Machine Learning-Aided Monte Carlo Simulation and Subset Simulation

Abstract

The use of probabilistic analysis (PA) of slopes as an effective method for evaluating the uncertainty that is so pervasive in variables has become increasingly common in recent years. This study presents a case study which was conducted to demonstrate the efficiency of an embankment which consists of an 11.693 m-high soil slope, placing emphasis on PA and reliability evaluation. The investigation employs Monte Carlo simulation (MCS) and subset simulation (SS) techniques, considering seismic coefficients (k h ) of 0.12 for Zone-III and 0.14 for Zone-IV, along with varying pore water pressure ratios (r u =0.0, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>05</mml:mn> </mml:mrow> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> ). MCS with 10,000 samples was used to test the probabilistic response of the proposed embankment. This work also discusses the results of SS, in which 1,400 samples are generated from UPSS 3.0 Excel add-ins, which permits rapid PA in such a way that they progressively shift toward the failure zone in successive stages. The study delves into the impact of uncertainty on the probability of failure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> . Findings reveal an increased <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> with rising coefficients of variation, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and k h values, underscoring the sensitivity to soil parameter variations. SS outperforms MCS in simulating low probabilities, demanding smaller sample sizes and less computational time. Furthermore, the machine learning technique has been used to optimize the worst <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> condition. In this current research, three neural network-based models, namely recurrent neural network, long short-term memory (LSTM), and Bayesian neural network, have been used. Based on the performance of the models, the three neural network-based models were compared in the testing phase, and the proposed LSTM outperformed the other neural networks ( R 2 = 0.9962 and root mean square error = 0.0051).

Topics & Concepts