## Session 4B: Stability and Displacement Performance of Slopes, Landfills and Earth Dams Under Earthquakes

#### Title

Seismic Stability of the Nailed Slopes

#### Location

San Diego, California

5-24-2010

5-29-2010

#### Abstract

The study undertaken in this project pertains to the determination of ultimate bearing capacity of nailed slopes. In this soil is modeled as composed of homogeneous layers of soils. Analysis has been carried out to obtain an upper bound solution of the problem. A two dimensional collapse mechanism has been assumed to ascertain the bearing capacity with the velocity discontinuities radiating from the applied strip load and satisfying the compatibility of the displacements. The mechanism is defined by relevant angles or lengths. Each velocity vector makes an angle of f¢ with the direction of discontinuity. For fu =0 there is no jump in the normal velocity and the velocity vector is parallel to the direction of the discontinuity. Foe-Mohr coulomb material the f¢ angle assumed between the velocity vector and the discontinuity facilitates the flow rule condition. Assuming that one of these velocities is equal to a specified value, the values of the velocities of the blocs are estimated such that compatibility of the displacements is satisfied. Work done by the external loading includes the boundary loading and the weight of each block. The algebraic sum of the work done is equal to magnitude of the force multiplied by the velocity in the direction of the force. The dissipated work is solely due to the cohesion. The internal work dissipated along the velocity discontinuity of length l is computed from the expression, ∫01 c’νcosφ’dl. By equating the work done by the external forces and the dissipated work, the upper bound solution of the bearing capacity is obtained. Above approach initially developed for unreinforced layered slopes has been modified to include the effect of reinforcement on the bearing capacity. The reinforcements are put in a regular fashion with equal vertical spacing. The tension developed due to the friction is estimated and work done by the same is estimated and added with the work done equations. Pseudo static analysis is carried out for considering the effect of earthquakes on the bearing capacity. At the centre of gravity of each block inertial force equal to the earthquake coefficient times the weight of the block is applied and the work done by each of these are estimated and added to the external work done for computational purpose. The correctness of the developed computer code is first established by checking the calculations with manually computed values. Thereafter, the effect of the depth of reinforcement (in case of single layer of reinforcement)/ depth of the placement of the first reinforcement (in case there are more than one layer of reinforcement and the spacing of reinforcement, earth quake force, values of cohesion and angle of friction on the bearing capacity has been studied. All these parameters are found to have significant influence on the bearing capacity of such nailed slopes.

#### Department(s)

Civil, Architectural and Environmental Engineering

#### Appears In

International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics

Fifth Conference

#### Publisher

Missouri University of Science and Technology

5-24-2010

Final Version

#### Document Type

Article - Conference proceedings

text

English

#### Share

COinS

May 24th, 12:00 AM May 29th, 12:00 AM

Seismic Stability of the Nailed Slopes

San Diego, California

The study undertaken in this project pertains to the determination of ultimate bearing capacity of nailed slopes. In this soil is modeled as composed of homogeneous layers of soils. Analysis has been carried out to obtain an upper bound solution of the problem. A two dimensional collapse mechanism has been assumed to ascertain the bearing capacity with the velocity discontinuities radiating from the applied strip load and satisfying the compatibility of the displacements. The mechanism is defined by relevant angles or lengths. Each velocity vector makes an angle of f¢ with the direction of discontinuity. For fu =0 there is no jump in the normal velocity and the velocity vector is parallel to the direction of the discontinuity. Foe-Mohr coulomb material the f¢ angle assumed between the velocity vector and the discontinuity facilitates the flow rule condition. Assuming that one of these velocities is equal to a specified value, the values of the velocities of the blocs are estimated such that compatibility of the displacements is satisfied. Work done by the external loading includes the boundary loading and the weight of each block. The algebraic sum of the work done is equal to magnitude of the force multiplied by the velocity in the direction of the force. The dissipated work is solely due to the cohesion. The internal work dissipated along the velocity discontinuity of length l is computed from the expression, ∫01 c’νcosφ’dl. By equating the work done by the external forces and the dissipated work, the upper bound solution of the bearing capacity is obtained. Above approach initially developed for unreinforced layered slopes has been modified to include the effect of reinforcement on the bearing capacity. The reinforcements are put in a regular fashion with equal vertical spacing. The tension developed due to the friction is estimated and work done by the same is estimated and added with the work done equations. Pseudo static analysis is carried out for considering the effect of earthquakes on the bearing capacity. At the centre of gravity of each block inertial force equal to the earthquake coefficient times the weight of the block is applied and the work done by each of these are estimated and added to the external work done for computational purpose. The correctness of the developed computer code is first established by checking the calculations with manually computed values. Thereafter, the effect of the depth of reinforcement (in case of single layer of reinforcement)/ depth of the placement of the first reinforcement (in case there are more than one layer of reinforcement and the spacing of reinforcement, earth quake force, values of cohesion and angle of friction on the bearing capacity has been studied. All these parameters are found to have significant influence on the bearing capacity of such nailed slopes.