Transient and Total Settlement Estimation of Shallow Strip Footing Subjected to Eccentrically Inclined Static Load and Cyclic Load on Granular Soil

Abstract

Analysis of response of shallow foundations due to eccentrically inclined static load is a problem domain of specific interest. With increase in number of structures in the vicinity of industrial areas, shallow foundations, in addition to static loads, are often influenced by machine induced cyclic loads. An analysis of established theories indicates that the former problem i.e. the static analysis has been dealt separately from the later one i.e. cyclic analysis. The bearing capacity of shallow foundations under eccentrically inclined static load was studied by Meyerhof (1953), Meyerhof (1963), Hansen (1970), Patra et al. (2012), Sahu et al. (2016), Pham et al. (2020). The settlement under cyclic load was observed by Raymond and Komos (1978). A similar methodology was adopted by Das et al. (1995), Tafreshi et al. (2011), Fatah et al. (2019). It is observed that “the incorporation of load eccentricity as well as load inclination is limited to static cases only”. Also it is key to note that “Incorporation of influence of cyclic load is limited to centric vertical cases only”. The objective of this work is to fill this gap by using both the concepts, in order to observe the foundation settlement in more practical situations. In order to achieve this objective, a numerical model for a strip footing is developed based on Beam on Nonlinear Winkler Foundation (BNWF) model. The initial results are validated with existing experimental results reported by Patra et al. (2012). Then, the study is extended for cyclic analysis problem. The model is developed for three relative densities (Dr) of 35%, 51% and 69% respectively. The embedment ratio Df/B is varied from 0 to 1. The eccentricity ratio i.e. e/B is varied from 0 to 0.15 in 0.05 increment. The value of angle of load inclination with the vertical (α) is varied from 0 to 15 in 5 increment. The intensity of cyclic load (qd(max)) is taken as 5%, 10% and 13% of the ultimate bearing capacity (qu). The footing settlement due to allowable static load and cyclic load is observed. The allowable static load is calculated as the ultimate load divided by a factor of safety. Then settlement of the foundation due to first load cycle and due to 106 load cycles are analyzed separately. The settlement of the footing as a response to first load cycle is termed as transient response which is the immediate response of the foundation to the change in loading state. The settlement due to 106 cycles is the long term response of the foundation. During the analysis of long term response, the settlement pattern is observed and a key phenomenon is noticed, i.e. the settlement becomes constant at a particular value of number of load cycles. While studying the long term response, the effect of minor viii variations in the frequency of loading is also considered. In total, 1728 models are simulated for transient settlement response and 5184 models are simulated for long term response. Based on the dataset obtained from the numerical analysis, artificial intelligence techniques are applied to analyze the generated dataset. These artificial intelligence techniques are Levenberg Marquardt Neural Network (LMNN), Bayesian Regularization Neural Network (BRNN), Support Vector Machine (SVM), Multivariate Adaptive Regression Splines (MARS), Adaptive Neuro Fuzzy Interface System (ANFIS) and Multi Gene Genetic Programming (MGGP). The outcomes of the above mentioned procedures indicate that, the settlement of the foundation is largely influenced by the amount of the static load already applied on the foundation. It is also noted that a minor variation of frequency of loading is not significant in determining the settlement of the footing.