Numerical Simulation of the Response of Sandy Soils Treated with PV-drains Antonios Vytiniotis, Andrew J. Whittle & Eduardo Kausel MIT Department of Civil & Environmental Engineering Progress Report for NEESR GC Workshop February 5 th 2009
Outline Planned activities for 2008 [NEESGC meeting January 2008] Treating of PV-drains Implementing an element for PV-drains Use a non-linear model to simulate response Implementing a soil model Progress during 2008 PV Drain elements in OpenSees Evaluation using Centrifuge Model Data Research Plans for 2009
PV-Drains Installation Centrifuge Model Outflow during shaking
Storage Capacity Effect GW Level Clay Storage Capacity Sand Bedrock Applied acceleration
Analytical Solutions Radial Dissipation of Excess Pore Pressure: Unit Cell Excess Pore Pressure Accumulation: Key References Seed & Booker: Perfect drains Onoue et al. Effect of well resistance Pestana et al.: FEQDRAIN (includes storage effect)
Validation : Importance of Drain Resistance [ Gravel drains: Onoue et al., 1987] Predictions of Seed & Booker Read r u Much lower than measured data Measured r u fit modified theory (well resistance) Onoue, 1987
2-D (Plane-Strain) Modeling Approximation Match the degree of consolidation (average diffusion) within soil Doesn t match the pore pressures at all points PV Drain Equivalent plane strain PV Drain k ax k pl For infinite permeability drains inside a uniform soil: k ax : true soil permeability, k pl : equivalent soil permeability in a plane stain analysis n :drain spacing ratio Hird et al., 1992
Equivalence between radial and plane strain drainage around a pre-fabricated drain Normalized Excess Pore Pressure Ratio around a perfect PV drain 1 Normalized Exces ss Pore Pressure Rati io 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 ABAQUS results 0.0 0.2 0.4 0.6 0.8 1.0 R R/Ro or x/ro Axisymmetric, t=1s Plane Strain, t=1s Axisymmetric, t=0.1s Plane Strain, t=0.1s Great match using Hird et al equation!!! x,r 0
PV-Drains: Hydraulics Darcy Weisbach Equation λ, dimensionless flow coefficient L, length of pipe D, diameter of pipe ρ, mass density of fluid V, average velocity of the flow
PV-Drain Elements: Laminar flow
PV-Drain Elements: Turbulent flow
PV-Drains: Opensees Implementation Laminar flow: element Pipelin2 eleid node1 node2 Material Area C l γ w Turbulent Flow element Pipe4 eleid node1 node2 Material Area C t γ w d c
PV-Drains: Scale Modeling Issues (I) Scaling of flow: Q P = Q M N 2 Scaling of Drain Flow Properties: Laminar flow C lp = C lm N 3 Turbulent flow C tp = C tm N 5/2
PV-Drains: Scale Modeling Issues (II) Scaling of Reynolds number For the same pore fluid: Re P = Re M N For different pore fluid (diffusion scaled) Re P = Re M N2 Problem Statement: What is the model scale diameter of a PVdrain (where flow is laminar) that corresponds to a selected prototype scale diameter (where flow is turbulent)?
PV-Drains: Scale Modeling Issues (III) Flow Rate, Q Q Laminar Drains max Fully Turbulent Drains i max Pressure Gradient, i The model scale diameter that minimizes differences between model scale laminar and prototype scale turbulent flow is:
PV-Drains Validation: Centrifuge Model Kamai et al, 2008
PV-Drains Validation: Centrifuge Model PV drains Yolo Loam 437mm 6.56m Loose Sand Loose Sand Dense Sand Dense Sand Applied acceleration 1650mm 24.75m
PV-Drains Validation: Centrifuge Model Shaking sequence
PV-Drains Validation: Base Case Scenario No-tension connection Yolo Loam* Drains Periodic Boundary Conditions #1 #2 #3 #4 #5 #6 #7 437 mm 6.56 m Loose Sand**, k pl Loose Sand**, k ax Nodal mass Dense Sand**, k pl 1650 mm 24.75 m Applied acceleration Dense Sand**, k ax *pressure independent multiyield model, QUAD Elements ** pressure dependent multiyield model, QUADUP Elements
PV-Drains Validation: Final Deformed Shape Numerical simulations indicate the effectiveness of PV-Drains!!
Flow Rate (m 3 /s) Volume (m 3 ) Displacement (m) 4 x 10-3 2 0 PV-Drains Validation: PV-drain outflow a. Flow coming out of drain No2 vs Time Solution Laminar limit (prototype scale) Laminar limit (model scale) -2 0 2 4 6 8 10 12 14 Time (s) x 10-3 b. Volume of water coming out of drain No2 vs Time 6 4 2 0 0 2 4 6 8 10 12 14 Time (s) 4 x 10-3 2 0 c. Vertical displacement on top of drain No2 Indirect Direct -2 0 2 4 6 8 10 12 14 Time (s)
PV-Drains Validation: Pore Pressures, a max =0.07g Treated side Untreated side 20 10 A D Pore Pressure, p (kpa) 0 60 50 40 30 80 70 B C E F 60 50 0 5 10 15 20 25 30 Time, t (s) 0 5 10 15 20 25 30 Time, t (s) Experiment Simulation
PV-Drains Validation: Horizontal Accelerations, a max =0.07g 2 Treated side Untreated side 1 A D 0-1 Horizontal Acceleration, α (m/s 2 ) -2 2 1 0-1 -2 1 B C E F 0-1 0 2 4 6 8 10 12 Time, t (s) 0 2 4 6 8 10 12 Time, t (s) Experiment Simulation
PV-Drains Validation: Surface Horizontal Displacements, a max =0.07g 0.2 Treated side Untreated side 0.1 C F 0-0.1-0.2 0.2 Horizontal, u (m) 0.1 0-0.1 B E -0.2 0.1 A D 0-0.1 0 2 4 6 8 10 12 Time, t (s) 0 2 4 6 8 10 12 Time, t (s) Experiment Simulation
Predicted Net Lateral Movements, a max =0.07g
PV-Drains Validation: Surface Settlements, a max =0.07g Treated side Untreated side 0 0.02 C F 0.04 Vertical Settlement, u y (m) 0 0.02 0.04 0.06 0.08 0 B E A D 0.05 0.1 0 2 4 6 8 10 12 Time, t (s) 0 2 4 6 8 10 12 Time, t (s) Experiment Simulation
PV-Drains: Validation Observations Excess Pore Pressures Reasonable agreement at mid layer Underestimate at top of sand Horizontal Accelerations Good agreement on treated side No deamplification in untreated sand No prediction of liquefaction event No prediction of liquefaction event Horizontal Displacements Reasonable magnitudes No slippage between sand and loam Vertical Displacements (surface) Mismatched across model Effect of variable g field (centrifuge) and/or slope failure mechanism?
PV-Drains: Summary Implementation of new PV Drain Elements Laminar & fully turbulent flow regimes Capability to evaluate mass balance in controlled experiments (centrifuge) Established new understanding for scale modeling of PV drains Include drain storage effect Evaluation using centrifuge model data SSK01, March 2007 (Kamai, et al., 2008a) Performance close to perfect drain case Field performance Long term performance? Effect of clogging, sedimentation & biofouling?
Constitutive Models Current application Multi-yield surface plasticity (Elgamal & Yang, 2001-2002) Advantages: Available in Opensees Parameters previously selected: Nevada sand, Yolo Loam Disadvantages: Re-calibration of parameters for each density Limited predictive capability (cyclic mobility) Future applications Bounding surface plasticity models (UC Davis & NTUA groups) Family of models (many sub-versions!) Dafalias, Manzari, Papadimitriou, Andrianopoulos (2004-2008) More predictive capability Unique set of material input parameters (void ratio as state variable) Implementation in Opensees V1: Dafalias-Manzari implemented Opensees wrapper: Jeremic currently being evaluated V2: Papadimitriou-Andianopoulos implemented in Flac To be ported to Opensees
Project Side Deliverables Publications Vytiniotis SM Thesis, February 2009 Draft paper to be submitted on PV drain implementation (Spring 2009) Opensees documentation: PV-drain elements
Research Goals 2009 Upgrade analyses with better constitutive model Evaluate predictive capabilities of UCD-NTUA models Effect on predicted performance Equivalent properties of improved soil mass Free-field properties for SSI research Application Colloidal Silica treatment Background studies completed Importance of gel compressibility? Immobilized pore space