Line Load Surcharge - (Rankine/Coulmb) Theory for Soil Pressures 3

[willowman]

Hi all,

I am considering a case whereby I have a 5m vertical retaining wall which supports a cohesionless fill of density 1.9g/cm3.

The top surface of the backfill is horizontal and there are two vertical line loads acting downwards onto the surface. I need to calculate the active thrust which is generated due to the two line loads.

Following the logic in Craigs Soil Mechanics I see that the following is true for a single line load surcharge:

Which gives a lateral pressure of:

And a total thrust of:

If anybody can help I need clarity on the following:

1. What is line of action of the total thrust? I understand it would be the centre of the pressure distribution but analytically how is this calculated?

2. Does the fact that in my application I have two separate line loads change the calculation of total thrust? Do I have two separate thrusts, one for each line load?

3. How does the analysis change if it is assumed there is friction between the soil and the vertical wall?

Thanks!!

 

[SlideRuleEra]

I don't know if there is "modern" way to solve this problem, but I do know how to solve it the "old-fashion" way:

Each line load will be distributed on the wall with a pressure distribution that resembles the blue curve.

1) Threat each line load separately. Calculate p_x at various depths (shown in red) and use numerical integration, such as Simpson's or the trapezoidal rule, to calculate area under the curve. The area calculated is the total force (per unit of wall length) from the line load on the wall.

2) Calculate the centroid of the area computed in Step 1. The resultant of the total force (per unit of wall length) is applied at this point.

3) Use superposition to apply both of the line loads on the wall simultaneously.

http://www.SlideRuleEra.net

 

[Ron]

@SRE....yep