## Reinforced Slope Example

The following problem for verification is reviewed in

*Duncan, J.M., Wright, S.G., and Brandon, T.L., 2014. Soil Strength and Slope Stability, Second Edition*, and is used to illustrate the difference between specifying allowable reinforcement strengths (already factored) from specifying reinforcement strengths which use the computed FOS for the soil mass.

The slope considered is 20 ft high at a slope of 1H:2V, and consists of a uniform soil with γ = 100 pcf, Φ = 0, and c = 500 psf, underlain by an impenetrable hard layer below. There is a horizontal reinforcement force of 10,000 lb/ft acting halfway up the slope.

The reinforcement force is modeled using a geosynthetic with 100% area coverage and a tensile strength of 10,000 lb/ft. As the reviewed problem does not consider pullout resistance, it is specified to be much stronger such that the tensile strength will always govern.

The geometry, material, and reinforcement parameters are shown below.

The Simplified Bishop's method was used to be consistent with the published results.

First the critical slip surface for the slope with no reinforcement is identified using auto search. The minimum factor of safety reported is 1.222.

### Reinforcement Force Using Allowable Strength

With the reinforcement specified using the allowable tensile strength of 10,000 lb/ft, the auto search is used to located the critical slip surface. The minimum factor of safety reported is 2.199, while the published result is 2.19.

The free body diagram for the slice intersected by the reinforcement is shown below. Note the force of 10,000 lb acting parallel to the reinforcement. The interslice normal forces are in tension, which is a consequence of the reinforcement and is physically inadmissible, although the slice is in force equilibrium. Inspecting the

*Trial Warnings* under the

*Selected Slip Center* tab in the Analysis Results view alerts the user to this condition.

### Reinforcement Force Using Computed FOS

Assigning the reinforcement a tensile strength of 10,000 lb/ft and this time using the computed FOS of the soil mass, the auto search is used to located the critical slip surface. The minimum factor of safety reported is 1.677, while the published result is 1.72.

The free body diagram for the slice intersected by the reinforcement is shown below. Note the force of 5,964.4 lb acting parallel to the reinforcement. This represents the 10,000 lb divided by the computed FOS of 1.677 (10,000 / 1.677 ~= 5,964.4). The interslice normal forces are still in tension, which is a consequence of the reinforcement and is physically inadmissible, although the slice is in force equilibrium. Inspecting the

*Trial Warnings* under the

*Selected Slip Center* tab in the Analysis Results view alerts the user to this condition.

Download the MacSlope file with the analysis results for this verification example

here.