Drilled pier
A straight drilled shaft (drilled pier, caisson) in layered soil and rock: the axial side and base resistance by FHWA GEC 10 (FHWA-NHI-18-024, 2018) Chapter 10, uplift, the moment and shear along the shaft from a p-y analysis of the lateral loads, and the structural design of the shaft as a circular reinforced concrete member by ACI 318-19 13.4.3.
Inputs of the drilled pier #
- Shaft: diameter B, length L, head condition for the lateral analysis (free, or fixed by a cap: the engineer's judgment), and whether the shaft weight (150 pcf) is added to the dead load.
- Soil and rock: the water table and the layers top down (the last runs on):
- cohesionless: N60 (for σ'p and the base) and φ' (GEC 10 Eq. 10-9 relates it to (N1)60), and the sand type that sets the preconsolidation correlation: clean sand σ'p/pa ≈ 0.47·N60^0.6, silty sand 0.47·N60^0.8 (Eq. 10-11), gravel 0.15·N60 (Eq. 10-12);
- cohesive: su and the test it came from (UU and UC values are converted to CIUC by Eqs. 10-16, 10-17);
- rock: the uniaxial compressive strength qu of intact core;
- per layer a side factor (0 where permanent casing or scour removes the side resistance; GEC 10 suggests 0.60 to 0.75 for permanent casing in contact with the soil), and the p-y parameters ε50 (clay) and k (sand API modulus, or the linear spring of rock).
- Exclusions: side resistance neglected over the top (GEC 10 10.3.5.2: 5 ft is common practice, or the depth of seasonal moisture change) and, if chosen, over one diameter above a base in clay (AASHTO practice).
- Loads: per load type at the top: axial P (compression positive, uplift negative), lateral H and moment M.
- Resistance factors (LRFD) from GEC 10 Table 8-4 (side 0.55 / 0.45 / 0.55, base 0.50 / 0.40 / 0.50, uplift 0.45 / 0.35 / 0.40 for cohesionless / cohesive / rock), or the factor of safety (ASD); the rock coefficients C (Eq. 10-21) and N*cr (Eq. 10-23).
- Shaft reinforcement: shaft type for ACI Table 13.4.3.2 (uncased cast-in-place 0.55; in rock or a permanent casing 0.60), f'c, fy, the number and size of longitudinal bars, ties or spiral and their spacing, clear cover, and the seismic design category.
Auto-design varies the diameter (6-in steps) and the length (1-ft steps) for the least concrete; the bars, soil, factors and loads are kept. See Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Axial compression | Σφs·RSN + φB·RBN ≥ the factored load (GEC 10 Eq. 10-2), or (ΣRSN + RBN)/FS ≥ the service load |
| Side, cohesionless | fs = β·σ'v, β = (1 − sinφ')(σ'p/σ'v)^sinφ'·tanφ' ≤ Kp·tanφ' (Eq. 10-13), β not above its value at 7.5 ft |
| Side, cohesive | fs = α·su(CIUC), α = 0.30 + 0.17/(su/pa) (Eq. 10-18), taken not more than 1.0 |
| Side, rock | fs = C·pa·√(qu/pa) with qu ≤ f'c (Eq. 10-21) |
| Base | Cohesionless 0.60·N60 tsf ≤ 30 tsf (Eq. 10-14); cohesive N*c·su (Eq. 10-19, Table 10-2; Eq. 10-20 below 3B); rock N*cr·qu (Eq. 10-23) |
| Uplift | Σφup·RSN (side only) against the largest net tension (the weight helps as dead load at 0.9) |
| Lateral p-y solution | FHWA GEC 9 Ch. 6 with API sand, Matlock (su < 1,000 psf) or Welch-Reese clay, and a linear spring in rock; gross EI; NOT FEASIBLE if the soil cannot hold the load |
| Shaft axial | Pu ≤ φ·Pn,max with φ of ACI 318-19 Table 13.4.3.2 |
| Shaft axial and flexure | The largest p-y moment with its axial load inside the φPn-φMn curve (strain compatibility, φ of Table 21.2.2) |
| Shaft shear | Vu ≤ 0.75(Vc + Vs), bw = D, d = 0.8D (22.5.2.2), two legs of the tie |
| Reinforcement required | ACI 318-19 13.4.4.1 where there is uplift or moment |
| Seismic minimum steel (advisory) | ACI 318-19 18.13.5: ρ ≥ 0.0025 (SDC C), 0.005 (SDC D-F) (to confirm against the code text) |
Each layer's resistance is computed at its mid-depth (as the GEC 10 examples do); split a thick layer to follow a change of strength with depth. The drawings show the shaft in its soil profile with its length, diameter and bars, the shaft section with the bars and ties, and the moment and shear along the shaft.
Limitations #
- No bells, no settlement analysis (GEC 10 10.3.7 load-transfer curves), no group effects, downdrag or scour.
- The Hoek-Brown base resistance of fractured rock (Eqs. 10-24 to 10-29) and the caving-rock reduction (Eq. 10-22) are not offered; enter a reduced C or N*cr.
- The cap of α at 1.0 is ILX's limit on Eq. 10-18 for very soft clay, where the fit leaves the data of Figure 10-6.
- The lateral analysis uses the gross EI; the moment is taken with the largest axial load at the top (conservative for the interaction); bars are assumed over the full length.
- ACI 318-19 18.13 detailing (length of the confined region, transverse steel) is the engineer's; only the minimum longitudinal ratio is shown.
Verification examples #
Verification status: 14 values compared in 5 examples (5 published, 0 hand calculations from the cited equations): 14 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
Published worked examples (backend/tests/test_verify_drilled_pier.py), FHWA GEC 10 (2018):
| Source | What it checks | Published | ILX Calcs |
|---|---|---|---|
| Example 10-1: 5 ft shaft, silty sand N60 9 and 27, φ' 38° and 41° | β; RSN of the two layers | 0.97, 0.98; 197.2, 635.6 kips | (test run) |
| Example 10-2: stiff clay su = 2,000 psf (UU) | su(CIUC), α, RSN | 2,571 psf, 0.44, 479.7 kips | (test run) |
| Example 10-3 | qBN, RBN | 23.1 ksf, 453.6 kips | (test run) |
| Example 10-5 | Factored demand and ΣφR | 766, 855.4 kips | (test run) |
| Example 10-4: 6 ft socket in sandstone, qu = 360 ksf | fs, RSN, RBN | 27.6 ksf, 5,202 kips, 25,447 kips | (test run) |
The example's own rounding of β puts its sand side resistances 0.3 to 0.6 % above the unrounded values. The shaft structural checks use the shared ACI 318-19 column library already verified for the concrete column type.