The University of Texas at Austin CE394M Advanced Analysis in Geotechnical Engineering

CE 394M Advanced Analysis in Geotechnical Engineering Spring 2019

Instructor: Dr. Krishna Kumar Lectures: MWF 10:00-11:00 ECJ 9.227B ECJ 3.402 krishnak@utexas.edu Office Hours: M 08:30 – 10:00, W 11:00 – 12:00 or by appointment

Textbooks: A formal textbook is not required for this course.

References: Duncan, J.M., Byrne, P., Wong, K.S., and Mabry, P. (1980) “Strength, Stress-Strain and Bulk Modulus Parameters for Finite Element Analyses of Stresses and Movements in Soil Masses,” Geotechnical Engineering Report UCB/GT/80-01, University of California, Berkeley, CA. (Available electronically on Canvas)

Potts, D. and Zdravkovic, L. (1999) “Finite Element Analysis in Geotechnical Engineering: Theory,” Thomas Telford, London.

Wood, D.M. (1990) “Soil Behaviour and Critical State Soil Mechanics,” Cambridge University Press.

Course Description The primary focus of this course is to introduce numerical modeling of geotechnical problems with a special focus on the finite element methods to stress-deformation and seepage problems. The specific aims are: ● To formulate geotechnical problems as a well-posed boundary value problem (boundary and initial conditions, free-surface problems) ● To introduce the basics of geotechnical finite element method (drained, undrained and coupled analysis), selective and reduced integration ● To perform finite element analysis of geotechnical structures, critically validate the results of the analysis and develop recommendations regarding realistic consulting projects. ● To model geotechnical processes (fills, excavation, subsurface flow) ● To introduce various soil constitutive laws for modeling the stress-strain-strength response of soil, familiarize with the derivation of model parameters from the element laboratory tests and express constitutive models in tensor form to implement them into a finite element code ● Specifically, linear elastic, linear elastic-perfectly plastic, nonlinear elastic (hyperbolic), and nonlinear elasto-plastic (Cam-Clay) models will be discussed.

Students will use the PLAXIS computer program to perform static analyses of earth structures and use Python/Matlab to develop constitutive models and simple FE programs.

Objectives On completion of this, students should be able to: ● Develop soil models in the three-dimensional tensorial form ● Perform non-linear finite element analysis of geotechnical problems ● Define appropriate boundary conditions and stress/strain measures ● Assess the results with deformation plots and stress path plots

Assignments/Projects The University of Texas at Austin CE394M Advanced Analysis in Geotechnical Engineering

Individual homework assignments and group projects will be the backbone of this course. Students will utilize selected numerical methods and constitutive models to analyze geotechnical problems. About four projects will be assigned throughout the semester and students will work in groups for the projects. Project reports should be written as consulting engineer letter reports. The reports should be concise and must be written individually. Groups will be required to present their findings for some of the assignments. Late assignments will be accepted, but grades will be reduced by 25%.

Exams There will be two examinations given in this course and will carry equal weighting. All examinations will be open-notes. The examination I will be given on the week of 25th March 2019 time TBD. The examination II will be given on the default date for the final examination for the courses taught on MWF from 10:00-11:00 AM, which is: Saturday, May 18, 2019, from 14:00 - 16:00.

Participation You are responsible for material covered in class. Classroom participation is strongly encouraged. Attendance is required during group presentations.

Grading: Assignments/Projects 40% Exam I 30% Exam II 30%

The plus/minus system of grading will be used. All assignments and exams can be resubmitted with the errors fixed for full credit in homework/projects and to a maximum of an extra 10% in the exams.

Students with Disabilities The University of Texas at Austin provides upon request appropriate academic adjustments for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471- 4241 TDD or the College of Engineering Director of Students with Disabilities at 471-4382.

Deadlines and Drop Policies Students are strongly urged to make any changes in their course schedules during the first week of classes so that other students who need to add the course can be accommodated.

From the 1st through the 4th class day, graduate students can drop a course via the web and receive a refund. During the 5th through the 12th class day, graduate students must initiate drops in the department that offers the course and receive a refund. After the 12th class day, no refund is given. No class can be added after the 12th class day. From the 13th through the 20th class day, an automatic Q is assigned with approval from the Graduate Advisor and the Graduate Dean. From the 21st class day through the last class day, graduate students can drop a class with permission from the instructor, Graduate Advisor, and the Graduate Dean. Students with 20-hr/week GRA/TA appointment or a fellowship may not drop below 9 hours. The University of Texas at Austin CE394M Advanced Analysis in Geotechnical Engineering

Course Outline/Lecture Schedule

1. Introduction to numerical modeling in geomechanics (2 lectures) ● Role of numerical modeling in geotechnical engineering ● Matrix analysis of structures

2. Finite Element Method (11 lectures) ● Finite Element formulation (strong and weak forms) ● Shape functions, element matrices, assembly and application of boundary conditions ● Two-dimensional problems ● Isoparametric elements (quadrilateral, triangle) ● Numerical integration ● Error estimations ● Time-dependent problems ● Application of Finite Element methods to geomechanics ● An introduction to PLAXIS

3. Constitutive modeling of soils (20 lectures) ● Introduction to tensors and continuum mechanics ● Soil behavior (stresses and strains) and stress paths 3.1 Linear elasticity ● Theory ● Isotropic/anisotropic ● Plane stress/plane strain/axisymmetry 3.2 Linear elastic-perfectly plastic ● Theory ● Yield functions and failure criteria ● Drucker-Prager and Mohr-Coulomb 3.3 Non-Linear, stress-dependent elastic hyperbolic model ● Theory ● Developing model parameters from laboratory data 3.4 Critical state soil mechanics and Cam-Clay ● Hardening laws ● Critical state soil mechanics ● Cam-Clay and modified Cam-Clay models

4. Seepage (6 lectures) ● Darcy’s law in one and two dimensions ● Laplace’s equation for flow ● Using the finite element method to solve Laplace’s equation

5. Other numerical methods (4 lectures) ● Finite Difference ● Material Point Method ● Discrete Element Method