bSLOPE: A Limit Equilibrium Slope Stability Analysis Code for iOS by Oliver C. Rickard and Nicholas Sitar Geotechnical Engineering Report No. UCB/GT/12-01 May 2012 Updated August 2012 bSLOPE: A Limit Equilibrium Slope Stability Analysis Code for iOS by Oliver C. Rickard and Nicholas Sitar Geotechnical Engineering Report No. UCB/GT/12-01 May 2012 Updated August 2012 Department of Civil and Environmental Engineering UC Berkeley Berkeley, CA, 94720 Table of Contents 1.1 INTRODUCTION ............................................................................................................................................. 1 1.2 LIMIT EQUILIBRIUM METHOD .................................................................................................................. 1 1.2.1 SPENCER SLICE FORMULATION .................................................................................................................................... 3 1.2.2 CRITICALITY ..................................................................................................................................................................... 4 1.2.3 CIRCULAR VS. NON-CIRCULAR ..................................................................................................................................... 4 1.3 SEARCH FOR CRITICAL FAILURE SURFACE ........................................................................................... 6 1.3.1 METHODOLOGY ............................................................................................................................................................... 6 1.3.2 CIRCULAR SEARCH .......................................................................................................................................................... 6 1.3.3 NON-CIRCULAR SEARCH ................................................................................................................................................ 6 Dynamic Programming ....................................................................................................................................................... 6 Conjugate-Gradient ............................................................................................................................................................... 7 Simplex ....................................................................................................................................................................................... 7 Monte Carlo Technique ....................................................................................................................................................... 7 Composite Differential Evolution (CoDE) .................................................................................................................... 7 2.1 BSLOPE ALGORITHM ................................................................................................................................... 8 2.1.1 OVERVIEW OF COMPUTATION ENGINE ....................................................................................................................... 8 Objective-C ................................................................................................................................................................................ 8 MATLAB ..................................................................................................................................................................................... 8 Functional Approach ............................................................................................................................................................ 9 SMUGMath ................................................................................................................................................................................ 9 Multithreading ..................................................................................................................................................................... 10 2.2 IMPLEMENTATION .................................................................................................................................... 12 2.2.1 PROBLEM SETUP .......................................................................................................................................................... 12 2.2.2 FS EVALUATION ........................................................................................................................................................... 12 2.2.3 SMOOTH SLIP GENERATION ....................................................................................................................................... 14 2.2.4 CODE IMPLEMENTATION ........................................................................................................................................... 15 2.3 EXAMPLE PROBLEMS ................................................................................................................................ 17 2.3.1 ZOLFAGHARI ET AL. (2005) INCLINED WEAK LAYER .......................................................................................... 17 2.3.2 ZOLFAGHARI ET AL. (2005) HORIZONTAL WEAK LAYER + GROUNDWATER ................................................. 19 2.3.3 DUNCAN AND WRIGHT (2005) - JAMES BAY DIKE .............................................................................................. 21 3 CONCLUSIONS ................................................................................................................................................. 22 4 REFERENCES .................................................................................................................................................... 23 APPENDIX A: FUNCTION DOCUMENTATION ............................................................................................ 26 Acknowledgments The iOS implementation of the Limit Equilibrium algorithm used herein is based on a MATLAB code written by Mr. Mohammed Tabarroki of the University of Science of Malaysia. His advice and generosity in sharing his insights into the computational aspects of the implementation are gratefully acknowledged. Professor Stephen Wright pointed out an error in the May 2012 report, and we are grateful to him for his assistance. The James Bay test case has been updated with the results from our corrected, released version of the application. 1.1 Introduction The purpose of this project was to demonstrate the capabilities of mobile devices for advanced computation and analysis. bSLOPE, is a slope stability code adapted for iOS and for iPad using a new computational engine based on the work of Tabarroki (Tabarroki 2012), and Wang (2011). To this end the fundamentals of Limit Equilibrium slope stability analysis are reviewed first and then the computational algorithms are introduced as they are implemented in bSLOPE. This report has two objectives: (1) To acquaint the user with the process that is used in bSLOPE to analyze a particular slope in order to understand the internal structure of the algorithms and the limitations of the code; and (2) To give other researchers the information necessary to improve and extend bSLOPE’s open source computation engine. bSLOPE represents a new approach to slope stability analysis and engineering applications in general. Traditional slope stability packages contain proprietary, closed-source computation engines, and have limited user interfaces. These user interfaces often become the bottleneck in processing of slopes. bSLOPE uses innovative touch interfaces and drafting systems that take advantage of new technology in graphical interfaces. These interfaces allow the user of bSLOPE to rapidly formulate cross-sections and quickly perform the necessary analyses in the field. bSLOPE focuses on the most common tasks that an engineer would need to do in order to verify a slope’s safety. Its aim is to be simple and easy to use, while still using the most recent advances in numerical limit equilibrium algorithms. bSLOPE is not intended to be a replacement for many commercially accepted codes which have more analysis options. It is intended to complement these applications with a field component. 1.2 Limit Equilibrium Method The limit equilibrium method of analysis for static slopes is still the most widely used tool to analyze the stability of a given soil slope. It considers a soil continuum of different strata, and given a particular failure surface in the form of lines or arcs, a “Factor of Safety” is found through the application of force and/or moment equilibrium. The factor of safety is defined as the ratio of the resisting force or moment to the driving force or moment. So if a particular failure surface has a Factor of Safety (FS) of 1, then it is at the “limit” of equilibrium assumptions. A Factor of Safety less than 1 means that the driving forces are greater than the resisting forces and the slope will fail either in rotation, translation, or a combination thereof. In order to take an arbitrary geometry and automate the procedure of calculating a FS for a particular failure surface geometry, it is necessary to divide the sliding mass into sections. There are a variety of methods for performing this task; however, the most common method is to divide the mass into vertical slices. This is called the method of slices. The equilibrium 1 conditions are applied to each slice and contributions to either driving or resisting force or moment