Ch. 12 Shear strengths of soil

35
Ch. 12 Shear strengths of soil

Transcript of Ch. 12 Shear strengths of soil

Page 1: Ch. 12 Shear strengths of soil

Ch. 12

Shear strengths of soil

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12.1 MOHR-COULOMB FAILURE CRITERION

※Mohr(1900)

※The failure envelop defined by Eq.(12.1) is a curved line

)(σfτ f = (12.1)

※Shear strength of a soil mass :The internal resistance per unit area that the soil mass can offer toresist failure and sliding along any plane inside it.

※Bearing capacity, slope stability, and lateral pressure on earth-retaining structure : need shear strength

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- Mohr-coulomb failure criteria

c = cohesion (점착력)ф = angle of internal friction (내부마찰각)σ = normal stress on the failure plane= shear strength

- The Mohr-Coulomb failure criterion, expressed in terms of effectivestress = + ′

φσcτ f tan+= (12.2)

12.1 MOHR-COULOMB FAILURE CRITERION

(12.3)

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12.1 MOHR-COULOMB FAILURE CRITERION

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12.1 MOHR-COULOMB FAILURE CRITERION

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12.2 INCLINATION OF THE PLANE OF FAILURE CAUSED BY SHEAR

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12.2 INCLINATION OF THE PLANE OF FAILURE CAUSED BY SHEAR

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or,902 'φθbad +== o∠

245 'φθ += (12.4)

12.2 INCLINATION OF THE PLANE OF FAILURE CAUSED BY SHEAR

From Figure 12.2

Again, from Figure 12.3,'sinφfaad = (12.5)

2 31 ''''cot σσφcOafOfa ++=+= (12.6a)

2 31 '' σσad -= (12.6b)

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Substituting Eqs.(12.5a) and (12.5b) into Eq.(12.5)

22 3131 ''''cot'''sin σσφc

σσφ+

+

-

=

12.2 INCLINATION OF THE PLANE OF FAILURE CAUSED BY SHEAR

or,

÷÷ø

öççè

æ-

+÷÷ø

öççè

æ-+

= 'sin 'cos'sin 'sin'' φφcφφσσ 121131 (12.7)

÷øö

çèæ +=

-+ 24511 2 'tan'sin 'sin φφφ

÷øö

çèæ +=

- 2451 'tan'sin 'cos φφφ-

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(12.8)- ′ = ′ 45 + + 2 45 + - = + - = + − = + ′

(12.9)

12.2 INCLINATION OF THE PLANE OF FAILURE CAUSED BY SHEAR

- = 45 + + 2 45 +

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12.3 LABORATORY TEST FOR DETERMINATION OF SHEAR STRENGTH PARAMETER

※The value of c for sand and inorganic silt is 0.- For normally consolidated clays, c can be approximated at 0. (CU, CD Condition)

- Overconsolidated clays have values of c that are greater than0. (CU, CD Condition)

※The angle of friction, ф, is sometimes referred to as the drainedangle of fraction.

- The shear strength parameters of a soil can be determined in thelaboratory.

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12.3 LABORATORY TEST FOR DETERMINATION OF SHEAR STRENGTH PARAMETER

※Several methods to determine the shear strengthparameters(, , , ′) of various soil specimens in the laboratory

• Direct shear test

• Triaxial test

• Direct simple shear test

• Plane strain triaxial test

• Torsional ring shear test

The direct shear test and triaxial test are the two commonly used

techniques for determining the shear strength parameters.

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12.4 Direct Shear Test

- Direct shear test(직접전단시험)- Triaxial test(삼축시험)

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12.4 Direct Shear Test

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12.4 Direct Shear Test

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- The soil specimens may be square or circular in plan. The size ofthe specimens generally used is about 2 in. X2 in. or X4 in.(51mmX51mm or 102mm X102mm)across and about 1 in. (25mm) high.

- The box is split horizontally into halves.

※ Stress – controlled or strain controlled test.

※ The advantage of strain – controlled tests is that, in the case ofdense sand, peak shear resistance(that is, at failure) as well aslesser shear resistance (that is, at a point after failure calledultimate strength) can be observed and plotted.

12.4 Direct Shear Test

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※In stress – controlled tests, only the peak shear resistance can beobserved and plotted.

※Peak shear resistance in stress – controlled tests can be onlyapproximated because failure occurs at a stress level somewherebetween the prefailure load increment and the failure loadincrement.

σ = Normal stress =

τ = Shear stress =

12.4 Direct Shear Test

(12.10)

(12.11)

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12.4 Direct Shear Test

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12.4 Direct Shear Test

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12.4 Direct Shear Test

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The following generalization can be developed from Figure 12.7

1. In loose sand, the resisting shear stress increases with sheardisplacement until a failure shear stress of τf is reached.After that, the shear resistance remain approximately any furtherincrease in the shear displacement.

2. In dense sand, the resisting shear stress increase with sheardisplacement until it reaches a failure stress of τf. This τf is calledthe peak shear strength.After failure stress is attained, the resisting shear stress graduallydecreases as shear displacement increase until it finally reaches aconstant value called the ultimate shear strength.

12.4 Direct Shear Test

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- Test in a dry sand'tan' φστ f =÷øö

çèæ= - 'tan' στφ f1

- It is important to note that in situ cemented sands may show a c’intercept

12.4 Direct Shear Test

(12.12)

(12.13)

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- The ultimate shear strength( ) = = (12.14)

12.4 Direct Shear Test

(12.15)

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12.5 Drained Direct Shear Test on Saturated Sand and Clay

- A drained test is made on a saturated soil specimen by keepingthe rate of loading slow enough so that the excess pore waterpressure generated in the soil is completely dissipated by drainage.

- The friction angle ф obtained from a drained direct shear test ofsaturated sand will be the same as that for a similar specimen ofdry sand.

- When a normal load is applied to a clay specimen, a sufficientlength of time must elapse for full consolidation – that is, fordissipation of excess pore water pressure.

time) all at 0 (ue =

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- The test may last from 2 to 5 days.

※ Note that σ = σ’ and the value of c’ ≈ 0 for a normally consolidated.

12.5 Drained Direct Shear Test on Saturated Sand and Clay

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12.5 Drained Direct Shear Test on Saturated Sand and Clay

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12.5 Drained Direct Shear Test on Saturated Sand and Clay

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12.5 Drained Direct Shear Test on Saturated Sand and Clay

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12.6 General Comments on Direct Shear Test

The direct shear test is rather simple to perform, but it has someinherent shortcomings.

1) Soil is not allowed to fail along the weakest plane but is forcedto fail along the plane of split of the shear box.

2) The shear stress distribution over the shear surface of thespecimen is not uniform.

※ In many foundation design problems, it will be necessary todetermine the angle of friction between the soil and the materialin which the foundation is constructed.

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12.6 General Comments on Direct Shear Test

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'tan'' δσcτ af += (12.17)

C’a = adhesion(부착력)δ' = angle of friction between the soil and the foundation material

※ Figure 12.15 show the results of direct shear tests conducted witha quartz sand and concrete, wood, and steel as foundationmaterials with 2100 mkNσ /'=

12.6 General Comments on Direct Shear Test

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12.6 General Comments on Direct Shear Test

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※ Figure 12.16 show the variation of δ’ and ф’ between the quartzsand(relative density = 45%) and the same foundation materialsas a function of σ’(ca=0).

※ It is important to realize that the magnitude of δ’ and ф’decreases with the increase of normal stress, σ’

- can be explained by referring to Figure 12.17

12.6 General Comments on Direct Shear Test

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12.6 General Comments on Direct Shear Test

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12.6 General Comments on Direct Shear Test