Numerical Modelling of Ground Improvement by Prof. Minna Karstunen Outline • Introduction • Numerical modelling of vertical drains • Numerical modelling of column methods – 2D axisymmetric unit cell – Volume averaging – 3D modelling
Numerical Modelling of Ground Improvement Prof Minna Karstunen Outline • Introduction • Numerical modelling of vertical drains • Numerical modelling of column methods – 2D axisymmetric unit cell – Volume averaging – 3D modelling Why numerical modelling? Current design methods are simplistic and limited Soft soils are very complex non-linear materials The problems have a complex 3D geometry Need to be able to model soil-structure interaction Difficult to demonstrate new technologies Important aspects in numerical modelling of ground improvement • Choice of constitutive model of soil and material added • Numerical model (2D, enhanced 2D or 3D) • Modelling of soil improvement – Discrete modelling of inclusions – Homogenisation technique – “Smeared” approach based on experience Important aspects in numerical modelling of ground improvement • Time dependent behaviour (creep and consolidation) • Installation effects: – Excess pwp – Changes in cu, OCR, K0, k etc Geometrical Truths • For ground improvement problems involving large groups of columns/drains under a large uniform load, axisymmetric unit cell is very useful Geometrical Truths • Mapping to 2D plane strain often introduces error/problems: you want to keep the axial stiffness equal (EA3D=EA2D) and hence have to modify either modulus or spacing Option 1: Keep column stiffness and modify geometry (problem: punching for floating columns) Option 2: Keep geometry and reduce column stiffness (ok for working loads only|) Geometrical Truths • Other problems are truly 3D, and cannot be modelled in 2Dmapping to 2D Vertical drains • to reduce the length of the drainage paths • to shorten consolidation time • to increase shear strength FE Analysis of Vertical Drains • Embankment analyses assume 2D plane strain conditions, but the consolidation of soil around a vertical drain is an axisymmetric problem • Thus, conventional 2D finite element method cannot be used directly • It is not practical to use a 3D finite element method because of the large amount of computation that is involved Outline: Introduction Deep mixed columns Geometry Constitutive models and parameters : Soft clay and Dry Crust Deep mixed columns Results Embankment on deep mixed columns Geometry: End bearing: Floating columns: 5m 5m 3.0m Dry Crust 10m Columns 0.6m 1.0 m-spacing GW: -1.0m Columns 0.6m 1.0 m-spacing 23m Bedrock 13m Vanttila Clay Embankment: • Soil parameters: laboratory tests on Vanttila clay (Koskinen & Karstunen 2004) • Column parameters based on back calculation of laboratory tests on deep mixed Vanttila clay • Dry crust and Vanttila clay are over-consolidated: Pre-overburden pressure POP=σ’p-σ’v K0oc=(1-sinϕ’)*OCRsinϕ’ Soil Parameters: Vanttila Clay S-CLAY1S: implemented as User defined soil model Depth [m] e0 POP [kPa] K0OC α x Dry Crust 0-1 1.7 30 1.0 0.63 90 Vanttila clay - 11 3.2 10 0.76 0.46 20 Soil Soil γ [kN/m3] κ ν’ λ M kx= ky [m/day] Dry crust 13.8 0.029 0.2 0.25 1.6 6.9E-5 Vanttila clay 13.8 0.032 0.2 0.88 1.2 6.9E-5 Soil β µ λi a b Dry crust 1.07 15 0.07 11 0.2 Vanttila clay 0.76 40 0.27 11 0.2 Deep Mixed Columns Parameters • Drained and undrained triaxial tests 180 160 q [kPa] 140 Eoedref Eurref ν’ur • MNhard model [kPa] [kPa] [kPa] 12000 12000 27000 0.35 100 80 60 40 – Stiffness is highly nonlinear and dependent on confining pressure E50ref 120 CADC C29 20 HS-model 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Axial strain, ε 1, % m c’ ϕ’ γ’ Tensil estreng th - kPa [ °] [kN/m3 ] [kPa] 0.8 14 36 15 20 Reference stress for stiffness, pref=100kPa 14.0 Embankment Parameters: Embankment fill: MC-model Soil E ν’ur Tensilestrength [kPa] c’ [kPa] ϕ’ [ °] 0.3 2 38 [kPa] Embankment 40000 Plane strain analysis Analysis: • Soil layers and column modelled as “undrained” material • Calculate greenfield conditions: K0oc and POP • Install columns: “wish in place” column “drained” • Construction of embankment in steps “undrained” • Consolidation analysis to excess pore pressure of kPa Geometry: 3D – Plane strain Schweiger 2005 Settlement trough: 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 Depth of the deposit: 23m Settlement [m] Settlement [m] Depth of the deposit: 10m natural ground end bearing columns 10 20 30 40 Distance from symmetry axis [m] 50 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 -2.0 natural ground end bearing columns floating columns 10 20 30 Distance from symmetry axis [m] Improvement ratio: smax/sc max End bearing: 7.3 End bearing: 3.6 Floating: 2.5 40 50 Lateral displacement: at the toe Depth of the deposit: 10m Depth of the deposit: 23m -5 Settlement [m] Settlement [m] -5 -10 -15 -15 natural grounds end bearing columns -20 0.00 -10 0.05 0.10 0.15 0.20 Distance from symmetry axis [m] natural grounds end bearing columns floating columns -20 0.00 0.05 0.10 0.15 0.20 Distance from symmetry axis [m] Improvement ratio: hmax/hc max End bearing: 4.06 End bearing: 3.54 Floating: 4.5 Deformed mesh: Differential vertical stresses dσ’v : Depth of the deposit: 10m Natural ground dσ’v [kPa] End bearing columns Differential vertical stresses dσ’v : Depth of the deposit: 23m End bearing columns Floating columns dσ’v [kPa] Differential vertical stresses dσ’v : Depth of the deposit: 23m End bearing columns dσ’v [kPa] stiff soft stiff soft Summary: Settlements: • Shallow deposit: Settlements are reduced by a factor of about • Deep deposit: • Floating columns are very effective in reducing settlements • Bending observed at the bottom of the column below the toe area Load transfer: • Load transfer mechanism is not uniform with depth (dependent on stiffness ratio and OCR of soil) • Arching observed up to the top of the embankment • Magnitude of load transfer in the upper part of the improved area is almost the same for floating columns and end bearing columns