Soil Nail and Anchored Walls: Method

Soil Nail and Anchored Walls

What the tool does

Two retaining systems built from the top down as the excavation proceeds, each by the Federal Highway Administration's own manual: the soil nail wall of Geotechnical Engineering Circular No. 7 (FHWA-NHI-14-007, 2015) and the ground anchor wall of Geotechnical Engineering Circular No. 4 (FHWA-IF-99-015, 1999). A soil nail is a passive bar grouted along its whole length that picks up load as the ground moves; a ground anchor is a prestressed tendon with a free (unbonded) length and a bond zone beyond the potential failure surface. Nail forces are per nail, wall forces per unit length of wall.

Conventions of the nail wall

The toe of the wall is the origin, x runs into the retained ground and y up. The face rises to the crest at the height H, leaning back by the batter; the ground behind rises at the backslope. A nail head lies on the face at its depth below the crest and the nail is inclined downward by i. Slip surfaces start at the toe. The surcharge acts on the ground from the crest back over its width.

Nail and facing resistances

Pullout per unit length r_PO = π q_u D_DH (GEC 7 equation 6.1) and R_PO = r_PO L_p over the length behind the slip surface; tendon R_T = A_t f_y. Facing flexure (equations 5.29 and 6.9 to 6.14): the facing is a two-way slab on the nails with yield lines at the nail head and at mid-span; each moment resistance per unit width is m = a f_y (h/2 − a f_y / (1.7 f′c)) with the steel at mid-depth, the area at the head being the mesh plus the added bars spread over the nail spacing, and R_FF = C_F (m_m + m_n) 8 S_H / S_V for vertical bending (S_V / S_H for horizontal bending). C_F allows for the soil pressure concentrating at the nail heads (Table 6.5: 2.0, 1.5, 1.0 for initial facings of 4, 6 and 8 in; 1.0 for final facings). The manual's simplified form for Grade 60 steel and 4,000 lb/in² concrete, R_FF [kip] = 3.8 C_F f_y [ksi] F (equation 6.15), is shown beside it; the two agree within a few percent. Punching shear V_F = 0.58 √f′c π D′_c h_c (equation 6.21, lb/in², ft, kip) on a cone of mean diameter L_BP + h_i through the initial facing, and around the stud group in the final facing with h_c = L_S + t_P − t_SH and D′_c the smaller of S_SH + h_c and 2 h_c. Headed studs R_FH = N_H A_S f_y. The reinforcement ratio and the stud head proportions are checked as the manual's example does.

Overall stability

The manual requires a limit-equilibrium analysis with factors of safety, followed by the strength verifications. Where a slip surface crosses a nail at the distance t from the head, the nail force is the smallest of the allowable pullout of the length behind the surface, the allowable tendon force, and the allowable head force plus the pullout of the length in front (the nail support diagram of GEC 7 Figure 5.7 and of FHWA's program SNAP-2), the allowables being the nominal resistances divided by their factors of safety of Table 5.1. The soil strength is divided by the overall factor FS. As in the manual's wedge example (equations 5.6 to 5.9), the component of a nail force along the slip surface is subtracted from the driving force and the component normal to it adds friction.

Two families of surfaces through the toe are searched. Planar wedges: FS = [c L + ((W + Q) cos α + ΣT sin(α + i)) tan φ] / [(W + Q) sin α − ΣT cos(α + i)], which is equation 5.9 with cohesion and several nails. Circles by Bishop's simplified method: vertical equilibrium of each slice with the vertical component of a nail force added to the slice it crosses, N = (W + T sin i − c l sin α / FS) / (cos α + sin α tan φ / FS), not below zero, and moments about the centre, FS = Σ(c l + N tan φ) / (ΣW sin α − ΣT cos(α + i)). The circle is described by its exit point and the inclination of the arc at the toe, which is kept between horizontal and the chord so that the arc neither dips below the toe nor overhangs. The lower factor governs. The same analysis is repeated for every construction stage (cut below the next row with the rows above in place) and with all nail lengths scaled, for the chart.

The largest nail force on the critical surface is T_max, and the nail-head load is T_o = T_max [0.6 + 0.057 (S_max − 3)], S_max in feet (Clouterre, equation 5.1). For comparison the tool lists the working loads measured on instrumented walls: 0.75 K_a γ H S_V S_H in the upper two thirds and half of that below (section 5.2.1).

Strength verifications

LRFD: CDR = φ R / (γ T) ≥ 1.0 with γ = 1.35 and the resistance factors of Tables 5.4 to 5.11 (pullout 0.65; tendon 0.75 or 0.65; facing flexure and punching 0.90; headed studs 0.70 or 0.80), which the manual back-calculated from the factors of safety. ASD: R / T against the minimum factors of Table 5.1 (pullout 2.0; tendon 1.8 or 2.0; facing 1.5; studs 2.0 or 1.7). Pullout and tendon are checked against T_max, the facing and the studs against T_o.

Sliding, basal heave, displacement

Sliding of the reinforced block on its base (equations 5.17 to 5.20): the active thrust P_a = γ H_1² K_a / 2 acts on the vertical plane behind the block, parallel to the backslope, with H_1 = H + (B_L − H tan α) tan β and Coulomb's K_a (equation 5.21); R_s = c_b B_L + (W + P_a sin δ) tan φ_b. Basal heave over soft clay: FS = N_c S_u / (γ H + q), equation 5.16 with the surcharge added. Displacement of the top of the wall: δ_h = H/1000, H/500 or H/333 for weathered rock and stiff soil, sandy soil and fine-grained soil, and ground movement up to D_DEF = C (1 − tan α) H behind the wall with C = 0.8, 1.25, 1.5 (Table 5.12).

Ground anchor wall

Apparent earth pressure (GEC 4 Figures 24 and 27): for sand the total load 0.65 K_A γ H², for stiff to hard clay a maximum ordinate of 0.2 to 0.4 γ H, both on a trapezoid that rises over two thirds of the depth of the top anchor and falls over the lowest two thirds of the bottom span. A surface surcharge adds K q uniformly. Tributary area method (Figures 33, 34, 39): each anchor carries the diagram between the mid-heights of the adjacent spans and the subgrade carries the rest; moments 13 H_1² p / 54 at the top anchor and p l² / 10 in the spans. Hinge method (Figures 34, 38): the wall is hinged at every support below the top anchor and at the subgrade; span moments at zero shear.

Anchor design load DL = T_h s / cos θ. The unbonded length reaches the larger of 1.5 m and H/5 beyond the critical surface, taken at 45° + φ/2 from the corner of the excavation unless another angle is entered, and is at least 4.5 m for strand and 3 m for bar. The bond length is DL times the factor of safety (2.0 in soil, 3.0 in rock) divided by the ultimate load transfer rate, for which the manual's Tables 6 and 8 give presumptive values. The tendon is sized so that the design load does not exceed 60 % of its specified minimum tensile strength, the lock-off load 70 % and the test load 80 %. The passive resistance of the ground behind the top of the wall is compared with the test load of the top anchor, F_p = 1.125 K_P γ h_1² s (equation 48).

Soldier beam: moment per unit length times the spacing, section modulus at 0.55 F_y. Embedment (section 5.5, Appendix B): the passive force on the beam below the subgrade must be 1.5 times the subgrade reaction plus the active pressure on the beam width. Wang and Reese's resistance per unit depth is the least of a single wedge (equation B-2), intersecting wedges, flow around the beam (B-5) and the continuous wall (B-6) in sand, and of equations B-8, B-10, 11 S_u b and B-13 in clay; Broms' is three beam widths of Rankine passive pressure in sand and 9 S_u b below 1.5 widths in clay.

Checks

Nail wall: the default is the design example of GEC 7 Appendix C. The tool reproduces its resistances and capacity-to-demand ratios (pullout 51.2 kip over 15.6 ft, tendon 45 kip, facing flexure 36 and 60.8 kip by the simplified form, punching 41.6 and 36.9 kip, studs 47.1 kip, reinforcement ratios, displacement 0.6 in) and, on the slip circle fitted to the manual's printed nail crossings, the nail forces of its Table C.5 (3.2, 7.5, 12.7, 18.9 and 25.0 kip against 3.2, 7.2, 12.5, 19.0 and 24.7). The overall factor of safety is not reproduced: SNAP-2 prints 1.51 for that wall (1.62 without the surcharge) where this tool finds 1.24 (1.31), and 1.31 on SNAP-2's own circle. Both use Bishop's method; SNAP-2's manual does not say how the nail forces enter its equations, and none of the usual variants gives its pair of values. This tool follows the manual's printed wedge equations and is the more cautious. Bishop's solution and the searches are checked against an independent scipy program on 20 seeded walls, the wedge against equation 5.9, and an unreinforced vertical cut against Culmann's 4c/γH and Taylor's stability number 0.261.

Anchored wall: Design Example 1 of GEC 4 Appendix A is reproduced to the printed digits (43.6 kPa, 168 and 172 kN/m, 37 kN/m, 76 and 66 kN-m/m, 435 and 445 kN, 8.9 m of bond, 501 and 469 kN tendons, section moduli, the embedment table of Figure A-4, 1,898 kN and 3.4 at the test load), as are the Wang-Reese and Broms spreadsheets of Appendix B in sand and clay and the closed forms of Figure 39.

Notes on the sources

GEC 7: Table 6.7b prints punching resistances for effective depths of 6 and 8 in that are a quarter to two fifths below equations 6.21 and 6.24 (the tool follows the equations, as the manual's example does); the example takes D_DEF = 0.8 H, the coefficient of weathered rock, for its sandy soil (Table 5.12 gives 1.25); equation 5.14 carries a minus sign before the surcharge term. GEC 4: equation B-5 as printed lacks the beam width in its second term and equation B-4 does not give the intersecting-wedge values of the manual's own spreadsheets (the tool reproduces the spreadsheets); Figure 39(a) gives the hinge-method loads under the name of the tributary area method; Table 9 prints 435.7 kips for 70 % of 778 kips.

Limits

One soil, no groundwater, static loads. Slip surfaces pass through the toe; deep-seated surfaces below the wall, layered ground and seepage need a general slope-stability analysis. The bond strength and the load transfer rate are estimates until verified by load tests. Soft to medium clay behind an anchored wall, base heave and staged excavation are in the Sheet Pile and Braced Excavation tool.