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Basic Slurry Wall Design

Giovanni Bonita, PhD, PE, PG

Traditional Design Practice

• Historically, structural and geotechnical engineers focused on their area of expertise

• Geotechs weren't ‘designers’, they were recommenders’

• Worked in interactive mode, at best.

• This was inefficient because each party treated the others expertise as a black box.

• “That’s a structural question…” or “That’s a geotechquestion...” – Inefficient!

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Example: Structural Design

• Design approach is subjective

• Results are highly dependent on how model below BOE.

• Staging not considered

Example: Structural Design

• May miss temporary critical construction conditions

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Result

Structural design for a geotechnical application

Design Considerations

• Type of and properties of soils

• Elevation of groundwater

• Dimensions of excavation

• Duration and sequence of excavation

• Location and type of lateral supports

• Preloading of lateral supports

• Presence of adjacent structures and allowable movement

• Temporary or permanent structure

• Transient and fixed surcharge loads

• Headroom

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• Limit Equilibrium

• Apparent Pressure

• Redistribution of Limit Equilibrium into Apparent Pressure

• Finite Difference

• Finite Element

Basic Design Concepts

• Intent of the approach is to compute brace loads, NOT to represent the actual stresses on the wall.

• Originated from empirical measurements of braced excavation on flexible walls.

• Use effective stress properties for sands, therefore add water back into analysis

• Total unit weight and strengths for clays, therefore don’t add water

• Compute brace loads using tributary area

• Assumes hinge at subgrade, therefore M=0 at subgrade

• If need to compute embedment of toe, assume triangular active and passive earth pressure distribution below subgrade and M=0 at subgrade

Apparent Pressure Approach

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Apparent Earth Pressure Diagrams

From FHWA (1999) Geotechnical Engineering Circular No 4 - Ground Anchors and Anchored Systems

Soft Clays - when N>6, m=0.4, otherwise m=1.0 (N = H/Su) (Peck, 1969)

Apparent Pressure Approach – Soft Clays

• The Terzaghi and Peck (1967) diagrams did not account for the development of soil failure below the bottom of the excavation.

From FHWA (1999) Geotechnical Engineering Circular No 4 - Ground Anchors and Anchored Systems

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• Use of classic apparent pressure diagram for cases where N>6, may result in unconservativeearth pressure estimations if don’t apply correction factor (m=0.4)

• Use of classic apparent pressure diagram for cases where 4<N<6, may result in over conservative earth pressure estimations if apply correction factor m=0.4

From FHWA (1999) Geotechnical Engineering Circular No 4 –Ground Anchors and Anchored Systems


FHWA (1999) recommendations:

• For 4<N<5.14, use Ka = 0.22

• For N>5.14, compute Ka

using Equation 12 or use chart

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• Use ‘Redistribution’ of Active pressures into Apparent Pressure Envelope Duncan (1990)

• Compute Total Active Earth Pressure Force using triangular active pressure

• Assume a shape of an apparent earth pressure diagram (sand, soft clay, stiff clay, etc)

• Compute a Ph using the shape of earth pressure diagram

• Factor Ph to an equivalent earth pressure (Factor = 1.1-1.5)

• Compute brace loads and embedment as described earlier

Multilayered Soils


Steps

1. Compute Active Earth PressuresA. h = (0.31) (240 psf) = 74 psf (Ka = tan2

(45 - /2)

B. h = 74 psf + (110 pcf) (20 ft) (0.31) = 682 psf

C. h = 682 psf + (110 pcf) (20 ft – 750 psf) = 2132 psf

D. h = 2132 psf + (110 pcf – 62.4 pcf) = (20ft) (750 psf) = 2334 psf

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2. Compute Active Earth Pressure Force

EA = (74 psf) (20ft) + (682 psf – 74 psf) (20ft) (½) + (2132 psf) (20ft) + (2334 psf – 2132 psf) (20ft) (½)

EA = 52.2 k/ft

3. Decide on Apparent Earth Pressure Diagram

IF N = = = 6

Since N>4, use diagram for soft clay

4. Compute Equivalent Earth Pressure

If (½) Ph) (10 ft + Ph) (30ft) = (52.2 k/ft)(F)

use F=1.2 (avg)

Then 5 Ph + 30 Ph + 62.6 k/ft

Ph = 1790 psf

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5. Compute Equivalent Unit Weight

eq = = 78.8 pcf

6. Check Kh = K(geq H + qs) or

K=

Keq = 0.52

7. Check with Henkel’s Equation

Assume d/H = 0.5 (toe ~ 20ft)

Ka =

Ka =

Ka = 0.49 Ka (Henkels) ~ Ka (Equivalent earth pressure)

ok for permanent, high for temporary

8. Compute Brace Loads using tributary areas.

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9. Confirm embedment is satisfactory by assuming hinge at subgrades, active and passive pressures below grade.

10. Check for temporary stages:

A. Compute active and passive pressure using, conventional earth pressure theory (i.e. Rankine)

B. ƩΜ about lowest brace to confirm embedment

C. Compute brace loads through force equilibrium.

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Limitations of Apparent Pressure Approach

• Empirical – Only valid for conditions that match the empirical data. Requires questionable extrapolation for other conditions.

• Intended for brace loads only – Need to use crude approximations to estimate bending moment for wall design.

• Still a debate whether apparent earth pressures are acceptable for permanent conditions.

• Developed for flexible wall systems which tend to act as simple beams spanning between the brace levels

• For rigid wall systems the pattern of wall displacement that develops during the actual excavation and bracing sequence can have a major effect on the bending moment in the wall and the distribution of load to the bracing.

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• Mostly applicable to conditions with a stable subgrade -Significant unbalanced pressures below subgrade (unbalanced water pressure on impermeable walls or unbalanced soil pressures in soft clays) require ad hoc corrections or supplemental calculations.

• Envelope design approach does not give the actual loads in the system at the end of excavation – needed for evaluating brace removal stages or designing walls that are incorporated into permanent structures.

• Envelope design approach does not provide insight into the actual behavior of the support system, which can be used for optimizing the design.

• Does not provide any information on wall displacements and ground movements.

Limitations of Apparent Pressure Approach

• Models the actual sequence of excavation and brace installation in a stage by stage analysis.

• Soil and water pressures applied to the wall represent actual pressures (not apparent pressure envelopes) and calculated loads represent actual loads (not upper bound design envelopes).

• Can incorporate soil-structure interaction (i.e., earth pressure varies with displacement)

Staged Construction Analysis

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• Three general methods have been used for staged construction analyses:

1. Equivalent Beam Method - no soil-structure interaction

2. Beam on Elastic Foundation Method - approximate soil-structure interaction model

3. Finite Element Method - models full soil-structure interaction

Staged Construction Analysis

Equivalent Beam Method

• Similar to the method used for design of anchored bulkheads, except that an analysis is performed at each excavation stage.

• Earth pressures based on classical active and passive earth pressure theory.

• At each excavation stage a pin support is assumed at a point below subgrade and the portion of the wall below this point is neglected.

• For granular soils a pin support can be assumed at the point of zero net pressure, but this can be unconservative for undrained cohesive soils. If the depth of the wall is less than the depth required for the pin support, the wall is assumed to cantilever below the lowest brace level.

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• Wall is modeled as continuous beam. Braces are modeled as rigid supports or springs. To account for the wall deflection that occurs prior to installation of each brace, an initial displacement is applied to the brace support, based on the results from the previous analysis stage.

• The analysis can be performed using any general purpose computer program capable of analyzing simple beams and frames, but requires extensive hand computations to set up the analysis of each stage.

• This method is outdated and not used as commonly as in the past.

Equivalent Beam Method

Beam on Elastic Foundation Analysis

• Earth pressures modeled with a series of independent spring supports (Winkler elastic foundation model). Springs start with initial load equal to at-rest pressure. Load increases or decreases with lateral wall displacement (modulus of subgrade reaction) until the limiting value of active or passive pressure is reached.

• Winkler elastic foundation model approximates the wall-soil interaction with a one-dimensional model, instead of a two-dimensional model that includes the soil mass.

• Required soil parameters: unit weight, Ko, Ka, Kp and modulus of subgrade reaction

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• Modulus of subgrade reaction is not a true soil property and should be adjusted based on the effective influence depth, which varies with the size of the loaded area.

• The Winkler model does not include the effects of arching within the soil mass.

• Displacements are sensitive to the values of subgrade modulus used in the analysis, but the brace loads and wall bending moments are usually not very sensitive to these values.

• Does not provide information on the ground movements behind the wall – need to estimate the ground movements based on the calculated wall displacement.


• Computer programs that automate the analysis are available (WALLAP). The WALLAP program uses Young’s modulus as input for the soil stiffness and automatically converts this to adjusted values of subgrade reaction modulus using a closed-form elastic solution for rectangular loadings.

• The analytical model is realistic enough to provide useful insight into the behavior of the wall-soil system, and the automated computer programs make it easy to perform multiple analyses for optimizing the design and evaluating sensitivity to input parameters.

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• Two-dimensional model includes the soil mass surrounding the excavation.

• Soil mass is subdivided into finite elements that are connected to each other at nodes. The mathematical formulation of the finite element represents the stress-strain response of the soil mass inside the element as interactions between the nodes. (The same approach is used for structural elements.)

• Forces are applied at the nodes and the displacements of the nodes are calculated by solving the system of simultaneous equations that define the interactions between the nodes.

Finite Element Analysis

• The stress-strain response of the soil is represented by a mathematical soil model that can vary from a simple linear-elastic model to a complex nonlinear elasto-plastic model. The stress-strain response can be defined in terms of effective stresses or total stresses. The required input parameters depend on the soil model used.

• Generally want to use a soil model that can model failure (plastic yield) when the soil strength is exceeded. In some problems, the ability to model volumetric changes in the soil (consolidation or dilation) may be important.

• A linear elastic-fully plastic Mohr-Coloumb soil model is often used. In this model the soil is linear elastic until it reaches failure defined by the Mohr-Coloumb criterion, and then it becomes perfectly plastic.


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• FE analysis provides information on the ground movements outside the excavation, and can also model the soil-structure interaction response of structures outside the excavation to the excavation-induced ground movements.

• FE analyses have been difficult and time consuming to perform in the past, but new user friendly programs (e.g., PLAXIS) are making their use more common.

• FE analysis can realistically model complex behavior - but the usefulness and accuracy of this method is ultimately limited by our ability to determine the input soil parameters.

• Beware of the black box!


Example: Evaluation of Impacts of Excavation on Tunnel

• Forces in the wall and shoring are important.

• Deformation of adjacent tunnel also important.

• Used PLAXIS with non-linear soil model

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EXAMPLE: EVALUATION OF IMPACTS OF EXCAVATION ON TUNNEL


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Example: Evaluation of Impacts of Excavation on Tunnel


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Generally Speaking…

Reinforced concrete slurry wall design

• Use ACI 318-05, Chapter 10 for design of vertical flexural reinforcing.

• Use ACI 318-05, Chapter 11 for shear. Shear reinforcing may be required depending on the demand.

• After computing the bending moment and shear for the internal wales, use Chapters 10 and 11 for design.

• Use ACI 318-05, Section 7.12 for remaining horizontal reinforcing as temperature and shrinkage steel.

Structural Design


SPTC Wall Design

• Use AISC LRFD or ASD for design of steel members

Structural Design

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Tiebacks

• Calculate Bearing Strength (ACI 318-05, Section 10.17)

• Calculate Punching Shear Strength (ACI 318-05, Section 11.12.2.1)

• Calculate Shear Capacity of Section (ACI 318-05, Section 11.12.2.1)

Structural Design

Three Dimensional Analysis

• Useful when have unequal surcharge loading

• Penetrations in shafts

• Skewed Tiebacks and unique geometry

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Three Dimensional Analysis

3-D Model

Horizontal Displacements

Principal Stress vectors showing arching –Stresses concentrate on sides of vault

Plan View

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Structural Design

• Generate Shear and Moment relationships over height of wall using conventionally accepted approach

• For reinforced concrete wall, size reinforcing per ACI 318

• Consider base reinforcing and then additional steel only where needed (both moment and shear).

• For SPTC walls, design steel per AISC ASD or LRFD

Movement of Adjacent Structures

(angular distortion)

h1

h2 - h1

1 2

h2

h = L12

Angular Distortion () = Measurement of shear in structure

Horizontal Strain () = Measurement of horizontal extension of structure

From Boscardin and Cording (1989)

Damage Estimation Tools

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Estimation of Damage to Adjacent Structures

From Son and Cording (2005)

Conclusions

• True structural approach to designing slurry walls can be inefficient

• Apparent pressure envelopes, although conservative, generally allow for reasonable brace loads. Use for permanent conditions is still debatable.

• Need to consider temporary staging, as it may be the critical case

• Always check toe embedment

• Advanced techniques (finite element and beam on an elastic foundation) can result in more efficient designs if performed properly. Some allow for movement estimations of adjacent structures.

• Beware of black box analyses.

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Thank You!

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