Probabilistic site characterization and reliability analysis of shallow foundations and slopes

Abstract

Uncertainty is pervasive in almost every field of engineering, and geotechnical engineering is no exception. Natural soils are heterogeneous and anisotropic in physical properties due to their composition and complex depositional processes. The uncertainty in geotechnical engineering is mainly attributed to inherent or spatial variability, limited number of samples, testing and measurement errors, and the analytical models which relate the laboratory or in situ properties with response characteristics in terms of stability and deformation behaviour of soil. Professional practice has realized that due to economic constraints, the risk cannot be reduced to zero, and the foundations of infrastructure projects need to be designed considering that the risk is “as low as reasonably practicable,” which society can perceive. Unless all the sources of uncertainty are clearly brought out and included appropriately in designs, it is not possible to explicitly assess the risk involved with respect to imposed loads on geotechnical systems. A blanket factor of safety, which is generally used in conventional design procedures to implicitly include all the sources of uncertainty arising in geotechnical property evaluation, does not truly account for the involved risk. Owing to the random nature of soil media, it is essential to extensively study, characterize, and evaluate the various sources of uncertainty in geotechnical parameter evaluation. The present work aims at characterization of these sites using probabilistic techniques, and the total uncertainty attributed to design parameters is evaluated from the individual sources. It also highlights the importance of quantifying the variability of engineering parameters in geotechnical engineering by extending probabilistic approaches to studies on stability of shallow foundations and slopes. For the present study, geotechnical data from four sites are considered. The data from the first three sites are used for reliability analysis of shallow foundations. The data from the fourth site are used to evaluate the stability of soil slopes. The first site consists predominantly of cohesionless soil within the significant zone of influence. The second and third sites contain saturated cohesive soils, and the fourth site pertains to an unsaturated soil. The CPT cone tip resistance data in cohesionless soil were collected from the Texas A&M Riverside Sand Site, USA. The first set of CPT data on cohesive soil pertains to Keswick Clay of the Adelaide University Campus, Australia. The second set of CPT data on cohesive soil was collected from a power plant site on the east coast of the Indian state of Andhra Pradesh. Both these clayey soil deposits were observed to be saturated, with degrees of saturation greater than 95%, and the water table is located at relatively deeper depths compared to the depth of significant influence. For the slope problem, data were obtained from the Powari landslide area in the Himalayan region, Himachal Pradesh, India. A set of closely spaced cone tip resistance (qc) profiles obtained from these sites are used in the analysis. Random field theory is used to analyse the influence of variability of vertical as well as horizontal cone tip resistance of the supporting stratum on the allowable pressure of foundations. The test data have been checked for statistical homogeneity, which is recognized as a prerequisite for any statistical analysis using random field theory. Several non parametric and parametric tests, available in the literature, have been used to identify statistically homogeneous layers. The stationary residual component is used to evaluate the experimental autocorrelation functions. Correlation distance and subsequently the scale of fluctuation are calculated using the method of moments. The variance reduction function is evaluated from the computed autocorrelation distance and spatial averaging distance, and is used to reduce the variance of the data within the statistically homogeneous layers. The computed statistical parameters for the first three sites-mean, variance, and autocorrelation characteristics-are used to evaluate the allowable pressure of shallow foundations using First Order Reliability Methods (FORM) for predefined target reliability levels. Additionally, the effect of anisotropy of correlation structure is studied in a 2 D space. The effect of using either isotropic scales of fluctuation or perfect correlation on the bearing capacity of shallow foundations is examined. It is observed that the transformation model plays a major role in total uncertainty associated with the design parameter. In the absence of appropriate scales of fluctuation for a particular site, it may be suggested to use an upper bound value from the range of observed values in similar sites, which produces conservative estimates of bearing capacity. The study shows that the scale of fluctuation and averaging distance play a prominent role in predicting inherent spatial variability of soil properties. To ease the work of design engineers who deal with large volumes of geotechnical data and time consuming processes, resistance factors are developed through calibration on a regional basis. These resistance factors are developed through calibration with both working stress design and reliability based design approaches, and can serve the purpose in routine geotechnical design when used with sound engineering judgement. For surface stability analysis of unsaturated slopes, soil water characteristic curves (SWCCs) were obtained from Agricultural University records for nearby sites. These SWCC data are analysed and fitted to obtain hydraulic properties for unsaturated soils using the van Genuchten model. A finite difference code is used to evaluate suction characteristics at different depths for various elapsed times after cessation of a single rainfall event, based on appropriate boundary and initial conditions. Due to limited soil property data, a range of variability from published literature is considered in the analysis. Sensitivity analysis is carried out on all input parameters to assess their importance and to identify which parameters need to be treated as random variables. The performance of infinite slopes is evaluated using both deterministic and probabilistic approaches. The effect of saturated hydraulic conductivity is also examined. Seismic stability analysis of soil slopes is also conducted using a probabilistic approach. The work focuses on evaluating the optimum slope angle considering the variability in soil properties, cross correlation, and socio economic factors such as importance and sensitivity of the project, initial cost, and consequences of failure. A pseudo static approach is used. It is demonstrated that optimum slope angles under both static and seismic conditions can be evaluated considering the variability in the material properties. The results of the present study clearly demonstrate that probabilistic analysis of soil profiles provides a framework for quantifying subsurface information and forms the basis for predicting the reliability of foundations.