AASHTO LRFD design code

How Rischio checks footings, walls, piles and drilled shafts by AASHTO LRFD, 10th edition: the load combinations, the resistance factors and each check.

Besides free mode, where only the designer’s limits give a verdict, Rischio checks footings, concrete retaining walls, MSE walls, piles and drilled shafts by the AASHTO LRFD Bridge Design Specifications, 10th edition (2024). With nothing selected, the editor shows the model’s Design code: choose AASHTO LRFD 10th (2024) there, or make it the mode new models start in, in Settings. Every check then has a verdict: it compares factored resistance with factored load, and shows its factor of safety without load or resistance factors beside it as a reference (Unfactored).

How a check reads

Every check is a ratio of factored resistance to factored load,

\frac{\phi R_n}{\Sigma \gamma_i Q_i} \ge 1

and says which load combination governed it. The resistance factor $\phi$ is the code’s. It can be edited in the open check, and an edited one is marked in the results, in the model’s properties and in the calculation report, with the code’s value beside it. Settlement is checked at Service I, every factor 1.0, against FHWA’s 25 mm (GEC 6, §8.3.1), which the designer can edit: AASHTO leaves the tolerable movement to the designer.

Loads: dead and live

Each load comes in its dead part and its live part. In free mode they are added; under AASHTO each takes its own factor (Tables 3.4.1-1 and 3.4.1-2):

Load	Maximum	Minimum
Dead load of a structure, DC	1.25	0.90
Live load, LL, and a live surcharge, LS	1.75	left out
Vertical earth load on a wall, EV	1.35	1.00
Active earth pressure, EH	1.50	0.90
A dead surcharge, ES	1.50	0.75
Water, WA	1.00	1.00

A load takes its minimum where it holds the structure up, and a live load is left out there, as Article 3.4.1 asks.

Footings

Combinations: Strength I at its maximum, the dead part at 1.25 and the live at 1.75, and at its minimum, the dead part at 0.90 without the live. Each check takes the more critical.
Bearing: $\phi_b q_n$ against the factored pressure on the effective area $B' \times L'$ . $q_n$ is AASHTO’s own equation by default (10.6.3.1.2a): the factors $N_c$ , $N_q$ and $N_\gamma$ , De Beer’s shape factors, a depth factor $d_q$ of at most 1.4, Vesic’s inclination factors and the water factors $C_{wq}$ and $C_{w\gamma}$ . The general bearing capacity equation can be chosen instead, one of the “accepted soil mechanics theories” the article admits (Bearing capacity). Where local or punching shear is possible, the bearing stratum takes $c^*$ and $\phi^*$ (10.6.3.1.2b). Over a weaker second stratum within AASHTO’s critical depth, $q_n$ is that of the two layers (10.6.3.1.2d to f).
Resistance factor (Table 10.5.5.2.2-1): 0.50 in clay and 0.45 in sand.
Eccentricity: $e \le B/3$ with factored loads (10.6.3.3).
Sliding, where a horizontal load pushes: $\phi_\tau = 0.80$ for concrete cast on sand, with $R_\tau = V \tan \phi_f$ ; 0.85 on clay, with the lesser of $s_u$ and half the normal stress (10.6.3.4). The vertical load takes its minimum and the horizontal its maximum.

Concrete retaining walls

Combinations: Strength Ia for bearing, every load at its maximum, the surcharge over the heel too; Strength Ib for sliding and eccentricity, the weights at their minimum and the thrusts at their maximum.
Bearing: $\phi_b = 0.55$ against $V/(B - 2e)$ , $q_n$ as for a strip footing (11.6.3.2).
Eccentricity: $e \le B/3$ on soil. It replaces the overturning check (11.6.3.3).
Thrust: on the code’s plane (C3.11.5.3), as free mode takes it by the data: Rankine on the vertical through the heel where the heel is long, Coulomb on the wall’s back where it is short or there is none. Rankine chosen over a short heel, or a back without one, under a granular backfill is refused.
Sliding: $\phi_\tau = 1.0$ , the soil shear component of Table 11.5.7-1, on 10.6.3.4’s resistance (Stability), the soil in front not counted (11.6.3.5 allows it).

MSE walls

Inside, each layer’s load by AASHTO’s method for its reinforcement (11.10.6.2.1): by the data the Coherent Gravity Method for steel strips and grids and the Stiffness Method for a geosynthetic with its stiffness, else the Simplified Method of Appendix B11. Each layer’s tension with the soil and a dead surcharge at 1.35 and the traffic at 1.75, apart (11.10.6.4.1), against $\phi T_{al} R_c$ , $\phi$ = 0.75 for steel strips (0.65 for steel grids on a rigid face), 0.80 for geosynthetics by the Stiffness Method and 0.90 by the Simplified; its pullout without the traffic (11.10.6.3.2), $\phi$ = 0.90, or 0.70 for geosynthetics by the Stiffness Method. The Stiffness Method’s strain is checked at Service I, at most 2.5 % (11.10.4.3). The check is the weakest layer’s, and each layer shows its ratio on the drawing.
Outside, the reinforced block as a rigid body: the retained soil’s Coulomb thrust with $\delta = 0.67\,\phi'$ (11.10.5.2), its vertical part holding the block, in every Strength I combination, each check taking the one that governs it; GEC 11’s three cases are among them: maximum (EV 1.35, EH 1.50, the traffic over the block too) for bearing, critical (EV 1.00, EH 1.50) for sliding and eccentricity, and minimum (EV 1.00, EH 0.90). Sliding $\phi_\tau$ = 1.0, soil on soil, two-thirds of the angle under a geosynthetic; $e \le L/3$ ; bearing $\phi_b$ = 0.65 on $L - 2e$ .
Verified against FHWA GEC 11 (2023), Example C1: the thrust, the bearing pressure, sliding at its maximum and each layer’s load for pullout within 1 %. The traffic’s vertical thrust that the example counts as resistance, and AASHTO doesn’t, makes its critical sliding 1.5 % lower.

Piles and drilled shafts

Each resistance factor is calibrated for one method, so under AASHTO a pile takes AASHTO’s methods, and each part of it the $\phi$ of its row (Tables 10.5.5.2.3-1 and 10.5.5.2.4-1). The check is

\frac{r \, \Sigma \phi_i R_{n,i}}{V_u} \ge 1, \qquad V_u = 1.25\,V_D + 1.75\,V_L

A drilled shaft (a bored pile of round section) by Article 10.8.3.5, which is Brown et al.’s method in FHWA GEC 10 (§10.3.5), Drilled shaft (FHWA GEC 10) in the methods; free mode takes it by the data too, where its data are. In clay, $q_s = \alpha S_u$ with $\alpha = 0.55$ up to $S_u/p_a = 1.5$ , then down to 0.45 at 2.5; the top 5 ft of the shaft carry nothing. In sand, $q_s = \beta \sigma'_v$ at each stratum’s middle, $\beta = (1 - \sin\phi')(\sigma'_p/\sigma'_v)^{\sin\phi'}\tan\phi'$ , with the stratum’s $\sigma'_p$ (typed, or from the SPT’s readings in it by AASHTO’s Eqs. 10.8.3.5.2b-4 and -5; without either, normally consolidated). The tip: $N_c S_u \le 80$ ksf on clay, $N_c = 6(1 + 0.2\,Z/D) \le 9$ ; $1.2\,N_{60}$ ksf $\le 60$ ksf on sand, $N_{60}$ from the tip down 2D; less within 1.5B above a weaker stratum. $\phi$ : side 0.45 in clay and 0.55 in sand, tip 0.40 and 0.50.
A driven pile by the strata’s strength: Nordlund’s in sand, shaft and toe, 0.45 (the shaft’s $\phi'$ held at 36°, $\sigma'_v$ at the toe at 3.2 ksf), and Tomlinson’s $\alpha$ in clay, 0.35, the tip on clay $9 S_u$ with the clay method’s $\phi$ . Where Nordlund’s charts stop, his own error says so. How each one is taken: the shaft and the toe.
Few elements: $r = 0.8$ for a driven pile alone or in a group of fewer than five (C10.5.5.2.3) and for a drilled shaft alone (10.5.5.2.4).
Groups: the sum of the piles, with $\eta$ from 0.65 at 2.5D to 1.0 at 6D on a soft clay at the surface (10.7.3.9), and a drilled shaft group in sand by Table 10.8.3.6.3-1; with the toe in clay, the block too, $\phi_{b1}$ 0.60 driven and 0.55 drilled. The lesser governs.
Lateral: the head load and moment factored by Strength I, the p–y curves as they are (C10.7.3.12). The bending against $\phi_f M_y$ , $\phi_f$ 1.00 for steel, 0.90 for concrete and 0.85 for timber. The head’s deflection at Service I, against FHWA’s 25 mm (GEC 9), which the designer can edit.
Verified against FHWA-NHI-16-064, the North and South Abutments, HP 12x74 piles: Nordlund’s shaft within 1.2 %, its toe within 1.6 % and the whole within 0.3 % at 30 ft; Tomlinson’s shaft within 0.3 %. The example’s toe at 60 ft takes the effective stress unlimited, where AASHTO holds it to 3.2 ksf: 7 % lower.
Verified against FHWA GEC 10 (2018), Examples 10-1, 10-3 and 10-5: the side in each sand and the tip in clay within 1 %, nominal and factored. The example’s side in clay takes GEC 10’s own $\alpha$ of 0.44, where AASHTO’s 10th edition gives 0.55.

Where the code is open, Rischio’s choice

A footing on sand: Table 10.5.5.2.2-1 has a row for a $\phi$ from the SPT (0.45) and one from the CPT (0.50), and none for a typed one, which takes the SPT’s 0.45, the lower.
A wall’s sliding: Articles 11.6.3.6 and 11.10.5.3 send its resistance to 10.6.3.4, whose footing factors are 0.80 and 0.85, while Table 11.5.7-1 lists 1.0 for the soil shear component, and 11.5.7 says its factors shall be used for wall design. Rischio takes 10.6.3.4’s resistance with the table’s 1.0.
Water between the rows of Table 10.6.3.1.2a-2: $C_{wq}$ and $C_{w\gamma}$ vary linearly.
Two strata in drained loading: the lower stratum’s $q_2$ is that of a footing on its surface, without the soil above it.
Rock below the strata isn’t counted, which stays on the conservative side; a note says so.
A single drilled shaft: AASHTO reduces $\phi$ by 20 % for one “supporting a bridge pier”. Rischio doesn’t know what it carries and reduces it always.
An edited $\phi$ on a pile is one for the whole pile, in place of each part’s and of the 0.8: the field verification’s (a load test, dynamic testing), as C10.5.5.2.3 uses it.
Nordlund’s toe: $q_L$ the lesser of GEC 12’s and AASHTO’s charts, which differ by 4–5 % above 35°.
A pile group’s cap: Rischio doesn’t know whether it bears on the ground, and takes it as not in firm contact.
A concrete pile’s bending takes the reinforced section’s 0.90, also when it’s prestressed (1.00).

What AASHTO doesn’t take

The open channel isn’t under AASHTO: it’s checked in free mode. A barrette (AASHTO’s drilled shaft, 10.8, is round) and an open-end pipe pile in sand by its strength (GEC 12 sends it to API’s method, which has no factor) are refused under AASHTO, with a message that says what is missing.

Reference

American Association of State Highway and Transportation Officials (2024). AASHTO LRFD Bridge Design Specifications, 10th ed. Sections 3, 5, 6, 8, 10 and 11.
Brown, D. A., Turner, J. P., Castelli, R. J., & Loehr, E. J. (2018). Drilled Shafts: Construction Procedures and Design Methods, FHWA-NHI-18-024 (GEC 10). Federal Highway Administration.
Chen, Y.-J., & Kulhawy, F. H. (2002). Evaluation of drained axial capacity for drilled shafts. Deep Foundations 2002, ASCE Geotechnical Special Publication 116, 1200–1214.
Kulhawy, F. H., & Chen, J.-R. (2007). Discussion of “Drilled shaft side resistance in gravelly soils”. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 133(10), 1325–1328.