Soil-Nail Interaction and Tensile Force Distribution in Stabilized Excavations by Nailing Method

Conceptual Model

The interaction between soil and nails (or reinforcing elements in nailing) behind the facing of a stabilized excavation wall is complex. The loads applied to the nails correspond to the reaction forces resisting the outward movement of the excavation face during soil excavation in front of the wall. A portion of the nail located behind the failure surface (e.g., anchorage zone) is pulled out from the soil wedge. The tensile forces in the nail, denoted as T, vary from zero at the nail tip, increase to a maximum tensile force Tmax at mid-length, and then decrease to a value T0 at the wall facing (Figure 1).

Figure 1. Stress transfer mechanism in soil nails

The maximum tensile force in the nail does not necessarily occur exactly at the failure surface intersection. The active shear stress along the soil-grout interface, q, is non-uniform and changes from positive to negative values (Figures 1-a and 1-b). A schematic distribution of tensile force T along the nail is shown in Figure 1-c.

Simplified Tensile Force Distribution

For design purposes, the tensile force distribution in the nail can be simplified as shown in Figure 2. The tensile force increases at a constant rate Qu (equal to the pullout capacity per unit length), reaches a maximum Tmax, and then decreases at the same rate to T0 at the nail head. The maximum tensile force Tmax is limited by three ultimate conditions:

  • Pullout capacity, RP

  • Tensile capacity of the nail, RT

  • Facing capacity, RF

If RP < RT and RF, pullout failure governs Tmax. If RT < RP and RF, tensile failure governs Tmax. Finally, if RF < RP and RT, facing failure governs Tmax depending on the ratio T0/Tmax.

To achieve a balanced design, all resistant components should have similar factors of safety; no component should be significantly weaker or stronger than others. Hence, RF, RT, and RP should be reasonably comparable.

Figure 2. Simplified tensile force distribution in soil nails

Where:

  • RT: tensile capacity of the nail

  • RF: capacity of the stabilized wall facing

  • RP: pullout capacity of the nail

  • Qu, qu: ultimate load transfer rate and bond strength

  • T0 ~ 0.6–1.0 Tmax

Maximum Tensile Force Distribution

The tensile force in a soil nail depends on the position of the nail relative to the failure surface. As shown in Figure 3, tensile force distribution varies along the wall section. Due to complexities in load transfer among individual nails, the maximum tensile force location typically coincides near the critical failure surface determined by global stability analyses. Measurements from instrumented walls indicate that maximum tensile force occurs approximately at 0.3H to 0.4H behind the wall facing in the upper portion and 0.15H to 0.2H in the lower portion of the wall (Plumelle et al., 1990; Byrne et al., 1998).

Furthermore, the contribution of tensile forces to overall stability varies from nail to nail depending on their intersection with the failure surface. Nails with longer embedment behind the failure surface develop higher pullout capacities. The gradual development of tensile forces during excavation proceeds from top to bottom as excavation progresses. Maximum tensile forces typically develop after two subsequent excavation stages and may increase mildly (about 15%) between construction completion and long-term steady state due to soil creep and stress relaxation. These additional loads are usually accounted for through safety factors in design.

Figure 3. Schematic location of maximum tensile force in soil nails

Measured Maximum Tensile Forces

Measured long-term tensile forces in soil nails, normalized by soil unit weight, nail spacing (horizontal SH, vertical SV), wall height H, and active earth pressure coefficient KA, are shown in Figure 4 (Byrne et al., 1998). These forces represent service conditions and exclude additional loads such as frost or facing loads. Normalized tensile forces in the upper two-thirds of the wall range from 0.4 to 1.1, averaging about 0.75. Maximum tensile force varies with depth, increasing from about 0.55–0.6 near the top to 0.75–0.85 in the mid-third, then decreasing to 0.4–0.5 near the bottom, reaching zero at the wall base. These results align with observations from Clouterre test walls (Plumelle et al., 1990).

In practice, tensile force in the upper two-thirds can be considered uniform at 0.75 KA γ H SV SH. Tensile force in the lower third decreases to about 50% of the upper value. Briaud and Lim (1997) suggested calculating average maximum tensile force in the upper nail row as 0.65 KA γ H SV SH and that tensile force in subsequent rows is about half of that.

Figure 4. Measured maximum tensile forces in soil nails

These findings show that tensile force distribution in soil nail walls is complex and the average nail force is smaller than what would be computed from the full lateral earth pressure distribution, an important factor in facing design.

Tensile Failure Design of Soil Nails

To achieve a balanced design in internal failure mode, soil strength and nail tensile strength must be fully mobilized simultaneously. When the global safety factor (FSG) equals 1.0 (full soil resistance activation), the tensile safety factor (FST) should also be 1.0 (ultimate tensile capacity of the nail). Under these conditions, the design tensile force Tmax-s is defined. If FSG > 1.0, Tmax-s increases due to partial soil resistance mobilization requiring compensating tensile force in nails, resulting in conservative design.

The SNAIL software reports average tensile forces but not the maximum tensile force at FSG=1.0. To estimate Tmax-s without full stability analysis, a simplified relation based on the ratio of Tmax to average force Tavg at FSG>1.0 can be used:

TmaxTavg≈Tmax−sTavg−s\frac{Tmax}{Tavg} \approx \frac{Tmax-s}{Tavg-s}

Where Tavg-s is the average design tensile force reported by SNAIL. Tmax-s is then used for tensile failure checks.

Tensile failure occurs if Tmax-s exceeds the tensile capacity RT of the nail, defined as:

RT=At⋅fyR_T = A_t \cdot f_y

Where AtA_t is the nail cross-sectional area and fyf_y is the yield strength. Bond strength in grout is neglected due to stiffness differences.

Allowable tensile capacity is reduced by a safety factor FST:

RT,allowable=RTFSTR_{T,allowable} = \frac{R_T}{F_{ST}}

Typically, a minimum safety factor of 1.8 is recommended for static loads.