Comparison of Current Design Methods for Granular & Grouted Inclusions

Transcription

1 Comparison of Current Design Methods for Granular & Grouted Inclusions Brandon BUSCHMEIER DENSIFY Rapid Impact Compaction Vibro-Densification Dynamic Compaction CONSOLIDATE Vacuum Consolidation Wick Drains + Surcharge Soil Mixing / Jet Grouting Rigid Inclusions / CMC / VCC Stone Columns / Aggregate Piers / DR GROUND IMPROVEMENT TECHNIQUES STIFFEN 2 1

2 GRANULAR Stone Columns Aggregate Piers ( Geopiers / VibroPiers ) Dynamic Replacement GROUTED Deep Soil Mixing Jet Grouting Vibro-Concrete Columns Controlled Modulus Columns 3 GROUND IMPROVEMENT CHALLENGES & MITIGATIONS Embankments Footing Local / Global BEARING CAPACITY Differential Total Sand Silts / Clays SETTLEMENT LIQUEFACTION 4 2

3 THE PRESSURE THAT A STRUCTURE / FOUNDATION / EMBANKMENT CAN APPLY ON THE SOIL WITHOUT CAUSING OVERSTRESSING (SHEAR FAILURE ) BEARING CAPACITY Embankments Footing Local / Global 5 Internal Stability of the Inclusions: Failure by Lateral Expansion (Bulging) Failure by Shearing Failure by Punching Failure by Lateral Expansion (Bulging) Failure by Shearing Failure by Punching 6 3

4 Bearing Capacity of Footings: Terzaghi (1943) showed that : Strip : Q ult = c N c + D f.n g + 0.5B..N Square : Q ult = 1.2 c N c + D f.n g + 0.4B..N Circular : Q ult = 1.2 c N c + D f.n g + 0.3B..N With: N q = e tan tan 2 ( 45 + /2 ) N c = ( N q -1) cot Several expressions proposed for N Meyerhoff : N N q -1) tan ( 1.4 BEARING CAPACITY UNDER FOOTINGS GRANULAR COLUMNS 7 Bearing Capacity of Footings: Shear Strain Compatibility Homogenized Soil Characteristics The inclusions carry a large part of the load and are internally stable. with The soil is unloaded as compared to the same footing without improvement. 8 4

5 Bearing Capacity of Footings: Load on Footing < bearing capacity of soil + reaction from rigid inclusion Simplified Approach : Verify that the load on the footing is less than the combination of : 1. Bearing capacity of the soil AND 2.The reaction from the Rigid inclusion at the top of the rigid inclusions The rigid inclusions are unloading the soil BEARING CAPACITY UNDER FOOTINGS 9 Embankment Stability: F = Driving Forces / Resisting Forces EMBANKMENT STABILITY- REMINDER 10 5

6 Embankment Stability: Shear Strain Compatibility Homogenized Soil Characteristics with The inclusions carry a large part of the load and are internally stable The soil is unloaded as compared to the same footing without improvement 11 Embankment Stability: Each granular inclusion intercepting the failure surface provides additional shear resistance because of : - Higher friction angle - Higher vertical load in the column The problem is simplified by assuming equivalent characteristics EMBANKMENT STABILITY 12 6

7 Embankment Stability: The block of equivalent improved soil is here seen in light blue EMBANKMENT STABILITY 13 Embankment Stability: Same principle as under footing : - The rigid inclusion provide three effects : 1. Unloading of the soils between the inclusions 2. Increased shear resistance along the failure plane 3. Vertical force across the failure plane similar to soil nailing EMBANKMENT STABILITY 14 7

8 Embankment Stability: In the absence of easy analytical methods, FEM analysis is therefore widely used to model embankments on rigid inclusions 1. Axisymmetric model not feasible 2. 2D Plane strain possible but need to adapt model: Rigid Inclusions = Thin wall => need to change EI and EA for equivalent wall Thin wall surface area is larger => need to change interface EMBANKMENT STABILITY 15 Embankment Stability: 2D plane strain gives a good approximation of deformations - Tends to over-estimate the load transfer to the rigid inclusions Limitations of FEM Modeling - Not easy to obtain the factor of safety against failure - C-Phi analysis can be done but it has limitations EMBANKMENT STABILITY 16 8

9 up us Equal settlement planes bulging Equal Planes / Strain compatibility Lateral expansion of column Load transfer function of area replacement ratio Equal plane strain Load transfer through arching Load transfer through negative skin friction 17 Several methods of calculation have been proposed but they all rely on the principle that the modulus of deformation of the aggregate inclusions and the surrounding soil are compatible 5 < Ec / Es / 10 The settlement are equal between the column and the soil Horizontal planes remain horizontal while the settlement occurs 18 9

10 From Conservation of Load : The ratio of stresses n is a fundamental parameter in all the calculation methods Typically : 3 < n < All the methods define the settlement reduction factor as : The factor is the best indication of the effectiveness of the design Typically : 2 < <

11 PURELY ELASTIC METHODS : HOMOGENEIZATION METHOD In the case of a purely elastic model, writing Hook s law together with the conservation of load and the hypothesis of strain compatibility leads to : 21 PURELY ELASTIC METHODS : HOMOGENEIZATION METHOD Nevertheless, there are some limitations : Overestimates the load in inclusions Overestimates and underestimates settlement Not traditionally applicable under footings This solution is simplistic: Elastic, no bulging lateral expansion Gives a first approximation of the settlements 22 11

12 ELASTO-PLASTIC METHODS : PRIEBE (1995) Priebe derives his formula from several simplifying assumptions : - The deformations in the soil are linear elastic and are assimilated to the deformation of a thick hollow pipe with an internal pressure equal to the difference of the horizontal stress in the column and in the soil - Oedometric conditions of the unit cell - The deformations of the column are following the deformations of the soil and are plastic (Mohr-Coulomb) - The aggregate is incompressible (deformations at constant volume) - He also assumes that all horizontal sections remain plane i.e. the vertical deformation (settlement) of the soil and the columns are always equal (strain compatibility) - Priebe assume that the soil is in hydrostatic conditions i.e. K=1 23 ELASTO-PLASTIC METHODS : PRIEBE (1995) - Priebe Charts are an easy way to find the settlement reduction factor Calculate settlement without improvement and apply Priebe reduction factor to get the improved settlement 24 12

13 MANY OTHER METHODS EXIST : - Elastic - Balaam & Booker (1981) - Elasto-Plastic - Ghionna & Jamiolkowski (1981) - Goughnour & Bayuk (1979) - Empirical - Thorburn - GreenWood - All are based on n,, and Es / Ec and give a factor β - Trend: - FEM analysis particularly for more complex geometries 25 COMPARISON ELASTIC / ELASTO-PLASTIC METHODS: Elastic Methods Increase of load on system has marginal effect Elasto-Plastic Methods Load is critical Progressive plasticization of the column with depth Priebe Popular but not conservative 26 13

14 SETTLEMENT UNDER FOOTINGS : All previous methods assume infinite number of columns under an infinite spread load Under footings, two (2) factors : 1. Limited loaded area => decrease of vertical stress with depth 2. At the outer edge of the footing, less confinement (radial stress) 27 SETTLEMENT UNDER FOOTINGS : Priebe developed a semi-empirical method to calculate the settlement of a footing on granular inclusions Method: Calculate the settlement for an infinite, uniformly loaded area on granular inclusion improved soil Apply an additional settlement reduction factor 28 14

15 The calculation of settlements for a structure supported by a network of rigid inclusions is not as straight-forward as the case of granular inclusion WHY? The ratio of moduli is such (several orders of magnitude) that there is no strain compatibility => Complex soilstructure interaction Equal plane strain Load transfer through arching Load transfer through negative skin friction 29 4 Main Components that interact with each other : - The structure / slab - The Load Transfer Platform - The rigid inclusion - The surrounding soils The design of a rigid inclusion solution must incorporate all components SETTLEMENT UNDER A SLAB 30 15

16 The Load Transfer Platform - Made of granular compacted material - Can also be made of cement or lime treatment sands and silts - Can have layers of geo-grid or geotextile depending on the design method - Generally 2 to 4 feet thick - Main Purpose : Transfer the load from structure to rigid inclusions SETTLEMENT UNDER A SLAB 31 The Load Transfer Platform H qs Several design approaches are possible : - FHWA : Collin Method : Beam Method - British Standard : Membrane Method - France ASIRI: Arching Method All methods have the same goal : Evaluate Qp and qs as function of H (Thickness) (Friction angle) E (Modulus) SETTLEMENT UNDER A SLAB 32 16

17 Some methods include at least one layer of geotextile: NEVERTHELESS: Geotextile layers are deemed too deformable Require large deformation to mobilize full tensile strength For Slabs Tight Criteria For Embankments Lateral Restraint Confinement SETTLEMENT UNDER A SLAB 33 ASIRI proposes Method of Diffusion Cone The angle of diffusion is assumed to be the peak friction angle of the material in the LTP From the proposed geometry, the load in the rigid inclusion Qp and the stress in the soil qs can be estimated and used for settlement calculation SETTLEMENT UNDER A SLAB 34 17

18 Additional Load Transfer Mechanism : Negative skin friction => as it compresses, the soil grabs onto the rigid inclusion and transfers load to it SETTLEMENT UNDER A SLAB 35 Full view of the load transfer mechanism below the LTP SETTLEMENT UNDER A SLAB 36 18

19 To take all these interactions into account : - Load transfer in LTP - Load transfer along rigid inclusion - Differential settlement between soil and inclusion USE OF FEM SETTLEMENT UNDER A SLAB 37 Axisymmetric models are commonly used under slabs Symmetry Simplification Comparable to more complex models => Unit Cell Analysis SETTLEMENT UNDER A SLAB 38 19

20 Under footings, since the thickness of the LTP is usually thinner and the rigidity of the footing forces the neutral plane to be at the bottom of footing, an analytical approach is feasible The problem is decomposed into two domains : Soil in between the inclusions Rigid inclusions Interaction between two domains is described by the shear friction along the rigid inclusion SETTLEMENT UNDER FOOTINGS 39 3D FEM ANALYSIS CAN ALSO BE USED FOR FOOTING WITH 2D PLANE STRAIN NOT FEASIBLE SETTLEMENT UNDER FOOTINGS 40 20

21 Liquefaction occurs from: Shaking Pore water pressure rises Effective stress is reduced to zero which corresponds to a complete loss of shear strength Typically observed in saturated loose sand and sandy silts Loose sands have a tendency to contract under shear stress while dense sand dilate under shear stress LIQUEFACTION 41 Soil Liquefaction Mitigation: Compaction with Vibration Shear Reinforcement Draining Effect Ductile Limited Compaction with Static Displacement Shear Reinforcement but no Strain Compatibility Brittle 42 21

22 Seed & Idriss Simplified ( 1971 ) NCEER workshop ( 1996 ) CSR : Cyclic Stress Ratio induced by earthquake CRR : Cyclic Resistance Ratio of the in-situ soil F = CRR/CSR CSR CRR mostly based on historical data of previous earthquakes CRR increase with (N 1 ) 60 The denser the ground, the higher the factor of safety LIQUEFACTION 43 Soil Liquefaction Mitigation: Baez & Martin ( 1993 ) Granular inclusions attract shear stresses because of higher shear modulus Reduce shear stress in surrounding soils Define new CSR reduction factor: Area replacement ratio Ratio of shear moduli Compaction through Vibration Shear Reinforcement Ductile 44 22

23 Soil Liquefaction Mitigation: Limited compaction through static displacement - Area Replacement ratios are limited to 2 to 10% - Static displacement does not allow significant improvement unless dense grid ( $$ ) Shear reinforcement but no strain compatibility - Main action of discrete rigid inclusions is to reduce earthquake induced shear strains, thereby limiting pore pressure generation - Increase composite strength - Provide support for structure in case of liquefaction - BUT : Research has shown that there is no strain compatibility + brittle behavior 45 Soil Liquefaction Mitigation: Olgun & Martin ( 2008 ) While the soil deforms mainly in shear, rigid inclusions deform both in shear and bending ( flexural deformation ) The column does not follow the deformation of the soil and is therefore less effective in reducing the shear strains and stresses ( soil flows around column ) The more rigid the column, the more predominant the flexural behavior Cannot apply Baez & Martin to rigid inclusions 46 23

24 Soil Liquefaction Mitigation: One development is the use of soil mixing panel to create cells and mitigate liquefaction The soil-mix panels are constructed using either secant soil mix columns or Cutter-Soil Mixing 47 Soil Liquefaction Mitigation: Results of current research are showing that the soil mix panels are changing the behavior of the ground and therefore reducing the level of ground shaking under a structure Stiff Panels attract a significant amount of shear stress ( Shear Wall ) Reduction of the induced loading on the soil Mitigation of liquefaction Provide support for structure 48 24

25 CONCLUSION Slab / Embankment Footing Slab / Embankment Footing BEARING CAPACITY HOMOGENI- -ZATION METHOD HOMOGENI - ZATION METHOD RIGID INCLUSIONS AS NAILS OR 2D OR 3D FEM / CHECK BENDING RIGID INCLUSIONS UNLOAD THE SOIL / CHECK INTERNAL STABILITY SETTLEMENT HOMOGENI -ZATION METHOD PRIEBE MODIFIED PRIEBE METHOD FEM AXISYMETRICAL ANALYTICAL ITERATIVE SOLUTION OR 3D FEM AXISYMETRICAL LIQUEFACTION SHEAR HOMOGENIZATION METHOD NCEER ( 1996 )??? SHEAR REINFORCEMENT OF PANEL SOLUTION 49 Questions!? THANKS! 50 25