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Shear Strength along Slip Plane Formula

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Shear Strength of Soil is the strength of a material against the structural failure when the material fails in shear. Check FAQs

ζ soil = (C s \cdot L) + (W \cdot \cos (\frac{θ \cdot π}{180}) \cdot \tan (\frac{φ \cdot π}{180}))

ζ _soil - Shear Strength?C_s - Cohesion of Soil?L - Length of Slip Plane?W - Weight of Wedge?θ - Slope Angle?φ - Angle of Internal Friction?π - Archimedes' constant?

Shear Strength along Slip Plane Example

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Here is how the Shear Strength along Slip Plane equation looks like with Values.

Here is how the Shear Strength along Slip Plane equation looks like with Units.

Here is how the Shear Strength along Slip Plane equation looks like.

0.025 = (5 \cdot 5) + (10.01 \cdot \cos (\frac{25 \cdot 3.1416}{180}) \cdot \tan (\frac{46 \cdot 3.1416}{180}))

0.025MPa = (5kPa \cdot 5m) + (10.01kg \cdot \cos (\frac{25° \cdot 3.1416}{180}) \cdot \tan (\frac{46° \cdot 3.1416}{180}))

0.025 = (5 \cdot 5) + (10.01 \cdot \cos (\frac{25 \cdot 3.1416}{180}) \cdot \tan (\frac{46 \cdot 3.1416}{180}))

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Shear Strength along Slip Plane Solution

Follow our step by step solution on how to calculate Shear Strength along Slip Plane?

FIRST Step Consider the formula

ζ soil = (C s \cdot L) + (W \cdot \cos (\frac{θ \cdot π}{180}) \cdot \tan (\frac{φ \cdot π}{180}))

Next Step Substitute values of Variables

∴

ζ soil = (5kPa \cdot 5m) + (10.01kg \cdot \cos (\frac{25° \cdot π}{180}) \cdot \tan (\frac{46° \cdot π}{180}))

Next Step Substitute values of Constants

∴

ζ soil = (5kPa \cdot 5m) + (10.01kg \cdot \cos (\frac{25° \cdot 3.1416}{180}) \cdot \tan (\frac{46° \cdot 3.1416}{180}))

Next Step Convert Units

∴

ζ soil = (5000Pa \cdot 5m) + (10.01kg \cdot \cos (\frac{0.4363rad \cdot 3.1416}{180}) \cdot \tan (\frac{0.8029rad \cdot 3.1416}{180}))

Next Step Prepare to Evaluate

∴

ζ soil = (5000 \cdot 5) + (10.01 \cdot \cos (\frac{0.4363 \cdot 3.1416}{180}) \cdot \tan (\frac{0.8029 \cdot 3.1416}{180}))

Next Step Evaluate

∴

ζ soil = 25000.1402692505Pa

Next Step Convert to Output's Unit

∴

ζ soil = 0.0250001402692505MPa

LAST Step Rounding Answer

∴

ζ soil = 0.025MPa

Shear Strength along Slip Plane Formula Elements

Variables

Constants

Functions

Shear Strength

Shear Strength of Soil is the strength of a material against the structural failure when the material fails in shear.

Symbol: ζ _soil

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Strength

Cohesion of Soil

Cohesion of Soil is the ability of like particles within soil to hold onto each other. It is the shear strength or force that binds together like particles in the structure of a soil.

Symbol: C_s

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Cohesion of Soil

Length of Slip Plane

Length of Slip Plane is the length of plane along which failure may occur.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Slip Plane

Weight of Wedge

Weight of Wedge is defined as the weight of total soil which is in the form of wedge.

Symbol: W

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Weight of Wedge

Slope Angle

Slope Angle is defined as the angle measured between a horizontal plane at a given point on the land surface.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Slope Angle

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force .

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other formulas in Slope Stability Analysis using Culman's Method category

Go Height of Wedge of Soil given Weight of Wedge

h = \frac{W we}{\frac{L \cdot γ}{2}}

Go Cohesive Force along Slip Plane

F c = c m \cdot L

Go Mobilized Cohesion given Cohesive Force along Slip Plane

c m = \frac{F c}{L}

Go Height of Wedge of Soil given Angle of Inclination and Slope angle

h = \frac{H \cdot \sin (\frac{(θ i - θ) \cdot π}{180})}{\sin (\frac{θ i \cdot π}{180})}

How to Evaluate Shear Strength along Slip Plane?

Shear Strength along Slip Plane evaluator uses Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180)) to evaluate the Shear Strength, The Shear Strength along Slip Plane is defined as the value of shear strength when we have prior information of other parameters used. Shear Strength is denoted by ζ _soil symbol.

How to evaluate Shear Strength along Slip Plane using this online evaluator? To use this online evaluator for Shear Strength along Slip Plane, enter Cohesion of Soil (C_s), Length of Slip Plane (L), Weight of Wedge (W), Slope Angle (θ) & Angle of Internal Friction (φ) and hit the calculate button.

FAQs on Shear Strength along Slip Plane

What is the formula to find Shear Strength along Slip Plane?

The formula of Shear Strength along Slip Plane is expressed as Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180)). Here is an example- 2.5E-8 = (5000*5)+(10.01*cos((0.4363323129985*pi)/180)*tan((0.802851455917241*pi)/180)).

How to calculate Shear Strength along Slip Plane?

With Cohesion of Soil (C_s), Length of Slip Plane (L), Weight of Wedge (W), Slope Angle (θ) & Angle of Internal Friction (φ) we can find Shear Strength along Slip Plane using the formula - Shear Strength = (Cohesion of Soil*Length of Slip Plane)+(Weight of Wedge*cos((Slope Angle*pi)/180)*tan((Angle of Internal Friction*pi)/180)). This formula also uses Archimedes' constant and , Cosine (cos), Tangent (tan) function(s).

Can the Shear Strength along Slip Plane be negative?

No, the Shear Strength along Slip Plane, measured in Pressure cannot be negative.

Which unit is used to measure Shear Strength along Slip Plane?

Shear Strength along Slip Plane is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Shear Strength along Slip Plane can be measured.

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Shear Strength along Slip Plane Formula

Shear Strength along Slip Plane Example

Shear Strength along Slip Plane Solution

Shear Strength along Slip Plane Formula Elements

Other formulas in Slope Stability Analysis using Culman's Method category

How to Evaluate Shear Strength along Slip Plane?

FAQs on Shear Strength along Slip Plane

Variable Name