Uncertainty in Earthquake-Induced Deformation Model Estimates: Case History of Calabasas Landslide Joseph Wartman and Patrick Strenk Department of Civil, Architectural and Environmental Engineering Drexel University, Philadelphia, USA
Sliding (Rigid) Block Procedure [Newmark 1965] Sliding Block/Plane Assumptions well-defined slip surface soil is rigid, perfectly plastic soil does not lose strength during shaking Failure Mass/Slip Surface
Decoupled Procedure 1. Dynamic Response Analyses 2. Sliding Block Analyses Makdisi and Seed (1978)
Fully Coupled Analysis
A variety of deformation models, and some basic questions Which models are most accurate? Which models are most precise? How confident can one be with model predictions? What are the sources of uncertainty in a slope deformation analysis, and of these, which are the most important? When is a model become sufficiently detailed for the task?
Research Methods Physical models + Significant insight to fundamental mechanisms + Limited variability in input parameters - Boundaries can be a concern for dynamic response - How well do they represent reality? Numerical simulations + Can provide insight to system-level performance + Parametric studies Case Histories + Full scale and entirely realistic How to account for variability/uncertainty in parameters?
Research Approach 1) Test a suite of slope deformation models against high quality case histories 2) Capture variation/uncertainty in input parameters (friction angle, water level, ground motion, etc.) using Monte Carlo simulations Assumptions Field measurements correct Representative samples Shear surface at its residual strength Plane strain (2D) conditions Wavelet-based ground motion generation procedure No uncertainty associated with location of shear surface and modulus reduction and damping curves
Case History Selection Selected Case Histories Calabasas Landslide (1994 Northridge) Ditullio Landslide (1989 Loma Prieta) Upper Laurel Landslide (1989 Loma Prieta) La Villita Dam (1985 Michoacan) Chiquita Canyon C Landfill (1994 Northridge) Chiquita Canyon D Landfill (1994 Northridge) Dynamic Soil Properties Earthquake Ground Motions Deformation Measurements Cross-Section Field-Testing Laboratory Testing - Present or “High-Quality” - Present or “Fair-Quality” - Not Present or “Poor-Quality”
Practice-Oriented Slope Deformation Models (Simple to Complex) Rigid-Block Simplified Decoupled Double-integration (Y-SLIP_PM) Makdisi & Seed (1978) Bray et al. (1998) Simplified Rigid-Block Newmark (1965) Sarma (1975) Franklin & Chang (1977) Hynes-Griffin & Franklin (1984) Ambraseys & Menu (1988) Yegian et al. (1991) Ambraseys & Srbulov (1994) Bray & Travasarou (2007) Jibson (2007) [3 equations] Saygili & Rathje (2008) [2 equations] Decoupled 1D FLAC & Y-SLIP_PM SHAKE & Y-SLIP_PM 2D FLAC & Y-SLIP_PM Coupled*
Simplified Rigid-Block Methods Slope Deformation Models: Input Parameters Simplified Rigid-Block Methods Input Parameters PGA PGV Tp Neq Mw Ms r Ia Newmark (1965) x - Sarma (1975) Franklin & Chang (1977) Hynes-Griffin & Franklin (1984) Ambraseys & Menu (1988) Yegian et al. (1991) Ambraseys & Srbulov (1994) Bray & Travasarou (2007) Jibson (2007) [Method A] Jibson (2007) [Method B] Jibson (2007) [Method C] Saygili & Rathje (2008) [Method A] Saygili & Rathje (2008) [Method B]
Slope Deformation Models: Input Parameters Methods Input Parameters PGA To D5-95 Tm Crest PGA Rock Outcrop HEA Rigid block (Y-SLIP_PM) - x Makdisi & Seed (1978) Bray et al. (1998) 1D Decoupled (FLAC, Y-SLIP_PM) (SHAKE, Y-SLIP_PM) 2D Decoupled
Case History: Calabasas, CA Landslide (Northridge Earthquake) Pradel et al. 2005 Many test borings Laboratory test results Shear wave profiles Close-vicinity ground motion stations Subsurface, direct measurements of ground deformation = 5 cm
Calabasas: Cross Section
Estimation of residual friction angle
Estimation of residual friction angle Liquid Limit, COV = 19%, Source: Phoon & Kulhawy (1999), Distribution: normal
Estimation of residual friction angle
Groundwater level GW Table, COV = n/a, Mean +/- 1 m, distribution: triangular
Monte Carlo Simulation: Yield Acceleration
Monte Carlo Simulation: Yield Acceleration
Monte Carlo Simulation: Shear Wave Velocity Profile Shear Wave Velocity over 30 m (vs30), COV = 3%, (measured), Moss (2008) Distribution: log-normal
Monte Carlo Simulation: Shear Wave Velocity
Monte Carlo Simulation: Earthquake Ground Motion
Monte Carlo Simulation: Earthquake Ground Motion
Monte Carlo Simulation: Earthquake Ground Motion Wavelet-based generation of spectrum-compatible time-histories, Mukherjee and Gupta (2002)
Monte Carlo Simulation: Earthquake Ground Motion
Monte Carlo Simulation: Earthquake Ground Motion
SHAKE vs. FLAC, 1D Simulations
Monte Carlo Simulations: Latin Hypercube Sampling
Results: Calabasas
Results: Calabasas extreme values large deformations with decoupled Close to measured site-specific decoupled more constrained newer models capture site-specific
Results: Calabasas – differences between two rigid block methods
Findings Which models are most accurate? Average percent errors: Simplified rigid block: -34% Rigid block: -66% Simplified decoupled: 192% Decoupled: -44% Which models are most precise? Simpler models generally have slightly lower standard deviations simplified site specific
Findings How confident can one be with model predictions?
Findings What are the sources of uncertainty in a slope deformation analysis, and of these, which are the most important? Variation in Ky is significant Ky is dominated by strength (ground water is less critical) Strength assessment should be an important component of an investigation program
Findings When is a model become sufficiently detailed for the task? Simple approaches may be sufficient when parameters are uncertain Complex models are not a very good “value” Users should consider parameter uncertainties when selecting a model A trade-off exists between: - Simple models exclude important details resulting in prediction biases - Complex models can have significant parameter uncertainties Model development should consider realistic uncertainties in parameters – Complex models are conceptually sound, but paired with real-world uncertainty, these can lead to a wide range of responses
Findings Under-prediction may result from: distributed straining and/or volumetric compression within soil mass, model limitations (e.g. tuning ratio effects) Wartman et al. 2003
Monte Carlo Simulation: Earthquake Ground Motion