Foundation Engineering in the Face of Uncertainty: Honoring Fred H. Kulhawy

Ranking schemes are widely used to screen a large population of potentially risky situations or facilities to identify those posing the greatest risk. Examples include screening flood levee reaches, classifying damaged foundations after an earthquake, and identifying potentially dangerous areas for landslides. These problems all share the circumstance that a large number of situations or facilities need to be inspected, which prohibits a detailed engineering evaluation of each, but some level of quantitative evidence and appraisal is needed to classify each as potentially dangerous. The typical ranking scheme uses simple weighted-sum scores or sometimes a pair of simple scores for both probability and consequence of failure. The ever-popular risk matrix is an example of such a ranking scheme. However, these simple metrics often violate fundamental measure-theoretic principles and, as a result, yield risk rankings that differ from what one would obtain from probabilistic risk analysis (PRA). This does not have to be the case. Using a Bayesian Factor scheme to construct simple risk scores, one can obtain simple but proper risk rankings for flood levee screening, forensic engineering, and pit mine slope inspection that are isomorphic with PRA. Bayesian Factor Theory is explicated and practical examples of its use are presented.

Probability is not a means of accommodating ignorance. Rather, it is the rational language of the uncertainty of nature. As examples, this paper demonstrates how the standard deterministic (Boussinesq) formulation for the bearing capacity of footings in geotechnical engineering is but a special case of a more general probabilistic solution. Of greater importance, three-dimensional slope stability analysis is introduced from probabilistic arguments.

Geologists and engineers view the world in complementary but different ways. Science seeks to explain all observed details, whereas engineering seeks to design with specific objectives and multiple constraints. National guidance in the United States calls for geotechnical site investigations to be performed by geotechnical engineers and engineering geologists. Site characterization should start with geologic models, which form the basis for ground models (geologic models with engineering parameters) and geotechnical models (ground models with predicted performance based on design parameters). If the geologic model is wrong, then neither the ground model nor the geotechnical model can be correct. Fundamental geologic variability makes some details unforeseeable. Insufficient geotechnical investigations, faulty interpretations, or failure to portray results understandably contribute to inappropriate designs or failures. If the geologist does not interpret the geology and explain it clearly, then the engineer will be forced to interpret it or ignore it. Incomplete or inaccurate geotechnical site characterization can lead to selection of incorrect models, geotechnical properties, and design values. Furthermore, project managers responsible only for design and construction may view geologic site characterization as extra cost if benefits result in improved life-cycle reliability or reduced maintenance costs but do not improve design or construction.

The geotechnical risk of a tunnel is strongly dependent on ground properties and on the construction techniques and rate of advance. In the urban environment, design is often determined by serviceability limit states of adjacent structures and, to a lesser extent, of the tunnel itself. The observational method (OM) is an effective risk management tool in geotechnical engineering and particularly in tunnel construction. It helps with deciding in the presence of uncertainty in ground conditions. A fundamental prerequisite for its application is that only epistemic uncertainties are present, so that uncertainty reduction of the relevant parameters may be achieved by monitoring. Deterministic models are often used, limiting the versatility and significance of the OM. In this paper conceptual considerations about the implications of ground uncertainty with due account of spatial correlation are presented. A combined computational framework for random finite difference models based on MATLAB and FLAC is introduced. A case study of a tunnel in stiff clayey ground is presented to evaluate the relative importance of the magnitude, type of variability, and spatial correlation of both deformability and shear resistance parameters. A simulated application of the OM is presented with a comparative analysis of the decisions in an OM approach.

A rational approach to uncertainties in geotechnical design is reliability-based design (RBD) and a readily useable form is load resistance factor design (LRFD). In LRFD, load and resistance factors are used to obtain an acceptable level of reliability or failure probability. This paper reviews the development of reliability-based design and the various uncertainties that control the resistance factor. These include uncertainties about material models, analytical models, and methods for reliability assessment. Data available from various sources are compared. The estimated uncertainties are compared with observed performance from case histories and current design codes. Implications on use of LRFD in practice are suggested. Uncertainty about the load is not considered here because an extensive literature already exists.

A database of hydrologic properties of cover soils is described that includes data from tests conducted on 325 intact block samples collected from 10 final cover test sections. For each test section, groups were created of soils having similar texture. The symbolic designations in the Unified Soil Classification System ranged from GC to CH, the saturated hydraulic conductivity (Ks) ranged between 5.1x10-9 and 2.2x10-2 cm/s, van Genuchten's α ranged between 0.00023 and 0.83k Pa-1, and van Genuchten's n ranged between 1.16 and 7.22. Goodness-of-fit tests showed that spatial variability of Ks and α can be described by the lognormal distribution, whereas n can be described by the normal distribution. The coefficient of variation varies between 0.02-0.30 for lnKs, 0.01-0.46 for α, and 0.01-0.41 for n. Saturated hydraulic conductivity is inversely related to fines content, 2-μm clay content, plasticity index (PI), compaction water content relative to optimum water content (w-wo), and initial saturation (Si). The α parameter is correlated directly to Ks, and is inversely related to 2-μm clay content, PI, and organic matter content (OM). The n parameter is inversely related to fines content and clay content and directly related to sand content, although each of these trends is captured in the trend defined by fines content. No effect of compaction condition was evident in the α and n data.

The engineering properties of soils can vary quite dramatically throughout a site, and even more so from site to site. Several soil test data have been collected from numerous projects to perform a statistical analysis to evaluate the variability of these properties and to study the effect of empirical equations on consolidation settlement calculations. A total of 203 soil samples from sites located throughout the State of Ohio were studied and analyzed. Some of the soil properties investigated include the water content, void ratio, Atterberg limits, and compression index. The study results showed that the soil properties varied significantly across the state. It is difficult to find good correlations among the properties due to the scatter in data, and the use of empirical equations may result in very unrealistic settlement predictions.

The undrained shear strength (su) of a clay is not a constant. In particular, su of a clay evaluated by different test procedures are different because these tests may have different stress states, stress histories, degrees of sampling disturbance, and strain rates. This study summarizes the mean value and variability of the normalized undrained shear strength (su/σ'v) from various test procedures based on a large clay database. These second-moment statistics can be seen as a probabilistic extension of Eq-4.55 developed in Kulhawy & Mayne (1990), which provides an estimation of the normalized undrained shear strength based on three factors accounting for test mode, overconsolidation ratio, and strain rate. The second-moment statistics are essential for reliability analysis and reliability-based design.

This paper focuses on procedures for estimating modulus values for soils that are useable with simple elastic solutions and linear finite element analyses for stresses and deformations. Relationships among Young's modulus, shear modulus, constrained modulus, and bulk modulus are defined so that correlations for any of these various measures of soil stiffness can be adapted to the purpose at hand. Because the stress-strain behavior of soil is nonlinear and stress-dependent, soil modulus values depend on confining pressure and load magnitude, as well as soil type, strength, stress history, and drainage conditions. Modulus correlations for gravel, sand, silt, and clay are discussed, and best practices for their use in geotechnical engineering are suggested, together with methods of judging their reliability.

The objective of this paper is to demonstrate the practical construction of a multivariate probability distribution function using an actual soil database containing su(CIUC), OCR, and four piezocone parameters. Five hundred and thirty-five multivariate data points were compiled from 40 clay sites around the world (Brazil, Canada, Hong Kong, Italy, Malaysia, Norway, Singapore, Sweden, UK, USA, and Venezuela). It was found that a multivariate probability distribution can be constructed by transforming each component of a multivariate normal distribution to a Johnson distribution. Existing bivariate regression equations focus on strong correlations. Weak correlations are typically discarded. Site investigation is a costly exercise, and, ideally, one should exploit all measured geotechnical data for design. The multivariate distribution is a concise model to summarize all available information. Conditional distributions can be easily derived to update the marginal distribution of any one parameter or the multivariate distribution of any group of parameters given information from other parameters. One of the objectives of site investigation is to perform cost-effective field tests and to evaluate design parameters based on these field measurements. Clearly, conditioning involving updating one or more design parameters using one or more field measurements is a natural probabilistic generalization of the current soil property evaluation methodology.

Fine-grained residual soils are widely used as compacted fill materials, although they are well known to be vulnerable to weakening when wetted, leading to fill slope failures. A practical approach to evaluate this wetting effect based on typically available properties is being developed. Extensive evaluations of laboratory-compacted soils and variability of field-compacted soils, followed by the development of a simple deformation-based stability model, are reported. The wetting effect is represented by the CBR soaked to unsoaked ratio, and the soil activity can be used as a predictor of this ratio. Compaction effort has a significant effect on this ratio. Effects of variability of compacted soils and uncertainty of prediction equation are incorporated into the stability model to evaluate the wetting effect on slope probability of failure.

This paper focuses on the Bayesian probabilistic modelling of uncertainty in the evaluation of drained sand strength (i.e., friction angle) and stiffness of natural sands in situ, as evaluated using the cone penetration test (CPT) and the probabilistic prediction of loading-induced settlements. For the sand strength, two special datasets are compiled from undisturbed (frozen) sands that were tested in triaxial compression following thawing. For stiffness, equivalent Young's moduli were back-calculated from full-scale footing load tests on sands via elastic continuum theory. Transformation uncertainty is parameterized by means of model factors, which can be directly implemented in geotechnical limit state design for any user-defined target reliability level.

The performance of a geotechnical structure is controlled not by the properties of soil at a point but by the average over a certain line, area, or volume, as pointed out by Vanmarcke (1977) who proposed the variance function. This paper develops his idea and attempts to specify the size of the local averaging of soil parameters to evaluate the resulting variability in performance of a geotechnical structure. In other words, the mean and variance of a local average of a geotechnical parameter for an appropriate volume are used to evaluate the effects of soil spatial variability on the performance of a geotechnical structure. The size seems to be highly dependent on the type of geotechnical problem under consideration. This paper examines the deformation and stability of a shallow foundation to specify the averaging volume size. The results suggest that the concept can be extended to many other geotechnical reliability analyses.

An essential parameter used in reliability analyses of geotechnical engineering systems, particularly foundations, and probabilistic modeling of soil profiles is the correlation distance, which is also known as the scale of fluctuation and the range of influence. This parameter is often difficult to measure, as it requires extensive field testing, which is usually beyond the scope of most geotechnical investigations, and is hence associated only with uncommon research studies. This paper presents the results of a number of investigations in clay and sand, which were designed to quantify the spatial variability and, hence, the correlation distance of these soils. The paper describes and makes use of random field theory, geostatistics, and fractal theory to facilitate the assessment of spatial variability and the correlation distances in both the vertical and horizontal directions.

In this study point data useful for characterizing site conditions have been isolated from both a number of computer-generated models of simplified geologic features and from a series of boreholes advanced across a selected site. A number of common exact and smoothing algorithms have been used to interpolate three-dimensional surfaces from the point data, and these subsurface planes extrapolated to the site extents. The reconstructed solid models have been compared back to the original data and the accuracy of each algorithm assessed. Closely spaced piles were installed upon the considered project site, which, by onsite surveillance, allowed the development of a near-continuous profile of a specific subsurface interface. This documented profile was compared against the corresponding interface interpolated by each of the analysed algorithms based on the available borehole data, and an assessment of the suitability of each algorithm has been completed. Of the six algorithms compared, a ranking based on an assessment of the consistency of the provided results has been achieved. The inverse distance to a power algorithm was assessed to provide the closest match to the observed profile for the site analyzed.

For a complete probabilistic characterization of a geotechnical parameter, its mean, variance, and the scale of fluctuation have to be known. While the mean and variance can be easily determined, determination of the scale of fluctuation is a little more complex. Knowledge of the scale of fluctuation is important in reliability-based design as it is used in implementing spatial averaging and computing the variance-reduction factor. Published values of scale of fluctuation of geotechnical parameters are based on widely sourced data and hence may not be most appropriate for local situations. Based on 11 CPTu soundings and laboratory test results of fine-grained soils from 15 boreholes at four different locations in Missouri, this paper uses the semivariogram function to determine the scale of fluctuation of geotechnical parameters. Owing to scale of fluctuation being dataset-dependent, differences between published values and the Missouri values determined in this study were observed. Spatial averaging effect, depending on magnitude of the reduction in variance of parameters, can potentially lead to a more optimal and cost-effective design.

Subsurface geological and geotechnical databases using geographic information systems have come to be known as virtual geotechnical databases (VGDB's). VGDB's can be employed to estimate the relative positions of stratigraphic horizons or bedrock surfaces, groundwater elevations, and seismic site response in most metropolitan areas. In the St. Louis metro area, most of the geotechnical borings do not pierce the Paleozoic-age bedrock, causing considerable uncertainty in estimating the depth of unconsolidated surficial materials, which exert marked impact on seismic site response, amplifying or attenuating seismic energy. The uncertainty associated with groundwater levels commonly results from limited sampling, measuring methods, and different water depths recorded at a given site. Subroutines for estimating the positions of bedrock surface and groundwater table were developed to circumvent prediction errors associated with interpolation methods, which are over-utilized and inappropriate for most uneven, eroded surfaces. The scarcity and uneven distribution of shear wave velocity (Vs30) measurements across the St. Louis area resulted in poor correlations between the codified NEHRP soil site classes and the measured Vs30 values. In these situations the surficial geologic units were employed to ascertain the appropriate site class assignments in areas bereft of Vs measurements.

With the extension of the offshore industry into deeper water, the types of offshore structures changed from gravity base structures and fixed platforms supported by driven piles to floating vessels supported with vertical tendons or catenary mooring lines. The anchors for these new systems also changed as increased water depths presented problems for underwater pile driving. Suction caissons then became the preferred foundation option for these facilities. A number of significant differences exist between how suction caissons and piles provide resistance and how the foundation system for a floating vessel performs compared to a fixed platform. One of the primary challenges with this new foundation system was the determination of the overall system reliability. An initial study for suction caissons by Clukey et al. (2000) showed that the overall system reliability for suction caissons was not as robust as for a fixed platform. The impact of a single suction caisson failing was found to be more severe and could more easily lead to a system failure. Based on this initial generic study, it was recommended that for extreme loading events the factor of safety (FoS) for Gulf of Mexico (GoM) 100-yr hurricane conditions should be increased from 1.5 (for piles) to 2.0 for suction caissons. This FoS is currently being used in API-RP2SK for vertically dominated loading. However, since that initial study significantly more reliability work has been done at the University of Texas, Det Norske Veritas, and the Norwegian Geotechnical Institute. These studies considered a wide variety of cases, including different floating vessel types, soil conditions, water depths, and loading conditions. The results from this more recent work are compared in this paper. These results show that the current design codes are robust and conservative. Based on the studies opportunities exist to make the design codes less conservative while still maintaining desired levels of reliability. In addition, the historical development of suction caissons is presented.

The p-y method has been commonly used for analysis of laterally loaded piles. Recently, a sampling-based approach for reliability analysis of laterally loaded piles has been developed by the authors. With the performance criteria defined for the laterally loaded piles, the probability of nonsatisfactory performance can be conveniently computed. However, at any project site, soil properties used as input in the computation, such as strength parameters and stiffness values, generally exhibit spatial variations. There is a need to take into account of this spatial variation in the reliability analysis. In this paper, the Monte Carlo simulation technique developed for reliability analysis of laterally loaded piles is briefly described first. Next, a statistical tool for taking into consideration spatial variability of pertinent soil properties in the developed reliability analysis is presented. A design example is given to illustrate the influences of spatial variability of soil properties on the computed outcome. Specifically, the correlation length of the soil properties at the site can exert significant influences on the computed results. It is recommended that spatial correlation of soil properties should be considered to accurately perform reliability analysis and design of piles under lateral loads.

For excavations in built-up areas with deep deposits of soft clays, it is essential to control ground movements to minimize damage to adjacent structures and facilities. This is commonly carried out by controlling the deflections of the retaining wall system. The limiting wall deflection or serviceability limit state is typically taken to be a percentage of the excavation height. In this study, extensive plane strain finite element analyses have been carried out to examine the excavation-induced wall deflections for a deep deposit of soft clay supported by diaphragm walls and bracing. Based on the numerical results, two polynomial regression approaches were used to develop the equations for estimating the maximum wall deflection. This paper describes how the developed equations can be used to perform reliability analysis of the diaphragm wall serviceability limit state to estimate the probability of exceeding the limiting wall deflection.

Probabilistic models for soil properties are used to calculate the first two moments and the distribution for the capacity of pile foundations. Resulting properties are used to develop design equations based on partial and complete characterization of soil properties. Partial characterization is limited to the first two moments of soil strength. It is shown that foundation design for specified reliability levels requires a complete probabilistic characterization of soil properties. Designs using only the first two moments of soil properties have variable reliability levels. It is argued that results in this study provide a framework for developing design equations for code specifications.

This paper scrutinizes the model error in the ultimate bearing capacity of grouped-pile foundations and shallow foundations. First, the model uncertainty of (observed value)/(calculated value) is evaluated for grouped-pile foundations using the statistics of the load test datasets of the several single piles at the same locations. The system reliability of a pile group is estimated considering the fact that the variability in the average bearing capacity of piles decreases as the number of the piles increases. Second, the model uncertainty is evaluated for shallow foundations, considering the scale effect on the bearing capacity. The statistics show that the model error is not dependent on the effective footing width when the calculation considers the scale effect relevantly. The bearing capacity on soft rocks tends to be overestimated and an additional modifier should be considered regarding the resistance factor or in-situ plate-loading tests should be conducted in addition to typical laboratory tests for estimating characteristic soil parameter values.

A three-dimensional stochastic model, proposed earlier for single-segment earth slopes having statistically homogeneous cross-sectional properties, is extended to multi-segment cases. For the two-segment model it is shown how the probability of a local failure, centered at a point near the segment boundary, rises or falls in function of various adjacent segment properties such as their mean safety factors. The method also enables evaluation of the "system reliability" for multi-segmented long linear slopes. The case study for the two-segment case indicates that single- and multi-segment models may be expected to yield significantly different system reliabilities. The proposed multi-segment model is suitable for use in risk assessment and management of this class of civil infrastructure systems and for extension to the case when there are external load conditions such as earthquake-induced shaking.

In this paper, an efficient framework based on the maximum likelihood principle for inverse analysis of soil parameters in braced excavations is proposed. With this framework, the observed maximum ground settlement and maximum wall deflection are used to back-calculate soil parameters through a semi-empirical model. The updated soil parameters from the current stage of excavation can be used to predict the maximum ground settlement and maximum wall deflection in the subsequent stages of excavations. The proposed framework is computationally efficient and can easily be implemented in a spreadsheet. The effectiveness of the proposed framework is illustrated with a well documented excavation case. The results of the case study show that the updated soil parameters improve the accuracy of predictions of the wall and ground responses in a braced excavation.

The effect of hydraulic hysteresis inherent in soil water characteristic curves is explored stochastically in seepage analysis of engineered soil covers. A multi-layer soil cover with random top boundary flux conditions is simulated with the First Order Second Moment method. Water inflow and outflow at the top boundary are chosen as two random variables. The capillary barrier mechanism is taken into account, and the breakthrough hydraulic head at the bottom boundary of the soil cover is adopted as the performance function. Results show that the hysteretic hydraulic model predicts a more conservative result than does the traditional nonhysteretic hydraulic model when simulating seepage in unsaturated, multi-layer soil covers. The dependence of the soil cover performance on its exterior environment during construction is also identified, with a relatively arid season significantly improving the soil cover's functionality. Furthermore, multi-layer soil covers with a proper selection of geotechnical materials provide better performance than a single layer of soil cover of the same thickness. The importance of hydraulic hysteresis in soil covers subjected to alternative climatic actions is emphasized.

In areas with significant seismic activity, earthquake-induced loading effects may constitute the major portion of the design loads on foundations. However, very few attempts have been made to apply reliability-based design concepts on footings under seismic loads. Therefore, this study aims to contribute to the reliability-based design methodology by estimating the resistance factors for shallow foundations in cohesionless soils under earthquake loads for the ultimate limit state (ULS), which is defined as the condition in which the seismic bearing capacity is equal to the design load including dynamic effects. The uncertainties in both the load and the capacity are considered. To evaluate the variation of the reliability index (β) with respect to each significant design parameter, a parametric study was conducted using the first order reliability method (FORM) and Markov Chain Monte Carlo simulations. These results were used to select the appropriate domains within the most influential design parameters for the calibration of the simplified RBD equations that can be presented for general use. The target reliability index for calibration, which turned out to be significantly smaller than that for static loading conditions, is selected after examining the range of reliability levels implicit in existing deterministic foundation designs. The resulting resistance factors are presented in the form of design charts that can be readily applied in foundation engineering practice.

In this paper, a system reliability-based load resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. First order reliability method (FORM) and series system approaches are used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analyses are conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure), and bearing capacity failure. Partial factors needed to maintain the series system stability against three modes of failure by targeting a series system reliability index of 3.0 are obtained for six combinations of component reliability indices against sliding failure (βsli), eccentricity failure (βe), and bearing failure (βb). The load and resistance factors are proposed for a 6.0 m high wall for various values of coefficients of variation (COV) of friction angle of backfill and horizontal seismic acceleration coefficient.

The paper is focused on key points and lessons learned from LRFD calibration of simple limit state functions for the internal stability of metallic reinforced soil walls. The example used in the paper is the ultimate pullout limit state for ribbed steel strip reinforced mechanical stabilized earth (MSE) walls and a single load due to soil self-weight plus a permanent surcharge load. The paper demonstrates how load and resistance measurements from instrumented walls and physical pullout tests can be used to generate bias values. Bias statistics are then used to a) improve the accuracy of underlying deterministic models used to compute nominal load and resistance values, b) remove hidden dependencies, c) select load factors, and d) calculate resistance factors to meet an acceptable probability of failure. While the paper is focused on the pullout limit state example, the model fitting approach and LRFD calibration methodology is applicable to a wide range of other soil-structure limit state design problems in geotechnical engineering.

Inherent spatial variability is a major source of soil property variability, and it affects the analysis and design of geotechnical structures, such as drilled shafts. The current reliability-based design (RBD) approaches, however, commonly address the inherent spatial variability in an indirect and implicit manner using an equivalent single random variable. Recently a Monte Carlo simulation (MCS)-based RBD approach, namely the expanded RBD approach, has been developed, and the inherent spatial variability can be conveniently modeled in a direct and explicit manner using the expanded RBD together with random field theory. This paper integrates the expanded RBD approach with random field theory to account, directly and explicitly, for inherent spatial variability of soil properties in the RBD of drilled shafts. The proposed methodology is illustrated through a drilled shaft design example and is applied to explore effects of inherent spatial variability on the RBD of drilled shafts. It is straightforward and convenient to integrate the expanded RBD approach with random field theory, and the inherent spatial variability of soil properties is shown to affect the RBD of drilled shafts significantly. Such effects are more profound for drilled shafts with relatively long shaft length.

Currently (2007-2010), AASHTO's LRFD design of deep foundations recommends resistance factors Φ for a variety of scenarios (e.g., method of analysis, number of load tests, etc.). Generally, Φ values account for a desired level of reliability and are based on comprehensive databases (not site specific) of predicted versus measured resistances. Unfortunately, no consideration is given to locations of boreholes with respect to foundation elements, spatial variability of design properties over the site, or the use of load testing on LRFD Φ assessment. The present work considers the case of side friction on axially loaded drilled shafts as assessed from laboratory analysis of rock core samples. Geo-statistical principles are used to rationally account for (1) the presence and amount of site-specific load testing with borehole data in the footprint, (2) the availability of off-site load test data, (3) the amount of site-specific borehole sampling, and (4) the presence or not of borehole data at production shaft locations. In agreement with previous studies, spatial variability within a site is identified as a dominating contributor to overall prediction uncertainty. Additionally, it is shown that spatial variability may only be eliminated by using borings inside shaft footprints and not through additional load testing or collection of borehole data at other locations on a site. A case study with field data is used to illustrate the approach for practice in Florida limestone.

This paper presents the results of the calibration of resistance factors for the pullout capacity of soil nails in three types of soil. The data and statistical parameters used in this calibration were obtained in a recent research program. The calibration was conducted using reliability methods, where the target reliability index was selected to be representative of structures with a relatively high degree of redundancy. The calibration used a Monte Carlo simulation with up to 10,000 random simulations for each variable. Calibrated resistance factors used in LRFD design were found to provide results that, on average, are comparable to those obtained using safety factors currently used in practice.

The design of foundations should satisfy various serviceability performance requirements. A structural foundation may concurrently experience vertical displacement, horizontal displacement, and angular distortion. While the limiting value of a single displacement has been studied, the limiting values of multiple displacements when they occur simultaneously have not yet been well studied. The objectives of this paper are to determine the limiting tolerable displacements when multiple movement components occur and to propose a composite limiting tolerable displacement criterion involving both vertical and horizontal displacements. To determine the limiting tolerable displacements for foundations subject to movements in multiple directions, performance information of 280 bridges with either vertical displacement and/or horizontal displacement has been collected and evaluated. Limiting tolerable displacements are determined by using a fragility curve to represent the cumulative probability distribution. The limiting tolerable vertical displacement and horizontal displacement when they occur concurrently are found to be smaller than their respective limiting values when only one component occurs. Both the observed intolerable horizontal displacement and limiting horizontal displacement are smaller than the corresponding vertical displacements of the same category of bridges. A linear function between the limiting vertical and horizontal displacements is proposed. The sum of two dimensionless limiting displacement terms is equal to 1.0. The composite function is modified to allow for construction tolerances in both vertical and horizontal directions. The characteristic tolerable displacements for limit state design or the allowable displacements for conventional design in both vertical and horizontal directions can be obtained based on the composite function.

Large tunnel cross-sections in soft ground require a design methodology that can adequately deal with the complex stress state surrounding the underground opening and the associated excavation stages; this is especially the case at bifurcations where adjacent tunnels merge to create a transition zone of a larger cross-section. Vertical profile design constraints may further lead to shallow overburden conditions that add to the risks that have to be addressed as part of the tunnel design. This paper presents an advanced NATM design methodology that is integrated with design and construction risk management schemes to meet major risk-bearing aspects; namely, large tunnel cross-section (area of up to 470 m²), a shallow overburden (as low as 10.5 m), soft-ground conditions (cemented sands and gravels), and the location of the tunnel inside an urban area. Special emphasis was paid to controlling the settlement risks associated with tunneling via an oriented risk triggers and alarm plan.

An extensive preproduction probe pile load testing program was conducted for a coal-fired power plant in New Jersey to minimize pile performance uncertainty resulting from variable subsurface conditions and identify the most cost-effective and technically suitable piling system for the project. Three types of piles were instrumented and tested:Monotube, closed-end pipe, and step-tapered. This manuscript includes a general description of the site and its geologic conditions, along with subsurface and groundwater conditions in the vicinity of the pile load test areas. A summary of the test pile installation, including driving records and dynamic monitoring, is provided, and results are compared with geotechnical data obtained from borings drilled in the pile load test areas. Compressive static pile load test results are presented, and pile instrumentation results are interpreted. Average unit shaft resistance values are calculated and compared to field-measured shearing strength of site soils. Comparison of pile behavior based on the results of the load test program, along with cost and schedule considerations, served as the basis for the selection of the production piles for the facility.

A special case study is presented to demonstrate the influence and evaluation of uncertainties involved in foundation design in geotechnical engineering. Site heterogeneity, variability in geometry, mechanical properties of bedrock, and seismic risk are the main sources of uncertainties considered. The subject structure is a new covered sports arena to be constructed in the Asian part of Istanbul, Turkey. The site is an old rock quarry and subsequently has been utilized as a landfill basin to accommodate soils and trash from various excavations within the city. Main lithological units underlying the upper uncontrolled fill are limestone, sandstone, and shale at varying locations and depths. Istanbul is seismically very active, and the planned structure for the sports arena is a dome supported on widely spaced columns. The high seismicity of the region combined with the very heterogeneous and poor subsoil conditions represent a big challenge for the decision process in design of foundations. Based on the various factors under consideration, it was decided to implement barrette foundations socketed in to the underlying bedrock to satisfy the specified vertical displacement-based performance criteria of the structure. The shear resistance of the socket interface was estimated during design stage using various empirical equations utilizing compressive strength of the bedrock. It was concluded that variability in lithology and mechanical properties of bedrock at various locations and depths results in a large range of unit skin friction values estimated, using various relations proposed, bringing further complication in the decision process in estimation of optimum socket length. O-Cell loading test procedure has been employed during design to verify and optimize the socket length.

A static loading test on a 406 mm diameter, strain-gage instrumented, 18.5 m long CFA pile presented an opportunity for arranging an impromptu prediction event. Several people known to be interested in deep foundation challenges were invited to submit a prediction of capacity and load-movement response of the pile ahead of the testing. Although the window of time was a mere week, no fewer than 41 persons responded, representing 15 countries and most continents. The soil profile at the site consisted of a transported and redeposited silty sandy medium plastic, very stiff, ablation clay till containing lenses of sand and gravel categorized by SPT N indices and low water content. Concern for safety of the test arrangement forced the static loading test to be aborted when the applied load was 1,790 kN before any tendency toward an ultimate resistance had developed. However, the extrapolated load-movement curve was used as reference to the predicted load-movement curves. Strain-gage instrumentation indicated a low E-modulus commensurate with the mere 13-day wait time between constructing and testing the pile. The records also indicated that only about 500 kN of the maximum applied load had reached the pile toe when the test was aborted. The paper presents the results of the test, the approach to determining the pile modulus from the strain-gage data, the load distribution, and extrapolated pile-head load-movement curves for reference to the predicted curves. The predicted values of pile capacity ranged from a low of 830 kN through a high of 3,600 kN with an average of 1,920 kN. Thirty-six of the predictions included the pile head movement at the predicted capacity and the movements ranged from 8 mm through 220 mm with an average of 35 mm. Clearly, the predictors' definitions of pile capacity differed. The compilation of the predictions presented in the following include bell curve distributions of submitted capacities and movements, showing that the widths of two standard deviations, thus encompassing two-thirds of all values, for capacity and movement were 1,090 kN and 2,760 kN and 9 mm through 61 mm, respectively.

Ground investigations for a high-rise tower in Jeddah Saudi Arabia revealed the presence of cavities in some of the boreholes. It was decided that a piled raft would be a suitable foundation option as it would provide a measure of redundancy in case some of the piles encountered cavities. Under such circumstances, the raft would permit the transfer of load from the affected piles to those founded in sound limestone. This paper sets out the design process adopted for the piled raft foundation and describes the post-design analyses undertaken to investigate the mechanism of load transfer from cavity-affected piles. Comparisons are made between the behavior of the piled raft when no cavities are present and that when cavities are randomly encountered by some of the piles. The increases in pile axial load and raft bending moments in such circumstances are presented.