The facing must be safely designed to resist earth pressure. Based on the earth pressure determined in Chapter 6 and the external loads acting on the crest of the facing, the stresses acting in the cross section of the facing are determined. The cross section is designed such that the stresses mobilized in it will be less than the allowable stresses. A schematic sketch of facing is given in Figure 7.1 where the facing and geosynthetic layers are modeled as beam and springs, respectively.

Consider a beam resting on an elastic foundation, the following fourth-order differential equation is solved for the displacement and stresses:

  (7.1)

where

y	: out-of-plane displacement of facing
EI	: flexural rigidity
ks	: spring constant
p	: earth pressure (from direct sliding or overturning analysis, whichever the greater)

The spring constant used for facing stress analysis is obtained form the tension test. The tensile stiffness is nonlinear with strains and varies according to the types of material. It is recommended to select the tensile load of geosynthetic reinforcement at 5% axial strain in calculating for the stiffness.

  (7.2)

where

ks	: spring constant (kN/m)
a s	: a correction factor used to consider soil-confinement effect
T5	: in-air geosynthetic tensile load at 5% axial strain level (kN/m)
L	: standard reinforcement length (= 1.5 m)

The spring constant as determined above is considered to be arbitrarily and usually gives conservative results. In reality, the geosynthetic is restrained by the soil and is expected to give higher stiffness. The back-calculated values from the lateral loading test have shown that the constant can be between 40 to 60 times larger than the value assumed in Eq. 7.2. Therefore, when calculating for facing deformation, the assumed spring constant has to be multiplied by a factor 40.