SOILS AND FOUNDATIONS Lesson 08

SOILS AND FOUNDATIONS SOILS AND FOUNDATIONS

Testing

Experience

Theory

Lesson 08 Lesson 08

Chapter 8

Chapter 8 –– Shallow FoundationsShallow Foundations

Topics Topics

ggTopic 1 (Section 8.0, 8.1, 8.2, 8.3, 8.4)Topic 1 (Section 8.0, 8.1, 8.2, 8.3, 8.4)

- -

ggTopic 2 (Section 8.5, 8.6, 8.7, 8.8, 8.9)Topic 2 (Section 8.5, 8.6, 8.7, 8.8, 8.9)

- -

- -

- -

ggTopic 3 (Section 8.10)Topic 3 (Section 8.10)

- -

Shallow Foundations Shallow Foundations

Lesson 08

Lesson 08 - - Topic 1 Topic 1

General and Bearing Capacity General and Bearing Capacity

Section 8.0 to 8.4

Section 8.0 to 8.4

Learning Outcomes Learning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:

be able to:

- -

- -

- -

in sand and clay

- -

- -

foundations

Stresses Imposed by Structures Stresses Imposed by Structures

ggAbutment and piers may have shallow or deep Abutment and piers may have shallow or deep foundations

foundations

General Approach to Foundation General Approach to Foundation

Design Design

ggDuty of Foundation DesignerDuty of Foundation Designer

- -

conforms to prescribed structural criteria and properly accounts for the intended function of properly accounts for the intended function of

the structure the structure

ggRational method of designRational method of design

- -

Recommended Foundation Design Recommended Foundation Design

Approach Approach

ggStep 1:Step 1:

Determine:

Determine:

- -

loads

- -

- -

•• UnderclearanceUnderclearance requirementsrequirements

•• Structure type, span lengthsStructure type, span lengths

•• Time constraints on constructionTime constraints on construction

•• Extreme event loadingExtreme event loading

•• Construction load requirementsConstruction load requirements

Recommended Foundation Design Recommended Foundation Design

Approach Approach

ggStep 2:Step 2:

Evaluate subsurface investigation and Evaluate subsurface investigation and

laboratory testing data for reliability and laboratory testing data for reliability and

completeness completeness

Choose design method consistent with Choose design method consistent with

quality and quantity of subsurface data quality and quantity of subsurface data

Recommended Foundation Design Recommended Foundation Design

Approach Approach

ggStep 3:Step 3:

Consider alternate foundation types Consider alternate foundation types

Foundation Alternatives Foundation Alternatives

ggShallow FoundationsShallow Foundations

ggDeep FoundationsDeep Foundations

- -

Foundation Cost Foundation Cost

gg Express foundation capacity in terms of $Express foundation capacity in terms of $

gg TOTAL cost of foundation system divided by the TOTAL cost of foundation system divided by the load supported by the foundation in tons

load supported by the foundation in tons

gg TOTAL cost of a foundation must include ALL TOTAL cost of a foundation must include ALL costs associated with the foundations

costs associated with the foundations

-- Need for excavation support system, pile caps, etc.Need for excavation support system, pile caps, etc.

-- Environmental restrictionsEnvironmental restrictions

-- All other factors as applicableAll other factors as applicable

Foundation Cost Foundation Cost

ggIf estimated costs of alternative foundation If estimated costs of alternative foundation systems during design are within 15%, the systems during design are within 15%, the

alternate foundation designs should be alternate foundation designs should be

considered for inclusion in contract considered for inclusion in contract

documents documents

Loads and Limit States Loads and Limit States

ggLoadsLoads

- -

- -

ggFoundation limit statesFoundation limit states

- -

•• Bearing capacity, eccentricity, sliding, global stability, Bearing capacity, eccentricity, sliding, global stability, structural capacity

structural capacity

- -

•• Excessive settlement, excessive lateral displacement, Excessive settlement, excessive lateral displacement, structural deterioration of foundation

structural deterioration of foundation

Types of Shallow Foundations Types of Shallow Foundations

ggIsolated Spread FootingsIsolated Spread Footings

- -

Types of Shallow Foundations Types of Shallow Foundations

ggCombined Strip Spread FootingsCombined Strip Spread Footings

- -

Shallow Foundations for Bridge Shallow Foundations for Bridge

Abutments

Abutments

Shallow Foundations for Retaining Shallow Foundations for Retaining

Walls

Walls

Combined Footings Combined Footings

2 1

Original Ground Abutment Fill

Toe of Side Slope

Toe of End Slope

Mat Foundations Mat Foundations

REINFORCED CONCRETE MAT

Spread Footing Design Procedure Spread Footing Design Procedure

ggGeotechnical design of spread footing is a Geotechnical design of spread footing is a two part process

two part process

ggFirst Part:First Part:

- -

failure in soil

ggSecond Part:Second Part:

- -

Allowable Bearing Capacity Allowable Bearing Capacity

gg Allowable bearing capacity is lesser of:Allowable bearing capacity is lesser of:

Applied stress that will result in shear failure Applied stress that will result in shear failure divided by FS

divided by FS

-- Ultimate limit criterionUltimate limit criterion

OROR

Applied stress that results in a specified amount of Applied stress that results in a specified amount of settlement of the structure

settlement of the structure -- Serviceability criterionServiceability criterion

Bearing Capacity Chart Bearing Capacity Chart

Effective Footing Width, ft (m)

Allowable Bearing Capacity, ksf (kPa)

Ultimate Bearing Capacity, qult

Contours of Allowable Bearing Capacity for a given settlement

S1 S2 S3 Allowable Bearing Capacity,

FS q_all = q^ult

Design Process Flow Chart Design Process Flow Chart

ggFigure 8Figure 8--1010

Bearing Capacity Bearing Capacity

ggBearing capacity failure occurs when the Bearing capacity failure occurs when the

shear strength of foundation soil is exceeded shear strength of foundation soil is exceeded

ggSimilar to slope stability failureSimilar to slope stability failure

II

I III

C D

A B E

Q

L = ∞ q

ψ

Bearing Bearing

Capacity Capacity

Failure Failure

Mechanisms Mechanisms

ggGeneral shearGeneral shear

ggLocal shearLocal shear

ggPunching shearPunching shear

(a) GENERAL SHEAR

(b) LOCAL SHEAR

(c) PUNCHING SHEAR

LOAD

SETTLEMENT

LOAD

SETTLEMENT

LOAD

SETTLEMENT

SURFACE TEST

TEST AT GREATER DEPTH

Footing Dimension Terminology Footing Dimension Terminology

ggBB_ff = Width of footing= Width of footing

- -

ggLL_ff = Length of footing= Length of footing

ggDD_ff = Depth of = Depth of

embedment of footing embedment of footing

L_f

D_f B_f

Basic Bearing Capacity Equation Basic Bearing Capacity Equation

ggEquation 8Equation 8--88

cc = cohesion= cohesion

qq = surcharge at footing base= surcharge at footing base

NN_cc, , NN_qq, N, N_γγ = Bearing capacity factors= Bearing capacity factors γγ = unit weight of foundation soil= unit weight of foundation soil

) f )(N

)(B (

0.5 q )

(N q

c ) (N ult c

q = + + γ γ

Assumptions of Basic Bearing Assumptions of Basic Bearing

Capacity Equation (Section 8.4.3) Capacity Equation (Section 8.4.3)

ggStrip (continuous) footingStrip (continuous) footing

ggRigid footingRigid footing

ggGeneral shearGeneral shear

ggConcentric loading (i.e., loading through the Concentric loading (i.e., loading through the centroid

centroid of the footing)of the footing)

ggFooting bearing on level surface of Footing bearing on level surface of homogeneous soil

homogeneous soil

ggNo impact of groundwaterNo impact of groundwater

Bearing Capacity Factors Bearing Capacity Factors

1 10 100 1000

0 5 10 15 20 25 30 35 40 45

Friction Angle, degrees

Bearing Capacity Factors

N_q

N_c

N_γ

Figure 8-15 Table 8-1

Example 8

Example 8 - - 1 1

γsub = 63 pcf

d = D = 5′ γT = 125 pcf

B = 6′

φ = 20°

c = 500 psf

Example 8

Example 8 - - 1 1

ggSolutionSolution

Effect of Variation of Soil Properties Effect of Variation of Soil Properties

and Footing Dimensions (Table 8

and Footing Dimensions (Table 8 - - 2) 2)

Cohesive Soil

Cohesionless Soil φ = 0

c = 1000 psf q_ult (psf)

φ = 30^o c = 0 q_ult (psf) A. Initial situation: γ = 120 pcf, D_f = 0',

B_f = 5', deep water table

5140 6720

B. Effect of embedment: D_f = 5', γ=120 pcf, B_f = 5', deep water table

C. Effect of width: B_f = 10' γ = 120 pcf, D_f = 0', deep water table

D. Effect of water table at surface:

γ = 57.6 pcf, D_f = 0', B_f = 5' Properties and Dimensions γ = γ_a = effective unit weight γ_b = submerged unit weight D_f = embedment depth

B_f = footing width (assume strip footing)

Effect of Variation of Soil Properties Effect of Variation of Soil Properties

and Footing Dimensions (Table 8

and Footing Dimensions (Table 8 - - 2) 2)

Cohesive Soil

Cohesionless Soil φ = 0

c = 1000 psf q_ult (psf)

φ = 30^o c = 0 q_ult (psf) A. Initial situation: γ = 120 pcf, D_f = 0',

B_f = 5', deep water table

5140 6720

B. Effect of embedment: D_f = 5', γ=120 pcf, B_f = 5', deep water table

5740 17760

C. Effect of width: B_f = 10' γ = 120 pcf, D_f = 0', deep water table

5140 13440

D. Effect of water table at surface:

γ = 57.6 pcf, D_f = 0', B_f = 5'

5140 3226

Properties and Dimensions γ = γ_a = effective unit weight γ_b = submerged unit weight D_f = embedment depth

B_f = footing width (assume strip footing)

Student Exercise 5 Student Exercise 5

ggFind the allowable bearing capacity assuming Find the allowable bearing capacity assuming a FS=3 for the condition shown below for a

a FS=3 for the condition shown below for a 10’x50’ footing with rough base

10’x50’ footing with rough base

30′

4′

10′

Final Grade

Sand

γ = 115 pcf φ = 35°

C = 0

Bearing Capacity Correction Factors Bearing Capacity Correction Factors

ggFooting shapeFooting shape

- -

ggDepth of water tableDepth of water table

ggEmbedment depthEmbedment depth

ggSloping ground surfaceSloping ground surface

ggInclined baseInclined base

ggInclined loadingInclined loading

Student Exercise 5 Student Exercise 5

ggSolutionSolution

Modified Bearing Capacity Equation Modified Bearing Capacity Equation

Equation

Equation 8 8 - - 11 11

gg ss_cc, s, s_γγ, s, s_qq shape correction factorsshape correction factors

gg bb_cc, b, b_γγ, , bb_qq base inclination correction factorsbase inclination correction factors

gg CC_wqwq, C, C_wwγγ groundwater correction factorsgroundwater correction factors

gg dd_qq embedment correction factorembedment correction factor

gg NN_cc, N, N_γγ, , NN_qq bearing capacity factors as function of bearing capacity factors as function of φφ

γ γ γ

γ

+ +

= cN s b qN C s b d 0 . 5 B N C s b

q

Estimation of

Estimation of φ φ for Bearing Capacity for Bearing Capacity Factors (Table 8

Factors (Table 8 - - 3) 3)

Description Very

Loose Loose Medium Dense Very Dense Corrected N-value

N1₆₀ 0 4 10 30 50

Friction angle

φ Degrees 25 –

30

27 –

32 30 – 35 35 – 40

38 – 43 Moist unit weight

(γ) pcf

70 – 100

90 – 115

110 – 130

120 – 140

130 – 150

Shape Correction Factors Shape Correction Factors

ggBasic equation assumes strip footing which Basic equation assumes strip footing which means

means LL_ff/B/B_ff ≥≥ 1010

ggFor footings with For footings with LL_ff/B/B_ff << 1010 apply shape apply shape correction factors

correction factors

ggCompute the effective shape of the footing Compute the effective shape of the footing based on eccentricity

based on eccentricity

Effective Footing Dimensions Effective Footing Dimensions

B′

= B

– 2e

; L′

= L

– 2e

; A′= B′

L′

Pressure Distributions Pressure Distributions

Structural design

Structural design Sizing the footingSizing the footing

Shape Correction Factors Shape Correction Factors

Factor

Friction Angle

Cohesion Term (s_c)

Unit Weight Term (s_γ)

Surcharge Term (s_q)

φ = 0 1.0 1.0

φ > 0 Shape

Factors, s_c, s_γ, s_q

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ φ

+ tan

L 1 B

f f

⎟⎟⎠

⎜⎜ ⎞

⎝ + ⎛

f f

L 5 1 B

⎟⎟⎠

⎜⎜ ⎞

⎝

⎟⎟⎛

⎠

⎜⎜ ⎞

⎝ +⎛

c q f

f

N N L

1 B ⎟⎟

⎠

⎜⎜ ⎞

⎝

− ⎛

f f

L 4 B . 0 1

ggIn routine foundation design, use of effective In routine foundation design, use of effective dimensions in shape factors is not practical dimensions in shape factors is not practical

Location of Groundwater table Location of Groundwater table

ggTo correct the unit weightTo correct the unit weight

D_W C_Wγ C_Wq

0 0.5 0.5

D_f 0.5 1.0

> 1.5B_f + D_f 1.0 1.0

Note: For intermediate positions of the groundwater table, interpolate between the values shown above.

Embedment Depth Embedment Depth

ggTo account for the To account for the

shearing resistance in shearing resistance in the soil above the

the soil above the footing base

footing base

Friction Angle, φ

(degrees) D_f/B_f d_q 32

1 2 4 8

1.20 1.30 1.35 1.40

37

1 2 4 8

1.20 1.25 1.30 1.35

42

1 2 4 8

1.15 1.20 1.25 1.30 See Note

Note: The depth correction factor should be used only when the soils above the

footing bearing elevation are as competent as the soils

beneath the footing level;

otherwise, the depth correction factor should be taken as 1.0.

Sloping Ground Surface Sloping Ground Surface

ggModify the bearing capacity equation as Modify the bearing capacity equation as follows:

follows:

ggUseful in designing footings constructed Useful in designing footings constructed within bridge approach fills

within bridge approach fills

) )(N

)(B (

0.5 )

(N c

q

=

+ γ

Footing in Slope

Footing in Slope

Footing Near Slope

Footing Near Slope

Inclined Base Inclined Base

ggFootings with inclined base should be Footings with inclined base should be avoided or

avoided or limtedlimted to angles less than 8to angles less than 8--1010ºº

ggSliding may be an issue for inclined basesSliding may be an issue for inclined bases

⎟⎠

⎜ ⎞

⎝

−⎛ α 3 . 1 147

⎟⎟⎠

⎞

⎜⎜⎝

⎛

φ

− −

tan N

b b 1

c q q

Cohesion Term (c)

Unit Weight Term (γ)

Surcharge Term (q)

b_c b_γ b_q

φ = 0 1.0 1.0

φ > 0 (1-0.017α tanφ)² (1-0.017α tanφ)² φ= friction angle, degrees;

α = footing inclination from horizontal, upward +, degrees Base

Inclination Factors, b_c, b_γ, b_q Factor

Friction Angle

Inclined Loading Inclined Loading

ggIf shear (horizontal) component is checked If shear (horizontal) component is checked for sliding resistance, the inclination

for sliding resistance, the inclination correction factor is omitted

correction factor is omitted

ggUse effective footing dimensions in Use effective footing dimensions in

evaluation of the vertical component of the evaluation of the vertical component of the loadload

Comments on Use of Bearing Comments on Use of Bearing

Capacity Correction Factors Capacity Correction Factors

ggFor settlementFor settlement--controlled allowable bearing controlled allowable bearing capacity, the effect application of correction capacity, the effect application of correction

factors may be negligible factors may be negligible

ggApplication of correction factors is Application of correction factors is

secondary to the adequate assessment of secondary to the adequate assessment of

the shear strength characteristics of the the shear strength characteristics of the

foundation soil through correctly performed foundation soil through correctly performed

subsurface exploration subsurface exploration

Local or Punching Shear Local or Punching Shear

c* = 0.67c c* = 0.67c

φφ*=tan*=tan^-1-1(0.67tan(0.67tanφφ))

ggLoose sandsLoose sands

ggSensitive claysSensitive clays

ggCollapsible Collapsible soils

soils

ggBrittle claysBrittle clays

Bearing Capacity Factors of Safety Bearing Capacity Factors of Safety

ggqq_allall = allowable bearing capacity= allowable bearing capacity

ggqq_ultult = ultimate bearing capacity= ultimate bearing capacity

ggTypical FS = 2.5 to 3.5Typical FS = 2.5 to 3.5

ggFS is a function ofFS is a function of

- -

- -

- -

FS

q

= q

Overstress Allowances Overstress Allowances

ggFor shortFor short--duration infrequently duration infrequently occuringoccuring loads, an overstress of 25 to 50 % may be loads, an overstress of 25 to 50 % may be

allowed for allowable bearing capacity allowed for allowable bearing capacity

Practical Aspects of Bearing Practical Aspects of Bearing

Capacity

Capacity

Presumptive Allowable Bearing Presumptive Allowable Bearing

Capacity Capacity

ggNOT recommended for soilsNOT recommended for soils

ggSee Tables 8-See Tables 8-8, 88, 8--9 and 89 and 8-10 for rocks-10 for rocks

Learning Outcomes Learning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:

be able to:

- -

- -

- -

in sand and clay

- -

- -

foundations

Any Questions?

Any Questions?

THE ROAD TO UNDERSTANDING

SOILS AND

FOUNDATIONS

Shallow Foundations Shallow Foundations

Lesson 08

Lesson 08 -- Topic 2Topic 2

Settlement, footings on embankments,

Settlement, footings on embankments, IGMsIGMs, , rocks, effect of deformations on bridge structures rocks, effect of deformations on bridge structures

Section 8.5 to 8.9 Section 8.5 to 8.9

Learning Outcomes Learning Outcomes

ggAt the end of this session, the participant will At the end of this session, the participant will be able to:

be able to:

- -

soils

- -

- -

deformations on bridge structures

Settlement of Spread Footings Settlement of Spread Footings

ggImmediate (shortImmediate (short--term)term)

ggConsolidation (long-Consolidation (long-term)term)

Immediate Settlement Immediate Settlement

ggHough’s methodHough’s method

- -

ggSchmertmann’sSchmertmann’s methodmethod

- -

- -

measurements

Charts Charts

Figure 2

Figure 2 - - 11 11

ggDD_ss = 4B to 6B = 4B to 6B for continuous for continuous footings where footings where LL_ff/B/B_ff ≥≥ 1010

ggDD_ss = 1.5B to 2B = 1.5B to 2B for square

for square

footings where footings where LL_ff/B/B_ff == 11

Trend of Analytical Trend of Analytical

Results and Results and

Measurements Measurements

Legend:

Legend:

Square footings Square footings

where

where LL_ff/B/B_ff =1=1

Continuous footings Continuous footings

where

where LL_ff/B/B_ff ≥≥ 1010

Vertical Strain, %

Depth below Footing

2B

4B

Schmertmann

Schmertmann Method Method

gg II_zz Strain Influence FactorStrain Influence Factor

gg EE Elastic Modulus, Table 5Elastic Modulus, Table 5--2020

gg XX Modification factor for EModification factor for E

gg CC₁₁ Correction factor for strain reliefCorrection factor for strain relief

gg CC₂₂ Correction factor for creep deformationCorrection factor for creep deformation

∑

Δ Δ

= ⁿ

1

i i

2 1

i C C p H

S

⎟

⎠

⎜ ⎞

⎝

= ⎛

Δ XE

H I

H

5 . p 0

5 p . 0 1

C₁ ^o ⎟⎟ ≥

⎠

⎜⎜ ⎞

⎝

⎛

− Δ

=

( )

⎟⎠

⎜ ⎞

⎝ + ⎛

= 0.1

years log t

2 . 0 1

C_{2 10}

5 . 0

pop 1 p . 0 5 . zp 0

I ⎟⎟

⎟

⎠

⎞

⎜⎜

⎜

⎝

⎛ Δ +

=

below )

b ( see

Plane Strain L_f/B_f ≥ 10 Axisymmetric

L_f/B_f =1

L_f = Length of footing B_f = least width of footing

po

pop

B_f/2 (for axisymmetric case) B_f (for plane strain case)

B_f

po p p = − Δ

Depth to Peak Strain Influence Factor, I_zp

Example 8

Example 8 - - 2 2

ggGiven: 6’x24’ footing on soil profile shown Given: 6’x24’ footing on soil profile shown below. Determine settlement at end of

below. Determine settlement at end of

construction and 10 years after construction construction and 10 years after construction

Clayey Silt Sandy Silt Coarse Sand

Sandy Gravel

γt = 115 pcf; N1₆₀ = 8 γt = 125 pcf; N160 = 25 γt = 120 pcf; N1₆₀ = 30

γ_t = 128 pcf; N1₆₀ = 68 3 ft

3 ft 5 ft

25 ft B_f = 6 ft

Ground Surface

Draw Strain Influence Diagram Draw Strain Influence Diagram

ggCalculate peak Calculate peak IzIz = 0.64= 0.64

Plane Strain L_f/B_f ≥ 10 Axisymmetric

L_f/B_f =1

0

4

8

12

16

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Influence Factor (Iz)

0

4

8

12

16

20

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Influence Factor (Iz)

Depth below footing

B

2B

3B

Strain Influence Diagram Strain Influence Diagram

Divide into layers Divide into layers

0

4

8

12

16

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Influence Factor (Iz)

0

4

8

12

16

20

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Influence Factor (Iz)

Depth below footing (ft)

Layer 1 Layer 2 Layer 3

Layer 4

Determine Elastic Modulus, E Determine Elastic Modulus, E

ggUse Table 5Use Table 5--20, Page 520, Page 5--9090

ggCalculate XCalculate X--factor, X = 1.42factor, X = 1.42

Layer 1: Sandy Silt: E = 4N1

tsf

Layer 2: Coarse Sand: E = 10N1

tsf

Layer 3: Coarse Sand: E = 10N1

tsf

Layer 4: Sandy Gravel: E = 12N1

tsf

Setup Table for Settlement Setup Table for Settlement

Computation Computation

Layer H_c N1₆₀ E XE Z₁ I_Z at Z_i

(inches) (tsf) (tsf) (ft) (in/tsf)

1 36 25 100 142 1.5 0.31 0.0759

2 12 30 300 426 3.5 0.56 0.0152

3 48 30 300 426 6 0.55 0.0599

4 96 68 816 1,159 12 0.22 0.0176

Σ H_i= 0.1686

Z c

i H

XE H = I

Compute Correction Factors C

Compute Correction Factors C

, C , C

ggAt end of construction, t=0.1 yearAt end of construction, t=0.1 year

ggAt t=10 yearsAt t=10 years

0.896 psf

1655

pcf 115

ft 0.5 3

Δp 1 0.5 p

1

C₁ ^o ⎟⎟ =

⎠

⎜⎜ ⎞

⎝

⎛ ×

−

⎟⎟ =

⎠

⎜⎜ ⎞

⎝

− ⎛

=

( )

⎟⎠

⎜ ⎞

⎝ + ⎛

= 0.1

years log t

2 . 0 1

C_{2 10}

0 . 1 1

. 0

1 . log 0

2 . 0 1

C_{2 10} ⎟ =

⎠

⎜ ⎞

⎝ + ⎛

=

4 . 1 1

. 0 log 10

2 . 0 1

C_{2 10} ⎟ =

⎠

⎜ ⎞

⎝ + ⎛

=

Determine Immediate Settlement Determine Immediate Settlement

ggAt end of construction, t = 0.1 yearAt end of construction, t = 0.1 year

ggAt t = 10 yearsAt t = 10 years

( )( )

inches 125

. 0 S

tsf 1686 in .

0 psf tsf

2000

psf 0 1655

. 1 896 . 0 S

H p

C C S

i i

i 2

1 i

=

⎟⎠

⎜ ⎞

⎝

⎛

⎟⎟

⎟

⎠

⎞

⎜⎜

⎜

⎝

⎛

=

Δ

= ∑

inches 175

. 0 0

. 1

4 . inches 1 125

. 0

S_i ⎟ =

⎠

⎜ ⎞

⎝

= ⎛

Consolidation Settlement Consolidation Settlement

ggSame procedures as in Chapter 7 (Approach Same procedures as in Chapter 7 (Approach Roadway Deformations)

Roadway Deformations)

Example 8

Example 8 - - 3 3

gg Calculate consolidation settlement for following case:Calculate consolidation settlement for following case:

130 kips

Rock Normally consolidated clay

γ_sub = 65 pcf, e₀ = 0.75, C_c = 0.4 10′

4′

10′

Gravel

γ_T = 130 pcf