**TI-84 Plus CE and Casio fx-5800P: Lateral Pressure of Cohesionless Soils**

**Introduction**

The following equations calculates the total thrust of soil against a wall. The soil is assumed to be cohesionless, free running soil. This applies to soils like sand and gravel, but not clay.

SI units (meters, seconds, kilograms) are assumed in these calculations.

Inputs:

Φ = angle of internal friction of soil. For cohesionless soils, such as medium and coarse sands, the angle of internal friction typically ranges from 30° to 35°. The program assigns Φ to the variable I.

H = the height of the wall (m).

γ = unit weight of soil (kg/m^3). The program assigns γ to W.

Outputs:

K_A = pressure coefficient (unit-less). The program assigns K_A to K.

P = total thrust of the soil (kg/m) of the wall.

Equations:

K_A = (tan(45° – Φ/2))^2

P = 1/2 * γ * H^2 * K_A (kg/m)

**TI-84 Plus CE Program SOILPRES**

(this program needs to be typed in)

Degree

Disp “LATERAL PRESSURE”,”SAND/GRAVEL”,”ANGLE INTERNAL”

Input “FRICTION: “,I

tan(45-I/2)²→K

Disp “WALL HEIGHT”

Input “(M): “,H

Disp “SOIL WEIGHT”

Input “(KG/M³): “,W

0.5*W*H²*K→P

Disp “PRESSURE COEF: “,K,”SOIL THRUST: “,P

**Casio fx-5800P Program SOILPRESSURE**

Deg

“LATERAL PRESSURE”

“SAND OR GRAVEL”

“ANGLE INTERAL”

“FRICTION: “?→I

(tan(45-I÷2))²→K

“WALL HEIGHT”

“(M): “?→H

“SOIL HEIGHT”

“(KG÷M^(3)): “?→W

0.5*W*H²*K→P

“PRESSURE COEF:”

K⊿

“SOIL THRUST:”

P

**Example**

Input:

Φ = I = 37°

H = 15 m

γ = W = 0.64 kg/m^3

Output:

K_A = K = 0.2485836199

P = 17.89802063 (kg/m)

Source:

Hicks, Tyler P.E. __Civil Engineering Formulas __2nd Ed. McGraw Hill: New York. 2000. ISBN 978-0-07-161470-2

Eddie

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