude of the total error term are reasonably well constrained by the data. The sensitivity study provides reasonable bounds on the effects of different interpretations, from which probabilistic and deterministic relationships for practice are recommended. [ABSTRACT FROM AUTHOR]

Bridge scour is the loss of soil by erosion because of water flowing around bridge supports. Scour has been the number one cause of bridge failure in the United States with an average annual rate of 22 bridges collapsing or being closed owing to severe deformation. This paper addresses three topics related to bridge scour. First, a set of databases was used to quantify the statistical parameters associated with the scatter between the predicted and measured pier scour depth, as well as the probability that a deterministically predicted pier scour depth will be exceeded. These databases also were used to provide the bias factors in current predictions. Secondly, these statistical parameters were used to develop a reliability-based load and resistance factor design for shallow and deep foundations subjected to scour. The goal was to provide a design procedure where the reliability of the foundation is the same with or without scour. Reliability only addresses the probability of success and, therefore, of failure. Finally, the discussion was broadened by using the concept of risk defined as the probability of failure times the value of the consequences. In this third part, the risk associated with bridge scour was quantified and compared to risks associated with other engineering structures. Target values of acceptable risk were recommended as part of the conclusions. [ABSTRACT FROM AUTHOR]

A probabilistic analysis of the face stability of a pressurized tunnel is undertaken in this article. First, two existing velocity fields based on the limit analysis theory are briefly described. They allow one to compute the values of the critical pressures of collapse and blowout of a pressurized tunnel face in cases of both frictional and nonfrictional soils. These models, which have the great advantage of a low computational cost, are validated by comparison with a computationally expensive numerical model. Then, an efficient probabilistic method called collocation-based stochastic response surface methodology (CSRSM) is applied on these velocity fields to perform the uncertainty propagation. This method makes it possible to compute the probability of failure of the tunnel face against both collapse and blowout. In the case of a frictional soil, it appears that the blowout of the face is extremely unlikely and that the collapse is the only probable failure mode. On the contrary, in a purely cohesive soil, it appears that both failure modes are likely to appear and should be considered in the analysis. Finally, this paper presents a discussion concerning the application of the proposed probabilistic method for an economic and safe design of a pressurized shield. [ABSTRACT FROM AUTHOR]

This research investigated the confined flow under hydraulic structures. The hydraulic conductivity of the soil was modeled as a spatially random field, which followed a lognormal distribution. Only porous media that have anisotropic heterogeneity were investigated. Results showed that larger anisotropic heterogeneity ratios (the ratio of horizontal to vertical scale of fluctuation) dramatically increased the seepage flow. This increase of flow was more pronounced at larger coefficients of variations. A similar trend was observed in the case of uplift force, although it was less sensitive to the increase in the anisotropic heterogeneity ratio. Moreover, both the seepage flow and the uplift force tended to their deterministic values as the ratio of anisotropic heterogeneity increased. Results also showed that the exit hydraulic gradient attained its greatest value at particular values of the anisotropic heterogeneity ratio. [ABSTRACT FROM AUTHOR]

Liner systems are increasingly being used to protect the environment from contaminated waste. At the same time, society is increasingly insisting on estimates of the probability that these liner systems will fail to achieve their design objectives, one of which is to limit hydraulic flow from the contaminated region to acceptably small levels. This paper presents a methodology to estimate the probability of excessive hydraulic flow, considering the spatial variability of the soil composing the liner (its mean, variance, and correlation length) as well as the liner thickness. Semiempirical equations predicting the mean and variance of the effective hydraulic conductivity of the liner, based on theory and calibrated by random finite-element method simulations, are presented and used to investigate the probability that a liner exceeds regulatory hydraulic flow requirements. The proposed methodology is illustrated by an example. [ABSTRACT FROM AUTHOR]

Response surface methods (RSMs) are attractive approaches for slope reliability analysis because such methods can integrate deterministic numerical slope stability evaluation and reliability analysis. For a slope in layered soils, its performance function is generally nonlinear and the system failure probability could be larger than the failure probability of the most critical slip surface. In this study, the applicability of the kriging-based RSM for system reliability of soil slopes is assessed through its application to two slopes with obvious system effects. It is found that the kriging method combined with Monte Carlo simulation (MCS) can deliver accurate system failure probability estimation. For comparison, the classical RSM based on the iterative local approximation of the performance function may fail to detect the most critical slip surface. The classical RSM can only calculate the failure probability of one slip surface even if the first-order reliability method or MCS is used. Even when the same calibration samples are used, the second-order polynomial-based RSM is not as accurate as the kriging-based RSM. The results in this study show that the kriging-based RSM is an advantageous and promising approach for calculating the system reliability of soil slopes. [ABSTRACT FROM AUTHOR]

A probabilistic porous model is used to simulate the retention curves of different types of soils. The model is based on the same principles of porous networks models; however, it shows important advantages over them. It considers two different elements: the sites and the bonds. It is able to simulate the retention curves of a material when its pore size distribution is known. It can also be used to interpret more realistically the results of mercury intrusion porosimetry tests. In this paper, the model is used to obtain the pore size distribution of different soils using the retention curve as its data source. The comparison between numerical and experimental results for different soils shows that the model approximately reproduces the pore size distribution obtained from mercury intrusion porosimetry tests. [ABSTRACT FROM AUTHOR]

Maximum seismic shear stresses () have been recognized as one of the important parameters in design practice. This study develops ground-motion parameters for and implements these in probabilistic seismic hazard analysis to provide the distribution of deep soil layers for design purposes. The application of improved ground-motion parameters for is demonstrated at the Oakland International Airport, where a thick Young Bay Mud deposit exists under the artificial fill. Model biases in the predictive equations of seismic shear-stress reduction coefficients () are evaluated by comparison with the site response analyses performed with a wide range of input ground motions. Based on these results, we introduce improved ground-motion parameters for as a linear combination of spectral accelerations, implemented in probabilistic seismic hazard analysis to calculate seismic hazard curves. Conditional mean spectra are calculated, given at 10% in 50 years to illustrate the variations in frequency contents with depth compared with the uniform hazard spectra. Finally, is calculated with depth by using hazard values of and compared with the peak-ground-acceleration-based and uniform-hazard-spectra-based calculations. Analysis results show that will be underestimated for deep soil layers by peak-ground-acceleration-based calculation if the median value of is used in design practice. [ABSTRACT FROM AUTHOR]

The use of jet grouting columns to increase the bearing capacity and reduce the settlements of foundations is dealt with, the aim being to formulate a complete design procedure where theoretical analyses and site observations are combined. The study is based on experimental results reported in the literature, which show that jet grouting columns are able to transfer high vertical loads to the surrounding soil but also that structural collapse may locally occur because of a sudden narrowing of their cross sections and/or poor soil cementation. Noticeable attention has been then given to these aspects by interpreting the results of full-scale tests specifically performed to investigate the characteristics of jet grouting columns and their mechanical interaction with the surrounding soil. The results of this analysis form the basis of a numerical method developed to simulate the response of vertically loaded rafts supported by arrays of columns. The nonlinear load-settlement response of axially loaded columns is modeled with the load-transfer curves method customized to account for the irregular shape of jet grouting columns. Extension of the analysis to the whole reinforced foundation is accomplished by considering the mutual interaction between the columns and the upper concrete raft. The variation of column properties is statistically evaluated from the results of field trials, simulated with probabilistic models and introduced into the calculation with a Monte Carlo simulation technique. The main advantages of the proposed method is that the design limit load of the foundation can be expressed in terms of acceptable probability of failure and that the uncertainty arising from the jet grouting process can be experimentally quantified and rationally introduced in the analysis. Benefits and limitations of reinforcement with jet grouting are finally discussed by applying the proposed method to a case study. [ABSTRACT FROM AUTHOR]

To advance the use of reliability-based design procedures, it is necessary to evaluate the sources of the design parameter uncertainty including inherent variability, measurement error, and transformation uncertainty. The results of a probabilistic evaluation of undrained footing bearing performance are discussed in the context of an extensive test site characterization described in a companion paper. Kriged cone tip resistance values are transformed into design parameters using a second-moment probabilistic approach and compared with the parameters obtained from the laboratory test analyses on specimens retrieved from the test site. The spatial, measurement, and transformation uncertainty are incorporated into probabilistic finite-element and bearing capacity analyses in which the results are compared against a full-scale load test performed at the test site. The results indicate that the reliable assessment of the spread footing response depends to a large degree on the assumed strength anisotropy and soil layering. A comparison of the probabilistic estimates of the bearing capacity to deterministic estimates developed from the correlations and average design parameters indicate that the consideration of uncertainty results in a desirable prediction accuracy. [ABSTRACT FROM AUTHOR]

The need for probabilistic slope analysis that takes into account the uncertainty of soil properties has been acknowledged by the geotechnical profession. Traditionally, probabilistic slope analysis involves only single-mode failure that is considered based on the critical slip surface. This may result in underestimating the failure probability. In contrast, system reliability analysis for slopes is deemed more rational. This study aims at improving the existing methods of slope reliability analysis by considering system reliability. A stratified response surface method (stratified RSM) is proposed to describe the performance functions of possible failure modes. The proposed method differs from conventional response-surface-based slope reliability analysis (which constructs a single approximate performance function) by generating a group of (stratified) response surfaces. Based on these stratified response surfaces, system reliability analysis can be efficiently carried out by means of either a first-order reliability method (FORM) or Monte Carlo simulations. The efficient FORM based on the concept of a dispersion ellipsoid in the space of the original variables is used. Application of the proposed approach to probabilistic assessment of slopes is illustrated by case studies, and the results obtained are compared with Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Liquefaction potential of four Pleistocene beach sand deposits in the Greater Charleston area, South Carolina, is assessed. The assessment is based on a review of 51 sites of conspicuous craterlets and horizontal ground displacement that occurred in beach sand deposits during the 1886 Charleston earthquake and an analysis of 82 seismic cone penetration tests with pore-pressure measurements. Of the 51 ground failure sites, 23 are associated with the Ten Mile Hill beds; 13 with the Wando Formation; 13 with the Silver Bluff terrace and younger deposits that lie adjacent to the harbor, rivers, and creeks; and two with the Ladson Formation. Liquefaction potential is analyzed using the seismic cone data with and without correction for age-related processes (diagenesis) and then expressed in terms of the liquefaction potential index (LPI). Probability curves are developed from the LPI calculations for different earthquake ground-shaking parameters. The probability curves for the Wando Formation overpredict liquefaction potential when no corrections for diagenesis are made. When corrections for diagenesis are made, the probability curves for all four sands generally agree with the observed field behavior. [ABSTRACT FROM AUTHOR]

A probabilistic version of the Idriss and Boulanger standard penetration test (SPT)-based liquefaction triggering correlation is derived using a maximum likelihood approach and an updated case history database. Measurement and estimation uncertainties in the cyclic stress ratio (CSR) and SPT values and the effects of the choice-based sampling bias in the case history database are taken into account. The results of sensitivity analyses show that the position of the most likely triggering curve is well constrained by the case history data and that the magnitude of the total error term is also reasonably constrained. The most likely value for the SD of the error term in the triggering correlation is, however, found to be dependent on the uncertainties assigned to the CSR and . The results of the sensitivity study appear to provide reasonable bounds on the effects of different interpretations on the positions of the triggering curves for various probabilities of liquefaction. Methods for including model and parameter uncertainties in probabilistic liquefaction analyses are briefly discussed. The derived triggering correlation is compared with relationships developed from cyclic laboratory test results for specimens obtained using frozen sampling techniques. [ABSTRACT FROM AUTHOR]

In this paper, a numerical procedure for probabilistic slope stability analysis is presented. This procedure extends the traditional limit equilibrium method of slices to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil strength parameters. In this study, two-dimensional random fields were generated based on a Karhunen-Loève expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation was then used to determine the statistical response based on the generated random fields. This approach makes no assumption about the critical failure surface. Rather, the critical failure surface corresponding to the input random fields of soil properties is searched during the process of analysis. A series of analyses was performed to verify the application potential of the proposed method and to study the effects of uncertainty due to the spatial heterogeneity on the stability of slope. The results show that the proposed method can efficiently consider the various failure mechanisms caused by the spatial variability of soil property in the probabilistic slope stability assessment. [ABSTRACT FROM AUTHOR]

Direct measurement of the soil-water characteristic curve (SWCC) is costly and time consuming. A first-order estimate from statistical generalization of experimental data belonging to soils with similar textural and structural properties is useful. A simple approach is to fit the data with a nonlinear function and to construct an appropriate probability model of the curve-fitting parameters. This approach is illustrated using sandy clay loam, loam, loamy sand, clay, and silty clay data in Unsaturated Soil Database. This paper demonstrates that a lognormal random vector is suitable to model the curve-fitting parameters of the SWCC. Other probability models using normal, gamma, Johnson, and other distributions do not provide better fit than the proposed lognormal model. The engineering impact of adopting a probabilistic SWCC is briefly discussed by studying the uncertainty of unsaturated shear strength due to the uncertainty of SWCC. [ABSTRACT FROM AUTHOR]

The compression index is an important soil property that is essential to many geotechnical designs. Over the decades, a number of empirical correlations have been proposed to relate the compressibility to other soil index properties, such as the liquid limit, plasticity index, in situ water content, void ratio, specific gravity, etc. The reliability and thus predictability of these correlations are always being questioned. Moreover, selection between simple and complicated models is a difficult task and often depends on subjective judgments. A more complicated model obviously provides “better fit” to the data but not necessarily offers an acceptable degree of robustness to measurement noise and modeling error. In the present study, the Bayesian probabilistic approach for model class selection is used to revisit the empirical multivariate linear regression formula of the compression index. The criterion in the formula structure selection is based on the plausibility of a class of formulas conditional on the measurement, instead of considering the likelihood only. The plausibility balances between the data fitting capability and sensitivity to measurement and modeling error, which is quantified by the Ockham factor. The Bayesian method is applied to analyze a data set of 795 records, including the compression index and other well-known geotechnical index properties of marine clay samples collected from various sites in South Korea. It turns out that the correlation formula linking the compression index to the initial void ratio and liquid limit possesses the highest plausibility among a total of 18 candidate classes of formulas. The physical significance of this most plausible correlation is addressed. It turns out to be consistent with previous studies and the Bayesian method provides the confirmation from another angle. [ABSTRACT FROM AUTHOR]

This paper presents a simplified model for evaluating damage potential of a building adjacent to a braced excavation. New developments include several component models for estimating the lateral ground movement profile, angular distortion and lateral strain in a building, and damage potential of a building adjacent to an excavation. These new developments along with an existing model for the vertical ground movement profile are integrated into the proposed simplified model. Case histories are used to verify the developed simplified model. Furthermore, the uncertainty in the developed model is quantified, which enables a probabilistic assessment of the excavation-induced building damage potential. An example probabilistic assessment of building damage potential is presented. [ABSTRACT FROM AUTHOR]

The paper discusses finite element models for predicting the elastic settlement of a strip footing on a variable soil. The paper then goes on to compare results obtained in a probabilistic settlement analysis using a stochastic finite element method based on first order second moment approximations, with the random finite element method based on generation of random fields combined with Monte Carlo simulations. The paper highlights the deficiencies of probabilistic methods that are unable to properly account for spatial correlation. [ABSTRACT FROM AUTHOR]

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted. [ABSTRACT FROM AUTHOR]

A maximum likelihood framework for the probabilistic assessment of postcyclic straining of saturated clean sands is described. Databases consisting of cyclic laboratory test results including maximum shear and postcyclic volumetric strains in conjunction with relative density, number of stress (strain) cycles, and “index” test results were used for the development of probabilistically based postcyclic strain correlations. For this purpose, in addition to the compilation of existing data from literature, a series of stress-controlled cyclic triaxial and simple shear tests were performed on laboratory-constituted saturated clean sand specimens. The variabilities in testing conditions (i.e., type of test, consolidation procedure, confining pressure, rate of loading, etc.) were corrected through a series of correction schemes, the effectiveness of which were later confirmed by the discriminant analyses results. Volumetric and shear strain boundary curves were developed in the cyclic stress ratio versus N1,60,CS or qc,1 domain. In addition to being based on significantly extended and higher quality databases, contrary to the existing judgmentally derived deterministic ones, proposed correlations have formal probabilistic bases, and so provide insight regarding uncertainty of strain predictions or probability of exceeding a target strain value. Probabilistic uses of the proposed correlations were illustrated by three sets of examples. A companion paper applied and calibrated the proposed volumetric strain correlation to semiempirically evaluate postearthquake settlement of level, free-field sites. For the calibration, case history soil profiles, composed of a broad range of sand types and depositional characteristics, shaken by a number of earthquakes, were used. Superior predictions of field settlements by this laboratory data-based cyclic strain assessment approach were concluded to be strongly mutually supportive. [ABSTRACT FROM AUTHOR]

A maximum likelihood framework for the probabilistic assessment of cyclically induced reconsolidation settlements of saturated cohesionless soil sites is described. For this purpose, over 200 case history sites were carefully studied. After screening for data quality and completeness, the resulting database is composed of 49 high-quality, cyclically induced ground settlement case histories from seven different earthquakes. For these case history sites, settlement predictions by currently available methods of Tokimatsu and Seed (1984), Ishihara and Yoshimine (1992), Shamoto et al. (1998), and Wu and Seed (2004) are presented comparatively, along with the predictions of the proposed probabilistic model. As an integral part of the proposed model, the volumetric strain correlation presented in the companion paper is used. The accuracy of the mean predictions as well as their uncertainty is assessed by both linear regression and maximum likelihood methodologies. The analyses results revealed that (1) the predictions of Shamoto et al. and Tokimatsu and Seed are smaller than the actual settlements and need to be calibrated by a factor of 1.93 and 1.45, respectively; and (2) Ishihara and Yoshimine, and Wu and Seed predictions are higher than the actual settlements and need to be calibrated by a factor of 0.90 and 0.98, respectively. The Wu and Seed procedure produced the most unbiased estimates of mean settlements [i.e., their calibration coefficient (0.98) is the closest to unity], but the uncertainty (scatter) of their predictions remains high as revealed by the second to last smaller R2 value, or relatively higher standard deviation (σ[variant_greek_epsilon]) of the model error. In addition to superior model predictions, the main advantage of the proposed methodology is the probabilistic nature of the calibration scheme, which enables incorporation of the model uncertainty into mean settlement predictions. To illustrate the potential use of the proposed model, the probability of cyclically induced reconsolidation settlement of a site after a scenario earthquake to be less than a threshold settlement level is assessed. [ABSTRACT FROM AUTHOR]

This paper aims to demystify the use of risk assessment as a decision management tool and present a methodology that places quantitative risk assessment within reach of every geotechnical engineer, even for routine engineering assignments. In particular, we propose using quantification of expert judgment (i.e., subjective probabilities) as a practical alternative for determining probability of slope failure. The writers present a semiempirical relationship between factor of safety and annual probability of failure that permits estimation of slope failure probabilities with relatively modest effort. The case study for a tailings dam shows that risk assessment based on quantification of expert judgment provides a framework to arrive at rational management and engineering decisions related to dam safety and other geotechnical problems. Using the semiempirical relationship presented here, practicing engineers can use this helpful tool by applying their current skills. [ABSTRACT FROM AUTHOR]

The reliability analysis of earth slopes is considered. For slope safety assessment, the first-order reliability method is employed for estimating the probability of failure or reliability index. Since the failure of any slip surfaces implies failure of the slope, the slope is considered as a series system. The system aspect of the slope in the reliability analysis is dealt with by defining a limit state of the system as a function of the minimum of the ratio of the shear strength to the mobilized shear strength for each of all potential slip surfaces. Such a ratio for a given slip surface is evaluated using the extended generalized method of slices. The reliability analysis procedure described is applied to example slopes to illustrate the impact of the probability distribution type, and the spatial variability of the soil properties on the probability of failure of the slopes. [ABSTRACT FROM AUTHOR]

Tunnel excavation in cohesionless soils implies the use of a temporary supporting structure prior to lining installation. This temporary structure has to couple safety and economy, and can be conveniently realized using ground improvement techniques (for instance, by creating an arch of partially overlapped subhorizontal jet grouted columns). The adoption of ground improvement techniques results in structures far from having a perfect shape because they are intrinsically affected by defects (in both geometrical and mechanical characteristics), and therefore their design may hide unforeseen risks. As a consequence, this is the typical case in which sophisticated numerical analyses may just give the illusion of being refined, if possible defects are not correctly taken into account. In this paper a simple yet rational analytical method for the design of a nonclosed tunnel supporting structure that may be of some help to this aim is presented. It is done with reference to a simple two-dimensional scheme. In the first part of the paper, a design chart of optimal shape and minimum structural thickness of the cross section of the supporting structure is shown. In the second part, an iterative procedure to verify the stability or to design the minimum structural thickness of an existing supporting structure with a predefined shape is described. This method, coupled with the analysis of structural demand, allows one in principle to plot design charts. This approach can easily take into account structural defects with a semiprobabilistic approach and therefore with a chosen risk level, which is of great help to the designer at least in a preliminary design stage. The proposed semiprobabilistic procedure is applied to the case of a temporary supporting structure realized by partially overlapped subhorizontal jet grouted columns, intrinsically affected by defects in diameter and position. The variability of these geometrical parameters was considered based on the large quantity of experimental evidence collected in field trials by the writers and published elsewhere. [ABSTRACT FROM AUTHOR]

In this paper, the excavation-induced settlement determined by the KJHH model, a recently developed semiempirical model, is used to assess the serviceability reliability of adjacent buildings. The calculated settlement, considered as the load in the context of reliability analyses in this paper, is compared with a tolerable settlement, considered as the resistance herein. The reliability of the adjacent building against “damage” (defined herein as the violation of serviceability requirements such as having intolerable settlement) is first analyzed and the probability of exceedance (i.e., exceeding the tolerable settlement) is calculated. Furthermore, as the excavation proceeds, observed settlement at the current excavation stage is used to update the prediction of settlement at subsequent stages, and the probability of exceedance is updated accordingly. [ABSTRACT FROM AUTHOR]

This paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to a vertical load with or without pseudostatic seismic loading. Only the punching failure mode of the ultimate limit state is studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters and the horizontal seismic coefficient. The Hasofer-Lind reliability index and the failure probability are determined. A sensitivity analysis is also performed. The influence of the applied footing load on the reliability index and the corresponding design point is presented and discussed. It was shown that the negative correlation between the soil shear strength parameters highly increases the reliability of the foundation and that the failure probability is highly influenced by the coefficient of variation of the angle of internal friction of the soil and the horizontal seismic coefficient. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability. [ABSTRACT FROM AUTHOR]

Sliding block displacements often are used to evaluate the potential for ground failure due to slope instability. The procedures used to assess sliding block displacement typically use deterministic or pseudoprobabilistic approaches, in which the uncertainties in the expected ground motion and resulting displacement are either ignored or not treated in a rigorous manner. Thus, there is no concept of the actual hazard associated with the computed displacement. This paper presents a fully probabilistic framework for assessing sliding block displacements. The product of this analysis is a displacement hazard curve, which provides the annual rate of exceedance, λ, for a range of displacement levels. The framework considers two procedures that will yield a displacement hazard curve: (1) a scalar hazard approach that utilizes a single ground motion parameter and its associated hazard curve to compute permanent displacements; and (2) a vector hazard approach that predicts displacements based on two (or more) ground motion parameters and the correlation between these parameters. The vector approach reduces the displacement hazard significantly, as compared with the scalar approach, because of the reduction in the variability in the displacement prediction. Comparison of the fully probabilistic approach with an approach using probabilistically derived ground motions reveals that using a ground motion for a given hazard level does not produce a displacement level with the same hazard. [ABSTRACT FROM AUTHOR]

Earthquake-induced sliding displacement is the parameter most often used to assess the seismic stability of slopes. The expected displacement can be predicted as a function of the characteristics of the slope (yield acceleration) and the ground motion (e.g., peak ground acceleration), yet there is significant aleatory variability associated with the displacement prediction. Using multiple ground motion parameters to characterize the earthquake shaking can significantly reduce the variability in the prediction. Empirical predictive models for rigid block sliding displacements are developed using displacements calculated from over 2,000 acceleration–time histories and four values of yield acceleration. These empirical models consider various single ground motion parameters and vectors of ground motion parameters to predict the sliding displacement, with the goal of minimizing the standard deviation of the displacement prediction. The combination of peak ground acceleration and peak ground velocity is the two parameter vector that results in the smallest standard deviation in the displacement prediction, whereas the three parameter combination of peak ground acceleration, peak ground velocity, and Arias intensity further reduces the standard deviation. The developed displacement predictive models can be used in probabilistic seismic hazard analysis for sliding displacement or used as predictive tools for deterministic earthquake scenarios. [ABSTRACT FROM AUTHOR]

Scour at a bridge pier is the formation of a hole around the pier due to the erosion of soil by flowing water; this hole in the soil reduces the carrying capacity of the foundation and the pier. Excessive scour can cause a bridge pier to fail without warning. Current predictions of the depth of the scour hole around a bridge pier are based on deterministic models. This paper considers two alternative deterministic models to predict scour depth. For each deterministic model, a corresponding probabilistic model is constructed using a Bayesian statistical approach and available field and experimental data. The developed probabilistic models account for the estimated bias in the deterministic models and for the model uncertainty. Parameters from both prediction models are compared to determine their accuracy. The developed probabilistic models are used to estimate the probability of exceedance of scour depth around bridge piers. The method is demonstrated on an example bridge pier. The paper addresses model uncertainties for given hydrologic variables. Hydrologic uncertainties have been presented in a separate paper. [ABSTRACT FROM AUTHOR]

The mean-value first-order second-moment (MFOSM) method is the main method for estimating the reliability of slopes in practice. It is well recognized that the method occasionally underestimates the probability of failure for inhomogeneous soil slopes, but there is as of yet no commonly accepted procedure to identify this problem. This study presents a solution by projecting MFOSM results to obtain an equivalent most probable failure point in the material space as defined by Hasofer and Lind. A stability analysis using this material point then provides a check for the validity of the MFOSM solution. If the resulting critical factor of safety is one, the MFOSM results are valid; whereas, if a factor of safety of less than one is obtained, the reliability index is overestimated and the failure probability underestimated. [ABSTRACT FROM AUTHOR]

A method of assessing the probability of failure of shallow foundations in saturated fine-grained soil under multidirectional seismic loading is presented. The method uses the distributions of two variables, the spectral acceleration at the fundamental period of the structure and the shear strength of the foundation soil, to form the joint probability density function. The performance function, which defines the required soil strength for the foundation to equilibrate the applied loading, is mapped on this domain. Numerical integration is used to ascertain the probability of failure. A bounded probability density function is used, namely a Pearson Type 1 (Beta) distribution, for soil strength. This distribution provides an upper and lower limit to in situ shear strength. The spectral acceleration is represented by the complementary cumulative distribution function of a Type 1 asymptotic extreme value (Gumble) distribution. Such a distribution is shown to be an accurate representation of real earthquake loading and may be found by a probabilistic seismic hazard analysis for a region. The method is based on pseudostatic seismic loading of the foundation and accounts for spectral acceleration acting along the two horizontal axes. The influence of the orientation of the foundation to the earthquake source is incorporated using the concept of principal directions of ground motion. The performance function is formulated for shallow foundations under eccentric and inclined loading using the recommendations in Eurocode 7. The function is shown to be nonlinear and compound, one part pertaining to the bearing mode of failure (for lower values of acceleration) and the remaining part pertaining to the sliding mode of failure (for higher values of acceleration). An equation is presented for the transition acceleration that separates the performance function into the two parts. A case study is presented and conclusions are drawn about the role of the bearing and sliding modes of failure. [ABSTRACT FROM AUTHOR]

A simple model for evaluating liquefaction probability using cone penetration test (CPT) data is developed based on logistic regression analyses of 396 case histories. The proposed model uses the normalized cone penetration resistance and soil behavior type index as input parameters; therefore, only CPT testing is necessary for evaluating the liquefaction probability of a site. The selection of the model parameters and the expression of equations are based on results of probability examinations and rigorous statistical analyses. Moreover, the derivation of the logistic regression model is presented in a system of equations. The incorporation of these procedures in developing the model not only fully satisfies the statistic requirements but also highlights the physical meanings of the model parameters. Comparisons of the proposed probability model with previously proposed deterministic and probabilistic approaches are performed to demonstrate the improvements. For practical purposes, the developed model is implemented to establish the relationship between the factor of safety against liquefaction and the probability of liquefaction. [ABSTRACT FROM AUTHOR]

The potential for liquefaction triggering of a soil under a given seismic loading is measured herein by probability of liquefaction. The first order reliability method (FORM) is used to calculate reliability index, from which the probability of liquefaction is obtained. This approach requires the knowledge of parameter and model uncertainties; the latter is the focus of this paper. An empirical model for determining liquefaction resistance based on cone penetration test (CPT) is established through “neural network learning” of case histories. This resistance model along with a reference seismic loading model forms a performance function or limit state for liquefaction triggering analysis. Within the framework of the FORM, the uncertainty of this limit state model is characterized through an extensive series of sensitivity studies using Bayesian mapping functions that have been calibrated with a set of quality case histories. In addition, a deterministic model for assessing liquefaction potential in terms of factor of safety is presented, and the probability-safety factor mapping functions for estimating the probability of liquefaction for a given factor of safety in the absence of the knowledge of parameter uncertainty are also established. Examples are presented to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the issue of model uncertainty is examined in detail within the framework of the first-order reliability method (FORM). The focus of the paper is on the characterization of the uncertainty of a shear wave velocity-based simplified model for liquefaction potential evaluation developed by Andrus and Stokoe. This simplified model is expressed as a boundary curve that defines liquefaction resistance as a function of the corrected shear wave velocity. The uncertainty of this simplified model is represented by a lognormal random variable, and characterization of the model uncertainty mainly involves the determination of its two statistics, namely, the mean and the coefficient of variation. A trial-and-error procedure is used to determine the two statistics of the model uncertainty based on a Bayesian mapping function that is calibrated with a database of case histories. This procedure is shown to be effective in the present study, and the uncertainty of the Andrus and Stokoe’s model is characterized. With the known model and parameter uncertainties, the probability of liquefaction can be determined through a routine FORM analysis. [ABSTRACT FROM AUTHOR]

Uncertainty and risk are central features of geotechnical and geological engineering. Engineers can deal with uncertainty by ignoring it, by being conservative, by using the observational method, or by quantifying it. In recent years, reliability analysis and probabilistic methods have found wide application in geotechnical engineering and related fields. The tools are well known, including methods of reliability analysis and decision trees. Analytical models for deterministic geotechnical applications are also widely available, even if their underlying reliability is sometimes suspect. The major issues involve input and output. In order to develop appropriate input, the engineer must understand the nature of uncertainty and probability. Most geotechnical uncertainty reflects lack of knowledge, and probability based on the engineer’s degree of belief comes closest to the profession’s practical approach. Bayesian approaches are especially powerful because they provide probabilities on the state of nature rather than on the observations. The first point in developing a model from geotechnical data is that the distinction between the trend or systematic error and the spatial error is a modeling choice, not a property of nature. Second, properties estimated from small samples may be seriously in error, whether they are used probabilistically or deterministically. Third, experts generally estimate mean trends well but tend to underestimate uncertainty and to be overconfident in their estimates. In this context, engineering judgment should be based on a demonstrable chain of reasoning and not on speculation. One difficulty in interpreting results is that most people, including engineers, have difficulty establishing an allowable probability of failure or dealing with low values of probability. The F–N plot is one useful vehicle for comparing calculated probabilities with observed frequencies of failure of comparable facilities. In any comparison it must be noted that a calculated probability is a lower bound because it must fail to incorporate the factors that are ignored in the analysis. It is useful to compare probabilities of failure for alternative designs, and the reliability methods reveal the contributions of different components to the uncertainty in the probability of failure. Probability is not a property of the world but a state of mind; geotechnical uncertainty is primarily epistemic, Bayesian, and belief based. The current challenges to the profession are to make use of probabilistic methods in practice and to sharpen our investigations and analyses so that each additional data point provides maximal information. [ABSTRACT FROM AUTHOR]