Depth of Prism given Factor of Safety for Cohesive Soil Calculator

✖Unit Cohesion is the force that holds together molecules or like particles within a soil.ⓘ Unit Cohesion [c_u]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%
✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%
✖Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination [I]			+10% -10%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism given Factor of Safety for Cohesive Soil [z]

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Formula

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Depth of Prism given Factor of Safety for Cohesive Soil

Formula

`"z" = "c"_{"u"}/(("f"_{"s"}-(tan(("Φ"_{"i"}))/tan(("I"))))*"γ"*cos(("I"))*sin(("I")))`

Example

`"2.336534m"="10Pa"/(("2.8"-(tan(("82.87°"))/tan(("80°"))))*"18kN/m³"*cos(("80°"))*sin(("80°")))`

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Download Stability Analysis of Infinite Slopes in Prism Formulas PDF

Depth of Prism given Factor of Safety for Cohesive Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination)))
z = c_u/((f_s-(tan((Φ_i))/tan((I))))*γ*cos((I))*sin((I)))
This formula uses 3 Functions, 6 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., tan(Angle)

Variables Used

Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the force that holds together molecules or like particles within a soil.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
Unit Weight of Soil - (Measured in Kilonewton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

STEP 1: Convert Input(s) to Base Unit

Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Factor of Safety: 2.8 --> No Conversion Required
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18 Kilonewton per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = c_u/((f_s-(tan((Φ_i))/tan((I))))*γ*cos((I))*sin((I))) --> 10/((2.8-(tan((1.44635435112743))/tan((1.3962634015952))))*18*cos((1.3962634015952))*sin((1.3962634015952)))

Evaluating ... ...

z = 2.3365343879461

STEP 3: Convert Result to Output's Unit

2.3365343879461 Meter --> No Conversion Required

FINAL ANSWER

2.3365343879461 ≈ 2.336534 Meter <-- Depth of Prism

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability Analysis of Infinite Slopes in Prism » Depth of Prism given Factor of Safety for Cohesive Soil

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 23 Stability Analysis of Infinite Slopes in Prism Calculators

Unit Weight of Soil given Factor of Safety for Cohesive Soil

Go Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))

Cohesion given Factor of Safety for Cohesive Soil

Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))

Depth of Prism given Factor of Safety for Cohesive Soil

Go Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination)))

Factor of Safety for Cohesive Soil given Cohesion

Go Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))

Inclined Length along Slope given Weight of Soil Prism

Go Inclined Length = Weight of Prism/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination)))

Unit Weight of Soil given Weight of Soil Prism

Go Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Weight of Soil Prism in Stability Analysis

Go Weight of Prism = (Unit Weight of Soil*Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Depth of Prism given Weight of Soil Prism

Go Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))

Angle of Inclination given Weight of Soil Prism

Go Angle of Inclination = acos(Weight of Prism/(Unit Weight of Soil*Depth of Prism*Inclined Length))

Unit Weight of Soil given Vertical Stress on Surface of Prism

Go Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))

Depth of Prism given Vertical Stress on Surface of Prism

Go Depth of Prism = Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))

Angle of Inclination given Vertical Stress on Surface of Prism

Go Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))

Inclined Length along Slope given Volume Per Unit Length of Prism

Go Inclined Length = Volume per unit length of prism/(Depth of Prism*cos((Angle of Inclination)))

Depth of Prism given Volume per Unit Length of Prism

Go Depth of Prism = Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))

Volume Per Unit Length of Prism

Go Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Vertical Stress on Surface of Prism given Unit Weight of Soil

Go Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))

Angle of Inclination given Volume per Unit Length of Prism

Go Angle of Inclination = acos(Volume per unit length of prism/(Depth of Prism*Inclined Length))

Inclined Length along Slope given Horizontal Length of Prism

Go Inclined Length = Horizontal Length of Prism/cos((Angle of Inclination))

Horizontal Length of Prism

Go Horizontal Length of Prism = Inclined Length*cos((Angle of Inclination))

Angle of Inclination given Horizontal Length of Prism

Go Angle of Inclination = acos(Horizontal Length of Prism/Inclined Length)

Weight of Soil Prism given Vertical Stress on Surface of Prism

Go Weight of Prism = Vertical Stress at a Point in Pascal*Inclined Length

Inclined Length along Slope given Vertical Stress on Surface of Prism

Go Inclined Length = Weight of Prism/Vertical Stress at a Point*5

Vertical Stress on Surface of Prism

Go Vertical Stress at a Point = Weight of Prism/Inclined Length

Depth of Prism given Factor of Safety for Cohesive Soil Formula

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Depth of Prism given Factor of Safety for Cohesive Soil?

Depth of Prism given Factor of Safety for Cohesive Soil calculator uses Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination))) to calculate the Depth of Prism, The Depth of Prism given Factor of Safety for Cohesive Soil is defined as the minimum depth required to prevent slope failure in cohesive soil with a specified factor of safety. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism given Factor of Safety for Cohesive Soil using this online calculator? To use this online calculator for Depth of Prism given Factor of Safety for Cohesive Soil, enter Unit Cohesion (c_u), Factor of Safety (f_s), Angle of Internal Friction of Soil (Φ_i), Angle of Inclination (I) & Unit Weight of Soil (γ) and hit the calculate button. Here is how the Depth of Prism given Factor of Safety for Cohesive Soil calculation can be explained with given input values -> 2.336534 = 10/((2.8-(tan((1.44635435112743))/tan((1.3962634015952))))*18000*cos((1.3962634015952))*sin((1.3962634015952))).

FAQ

What is Depth of Prism given Factor of Safety for Cohesive Soil?

The Depth of Prism given Factor of Safety for Cohesive Soil is defined as the minimum depth required to prevent slope failure in cohesive soil with a specified factor of safety and is represented as z = c_u/((f_s-(tan((Φ_i))/tan((I))))*γ*cos((I))*sin((I))) or Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination))). Unit Cohesion is the force that holds together molecules or like particles within a soil, Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Angle of Internal Friction of Soil is a shear strength parameter of soils, Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object & Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

How to calculate Depth of Prism given Factor of Safety for Cohesive Soil?

The Depth of Prism given Factor of Safety for Cohesive Soil is defined as the minimum depth required to prevent slope failure in cohesive soil with a specified factor of safety is calculated using Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination))). To calculate Depth of Prism given Factor of Safety for Cohesive Soil, you need Unit Cohesion (c_u), Factor of Safety (f_s), Angle of Internal Friction of Soil (Φ_i), Angle of Inclination (I) & Unit Weight of Soil (γ). With our tool, you need to enter the respective value for Unit Cohesion, Factor of Safety, Angle of Internal Friction of Soil, Angle of Inclination & Unit Weight of Soil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Depth of Prism?

In this formula, Depth of Prism uses Unit Cohesion, Factor of Safety, Angle of Internal Friction of Soil, Angle of Inclination & Unit Weight of Soil. We can use 3 other way(s) to calculate the same, which is/are as follows -

Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))
Depth of Prism = Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))
Depth of Prism = Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))

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