**A Two-Day Short Course by Dr. Gordon Fenton, Professor of Civil Engineering and Engineering Mathematics at Dalhousie University and Dr. Vaughan Griffiths, Professor of Civil Engineering at the Colorado School of Mines**

**Risk Assessment in Geotechnical Engineering**

**Monday & Tuesday, May 9 and 10, 2016**

**Course Program**

**Day 1:**

**8:30 - 9:15 Introduction to Risk in Geotechnics (DVG)**

- motivation for this course
- applications of probabilistic methods in current practice
- examples of slope stability
- introduction to event trees

**9:15 - 10:00 Basic Probability Theory (DVG)**

- basic set theory
- conditional probability
- total probability theorem
- Bayes' theorem

**10:00 - 10:15 Break**

**10:15 - 11:00 Introduction to Random Variables (DVG)**

- discrete and continuous random variables
- common probability density functions

**11:00 - 11:45 Use of Random Variables (DVG)**

- expected values and variance
- covariance and correlation
- examples of bearing capacity and slope stability

**11:45 - 1:00 Lunch**

**1:00 - 1:45 Reliability-Based Design (GAF)**

- history of geotechnical design
- development of LRFD
- LRFD examples

**1:45 - 2:30 Reliability Assessment and LRFD Theory (GAF)**

- resistance vs load reliability analysis
- reliability index
- going beyond calibration with WSD
- implementation problems in geotechnical engineering

**2:30 - 2:45 Break**

**2:45 - 3:15 Modeling Spatially Variable Soil Properties (GAF)**

- types of random fields
- mean, variance, and correlation structure

**3:15 - 4:15 Basics of Simulation and RFEM (GAF)**

- Monte Carlo simulation
- pseudo-random number generators
- simulation of random variables
- simulation of random fields
- the Random Finite Element Method (RFEM)

**Day 2:**

**8:30 - 10:15 Simple Tools for Probabilistic Analysis (DVG)**

- the First Order Second Moment (FOSM) method
- the First Order Reliability Method (FORM)

**10:00 - 10:15 Break**

**10:15 - 11:00 Simple Tools for Probabilistic Analysis (DVG)**

- the First Order Reliability Method (FORM) method (continued)
- simple Monte-Carlo (M-C) analysis assuming Single Random Variables

**11:00 - 11:45 Geotechnical example problems and software demonstrations (DVG)**

**11:45 - 1:00 Lunch**

**1:00 - 1:45 Estimation of Soil Statistics (GAF)**

- sample mean, sample variance, sample correlation length
- interpolation vs extrapolation
- choosing a distribution
- effect of correlation
- classical estimators
- the three averages

**1:45 - 2:30 Advanced Estimation Methods (GAF)**

- Best Linear Unbiased Estimation (BLUE)
- Geostatistics: Kriging

**2:30 - 2:45 Break**

**2:45 - 3:30 Risk-Based Decision Making (GAF)**

- decision making framework
- decision trees
- maximum expected value criterion

**3:30 - 4:00 Calibration of the 2014 Canadian Highway Bridge Design Code (GAF)**

- major philosophical changes
- floating resistance factor and level of understanding
- floating consequence factor and failure consequences

**4:00 - 4:15 Summary and Closure (GAF)**