Lateral Earth Pressure Evaluation

In excavation stabilization projects, retaining walls and supporting structures are designed to withstand lateral earth pressure and possible water pressure behind the wall. Earth pressure arises from the weight of retained soil, various surcharges, and seismic ground movements.

For proper design of supporting structures in excavation stabilization, a precise understanding of the lateral pressure between soil and structure is essential. Two main theories exist to determine the lateral earth force acting on a retaining wall: Coulomb’s theory and Rankine’s theory.

Rankine’s theory, which provides the distribution of lateral pressure on the wall, is commonly used for design. Considering wall displacement, retaining walls are often designed similarly to braced frame structures, with earth thrust calculated based on the active earth pressure coefficient.

Ka=tan⁡2(45∘−ϕ2)K_a = \tan^2 \left(45^\circ – \frac{\phi}{2}\right)

This coefficient KaK_a is called the active lateral earth pressure coefficient and is derived assuming:

  • The wall surface is smooth (no friction),

  • The wall is vertical,

  • The soil surface is horizontal.

Determining Lateral Load on Each Bracing Structure

If the spacing between adjacent bracing frames is LL, the linear load intensity on each frame is:

P=Ka⋅γ⋅H2/2⋅LP = K_a \cdot \gamma \cdot H^2 / 2 \cdot L

where the total lateral pressure PP includes both effective earth pressure and hydrostatic pressure (if present).

By determining this load distribution, the forces can be transferred to the vertical nodes of the bracing frame to calculate axial forces and support reactions.

Tensile Capacity and Length of Piles

The tensile capacity of piles arises from their self-weight and skin friction with surrounding soil. The ultimate tensile capacity QuQ_u of a single pile is:

Qu=W+FsQ_u = W + F_s

where WW is the pile weight, calculated by multiplying the unit weight of reinforced concrete by the pile volume.

To evaluate the skin friction resistance in granular and cohesive soils, various methods exist, such as the Alpha method (Tomlinson’s method). The unit skin friction resistance fsf_s can be calculated by:

fs=α⋅cu+K⋅σv′⋅tan⁡δf_s = \alpha \cdot c_u + K \cdot \sigma_v’ \cdot \tan \delta

where:

  • α\alpha = adhesion factor between soil and pile material,

  • cuc_u = undrained cohesion of soil,

  • σv′\sigma_v’ = average effective overburden pressure along pile length,

  • KK = horizontal earth pressure coefficient,

  • δ\delta = effective friction angle between pile surface and soil.

Values of α\alpha usually range from 0.3 to 0.7, depending on soil type, pile installation method, and pile geometry. The coefficient KK typically lies between the soil’s at-rest and active earth pressure coefficients.

For bored piles, soil displacement is limited, so conditions are closer to at-rest pressure; for driven piles, soil displacement is greater, making active pressure more applicable.

The tensile capacity from skin friction is:

Fs=fs⋅As=fs⋅πDLpF_s = f_s \cdot A_s = f_s \cdot \pi D L_p

where AsA_s is the surface area of the pile, DD diameter, and LpL_p length of the pile.

Allowable tensile capacity is calculated by applying a safety factor γ\gamma:

Qallow=QuγQ_{allow} = \frac{Q_u}{\gamma}

Expressing allowable capacity in terms of pile length allows determination of required pile length to resist tensile forces from bracing reactions.

Design of Footing for Inclined Bracing Members

To determine soil bearing capacity under footing, Terzaghi’s bearing capacity equation is used:

qallow=0.5Bγ+q+CNcq_{allow} = 0.5 B \gamma + q + C N_c

The minimum footing width BminB_{min} ensures that the pressure under the footing does not exceed soil bearing capacity, calculated by:

Bmin=RqallowB_{min} = \sqrt{\frac{R}{q_{allow}}}

where RR is the compressive reaction force at the footing.

Sliding Stability of Braced Retaining Wall

Checking sliding stability is critical. The factor of safety against sliding is:

FS=RSFS = \frac{R}{S}

where the driving force SS is the active earth thrust, and the resisting force RR is the sum of shear strength of soil beneath footing and pile tensile resistance, including lateral resistance.

The driving lateral force can be calculated by:

S=KaγHL+qLS = K_a \gamma H L + q L

Resisting forces include cohesion, friction under footing, and lateral skin friction on piles:

R=C⋅A+Ntan⁡ϕ+12γBLtan⁡ϕR = C \cdot A + N \tan \phi + \frac{1}{2} \gamma B L \tan \phi

where NN is the resultant vertical force, CC cohesion, and ϕ\phi soil friction angle.

Typically, a safety factor of 1.5 is recommended against sliding.