# Basis of geotechnical design (Retaining Wall)

According to  2.1 three Geotechnical Categories 1, 2 and 3 may be introduced to establish geotechnical design requirements. Retaining walls comply with Geotechnical Category 2.

# Geotechnical design by calculation

## Design values of geotechnical parameters

According to  2.4 the design values id calculated in the following way:

Xd = Xk / γM

The partial factors γM are chosen as below. Swedish Annex

Xd = η Xk / γM

η is a factor considering uncertainties relating to properties for the earth defined by the user. See  3.2.3. To consider this the defined characteristic value should be according to .

## Ultimate Limit State

According to  2.4.7 five types of ultimate limit states are possible. For retaining walls the following three types are relevant:

EQU (Loss of equilibrium of the structure considered as a rigid body, in which the strength of structural material and the ground are insignificant. This case will be used for foundation on rock or very firm earth material.

(STR) Internal failure or excessive deformation of the structure in which the strength of structural materials is significant in providing resistance.

(GEO) Failure or excessive deformation of the ground, in which the strength of soil or rock is significant in providing resistance, e.g. overall stability and bearing resistance of retaining walls.

Design Approaches

According to  2.4.7.3.4 and Annex A one of three Design Approaches should be used. EC Standard

All three approaches are available for the user to choose. British annex

Design approach 1 is used. Danish annex

Design approach 3 is used. Finnish annex

Design approach 2 is used.

Swedish annex

Design approach 3 is used.

# Description

The stability for the structure is checked by calculating size, location and direction for the earth- and ground pressure resultant following from load- and material characteristics.

Section forces at toe, wall and heel is calculated for current earth pressure and ground pressure for both Ultimte- and Serviceability Limit State.

Earth pressure calculation is performed according to  ch. 175:4.

System figure: # Design criteria’s

The structure is with regard to a stability failure assumed to rotate around the slab and the failure surface in the fill is assumed to be situated as section I-I above. The least favourable value for ω is chosen by experience or is calculated by inserting different input values (see  ch. 31). A traditional earth pressure calculation is obtained with ω = 0 and ϕ = 0. The means a horizontal earth pressure and the calculation are on the safe side with regard to stability.

The part of the back fill situated between the wall and the failure surface is assumed to be stabilizing.

The structure is designed for the forces generated for the above approach. The ground pressure is assumed to be uniformly distributed. If passive earth pressure should be considered is up to the user, (Risk for removal of the front fill).

# Earth pressure

Earth pressure coefficient Ka

The structure is designed for active earth pressure. The distribution of the back fill is assumed to be large enough for active earth pressure to occur. With designations according to  175:413, constant earth slope and constant surcharge
load the earth pressure resultant is calculated as: and the earth pressure intensity: where:

• • h and z are measured vertically from the point where the failure surface intersects the earth level,
• ϕa = used friction slope at the failure surface, ϕav or ϕ depending on if wall or failure surface is considered,
• ϕ = the friction slope for the back fill,
• q = surcharge load (see system figure),

Consideration to shaking effects is taken by enlarging Ka with the shaking factor ks.

## Earth pressure against failure surface

For the case Earth pressure against the failure surface the earth level slant is assumed to be long with the slope α. If the failure surface intersects the horizontal surface the actual earth pressures will be smaller than the assumed. The direction of the earth pressure forms the slope ϕ with regard to the normal to the failure surface. ϕ ought not to be used to a higher value than 2/3 of the friction ϕ for the fill. The case Reduced surcharge load means that the favorable part of the surcharge load that counteracts overturning is neglected. The case Full surcharge load means that the total load is considered.

When the failure surface intersects the earth level the earth pressure acts toward the failure section and the vertical side of the heel. When the failure surface intersects the wall the earth pressure is divided in two parts, one part acting towards the back side of the wall calculated with wall´s φa and one part calculated as above.

## Earth pressure against wall

The case Earth pressure against the wall is calculated with two different ways, first with earth pressure from the fill behind the failure section (see above) and second for the fill adjacent to the wall (see below). For the case earth pressure against failure surface the earth pressure is assumed to propagate through the fill and act towards the wall.

When calculating the earth pressure against the wall from the fill adjacent to the wall the earth level slant is assumed to be long with the slope α. If the rear sliding part of the fill intersects the horizontal surface the actual earth pressures will be smaller than the assumed.

When the wall rear is not straight the slope of the sliding surface is calculated in order to maximize the earth pressure resultant, where after the earth pressure coefficients for the upper and lower wall part is calculated.

The case Reduced surcharge load means that the calculation is performed without this load. The case Full surcharge load means that the total surcharge load is considered.