Sliding Stability Check — Basal-Reinforced Embankment (BS 8006:1995)

Scope. Check the risk of a preferential slip along the interface between the embankment fill and the basal reinforcement, and verify that the reinforcement has sufficient bond length to mobilise the required tensile resistance.

1) Compute the active earth pressure coefficient

\[ K_a \;=\; \tan^2\!\left(45^\circ - \frac{\varphi'_{cv}}{2}\right) \] where \(\varphi'_{cv}\) is the large-strain (constant-volume) friction angle of the embankment fill.

2) Tensile demand in the reinforcement from lateral thrust

\[ T_{ds} \;=\; \tfrac{1}{2}\,K_a\,H\;\Big(f_{fs}\,\gamma\,H \;+\; 2\,f_q\,w_s\Big) \] with \(T_{ds}\) in kN per metre run, \(H\) = embankment height (m), \(\gamma\) = unit weight of fill (kN/m³), \(w_s\) = surcharge intensity (kPa = kN/m²), \(f_{fs}\) = partial factor for soil unit weight, and \(f_q\) = partial factor for external loads.

3) Minimum bond length to prevent sliding at the interface

Require the available factored interface resistance along both faces of the reinforcement over the length \(L_e\) to be no less than the factored tensile demand. A convenient design form is: \[ L_e \;\ge\; \frac{f_n\,f_s\,f_{ms}\;T_{ds}}{2\,h\,\gamma\,\alpha'\,\tan\!\left(\varphi'_{cv}\right)} \] where \(L_e\) = required reinforcement bond length within the embankment (m), \(h\) = average height of fill above the bond length (m), \(\alpha'\) = interaction coefficient for fill–reinforcement bond, \(f_s\) = partial factor for sliding resistance, \(f_{ms}\) = partial material factor applied to \(\tan\varphi'_{cv}\), and \(f_n\) = factor reflecting economic ramifications of failure.

4) Pass/Fail

Provide (or check) a bond length \(L_{\text{provided}}\). Sliding stability at the fill/reinforcement interface is satisfied if \[ L_{\text{provided}} \;\ge\; L_e. \] Otherwise, increase the bond length, improve the interface (increase \(\alpha'\)), reduce loading (smaller \(H\) or surcharge), or redesign the section.

5) Notes

(i) The maximum \(T_{ds}\) occurs near the edge of the crest. (ii) Use consistent units (kN–m–kPa). (iii) For overall safety you must also check other limit states (local/rotational stability and foundation extrusion), but the equations above are the specific sliding checks at the fill–reinforcement interface.

Symbols: \(H\) embankment height; \(\gamma\) unit weight of fill; \(w_s\) surcharge; \(\varphi'_{cv}\) large-strain friction angle of fill; \(\alpha'\) bond interaction coefficient; \(K_a\) active earth pressure coefficient; \(f_{fs}, f_q, f_s, f_{ms}, f_n\) partial factors per BS 8006:1995.

Determination of Sideslope Length \(L_s\) — Foundation Extrusion Check

For embankments over very soft, limited-depth foundations, the critical stability mode may be foundation extrusion. The sideslope length \(L_s\) must be great enough to limit outward shear stresses in the soft foundation soil. According to BS 8006:1995, extrusion is prevented if:

\[ R_{ha} \;\leq\; R_{hp} + R_s + R_R \]

where \(R_{ha}\) is the factored horizontal force causing extrusion, \(R_{hp}\) is the passive resistance developed in the foundation, \(R_s\) is the shear resistance at depth \(z_c\), and \(R_R\) is the shear resistance at the underside of the basal reinforcement.

If the soft foundation has constant undrained shear strength \(c_u\) with limited depth, simplified relationships (BS 8006:1995 Figure 64b) may be used to compute the minimum sideslope length:

\[ L_s \ge \frac{\left( f_{fs}\,\gamma_{1} H \;+\; f_{q} W_{s} \;-\; \frac{4\,c_{u}}{f_{ms}} \right) z_{c}} {\dfrac{(1+\alpha'_{bc})\,c_{u}}{f_{ms}}} \]

where \(z_c\) is the thickness of the soft layer. The reinforcement must also provide tensile capacity to resist the outward shear transmitted from the foundation. A sensitivity analysis using different values of \(z_c\) is recommended to identify the governing condition.

Thus, the design sideslope length \(L_s\) is obtained by checking that the available confinement at the base of the embankment (through slope geometry and basal reinforcement) is sufficient to satisfy the extrusion criterion.