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**Chapter 9****Shear Strength of Soil**

**SHEAR STRENGTH**

Shear strength of a soil is the capacity of the soil to resist shearing stress. It can be defined as the maximum value of shear stress that can be defined as the maximum value of shear stress that can be Mobilized within a soil mass.

-Plane a -a is critical plane

-θ_{c} = Angle of critical plane (a – a)

-σ_{1} and σ_{3} are stresses on given planes

**(i) **

where, β_{max }= Angle between resultant stress and normal stress on critical plane=Friction angle of soil = ∅

for clay, ∅= 0

(ii) , for sands or Φ -soil.

(iii), for C- Φ soil.

(iv) , for C-soil (clays).

(v)

for C-∅ soil.

(vi), for Φ soil.

(vii) σ_{1}= 2C , for C– soil.

**MOHR COULOMBS THEORY**

where, C’ = Effective Cohesion

= Effective normal stress and ∅' = Effective friciton angle

**DIRECT SHEAR TEST:**

**UNCONFINED COMPRESSION T****EST**

-q_{u} = (σ_{1})_{f}

where, q_{u} = unconfined compressive strength.

Here, σ_{3}= 0

- (σ_{1})f =2C , for C-soil

- for clay’s or C-soil.

**VANE SHEAR TEST:**

-It is suitable for sensitive clays.

Lab size | Field Size | |

Height of vane (H) | 20 mm | 10 to 20 cm |

Dia of vane (D) | 12 mm | 5 to 10 cm |

Thickness of vane (t) | 0.5 to 0.1 mm | 2 to 3 cm |

**Shear Strength**:

-When top and bottom of vanes both pertain in shearing.

-When only bottom of vanes pertain in shearing.

where S_{f} = Sensitivity

**PORE PRESSURE PARAMETER:**

where,

B = Pore pressure parameter

ΔU_{c} = Change in pore pressure due to in crease in cell pressure

Δσ_{c }= Δσ_{3} = Change in cell pressure.

-0 ≤ B ≤ 1

-B = 0, for dry soil.

-B = 1, for saturated soil.

**(ii) **

where A = Pore pressure parameter

where ,

ΔU_{d} = Change in pore pressure due to deviator stress.

Δσ_{d} = Change in deviator stress

**(iii) ΔU=ΔU _{c} +ΔU_{d}**

ΔU = change in pore pressure

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