10.2 Drilled Shaft Axial Design & Construction Methods

10.2 Drilled Shaft Axial Design & Construction Methods

Drilled shafts (also termed bored piles, cast-in-drilled-holes [CIDH], or caissons) are constructed by excavating cylindrical holes in the ground and filling the void with reinforced concrete. Ranging in diameter from 0.6 m to over 3.0 m, drilled shafts offer immense structural load capacity, minimal installation vibration, and the ability to penetrate dense soil layers or socket directly into bedrock.

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Drilled Shaft Construction Methods

Geotechnical performance depends directly on construction quality. Excessive bottom debris, borehole caving, or slurry filter cake buildup severely reduces axial capacity.

                    DRILLED SHAFT CONSTRUCTION METHODS
  ┌─────────────────────────┬─────────────────────────┬─────────────────────────┐
  │       DRY METHOD        │      CASING METHOD      │   WET / SLURRY METHOD   │
  ├─────────────────────────┼─────────────────────────┼─────────────────────────┤
  │ • Stable clay / rock    │ • Caving sands/gravel   │ • High groundwater table│
  │ • No groundwater entry  │ • Water-bearing strata  │ • Deep uncased shafts   │
  │ • Open auger excavation │ • Temporary/permanent   │ • Mineral / Synthetic   │
  │ • Direct concrete pour  │   steel casing driven   │   slurry holds borehole │
  └─────────────────────────┴─────────────────────────┴─────────────────────────┘

1. Dry Construction Method

• Applicable only in stable, low-permeability cohesive soils or competent rock above the water table.
• A rotational auger drills to design depth without fluid or support casings.
• Reinforcing steel cage is lowered, and concrete is placed directly via drop chute (ensuring no concrete strikes rebar cage walls to prevent segregation).

2. Casing Method

• Utilized when soil is prone to cave or collapse (e.g., loose sand, soft muck) or when groundwater seepage threatens borehole stability.
• Temporary or permanent steel casings are vibrated or rotated into the ground ahead of the excavation drill bit.
• After excavation and rebar cage placement, concrete is placed. For temporary casing, the casing is slowly extracted as concrete is poured, maintaining a hydrostatic concrete head inside the casing to prevent soil influx.

3. Wet (Slurry) Construction Method

• Required for deep boreholes penetrating water-bearing sands or unstable strata where casing is impractical.
• The borehole is kept filled with drilling fluid (slurry) to maintain positive hydraulic head pressure against surrounding soil walls.
• Slurry Types: Mineral slurry (bentonite or attapulgite clay suspensions) or synthetic polymer slurry.
• Slurry Quality Control Criteria (FHWA GEC 10 Specs):
  • Density (Unit Weight): (< 1.15\text{ g/cm}^3) (72 pcf) for mineral slurry; (< 1.05\text{ g/cm}^3) for polymer slurry prior to concreting.
  • Marsh Funnel Viscosity: 30 to 50 seconds/quart for bentonite; 45 to 125 seconds/quart for polymer.
  • Sand Content: (< 4.0%) by volume measured at the bottom of the shaft prior to concrete placement.
  • pH: 8 to 11 for mineral slurry.
• Concrete is placed using a submerged tremie pipe. The tremie pipe must remain embedded at least 1.5 m to 3.0 m (5 to 10 ft) inside the fresh concrete pool at all times to displace slurry upwards without trapping slurry pockets.

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FHWA GEC 10 Axial Capacity Design (O'Neill & Reese Method)

The nominal ultimate axial capacity (R_n) of a drilled shaft is:

[ R_n = R_s + R_b = \sum f_s A_s + q_b A_b ]

Under LRFD design criteria, factored axial resistance (R_R) must satisfy:

[ R_R = \phi R_n = \phi_s R_s + \phi_b R_b \ge \sum \gamma_i Q_i ]

Where typical resistance factors are (\phi_s = 0.45\text{ to } 0.55) and (\phi_b = 0.40\text{ to } 0.50).

1. Cohesive Soils (Clay Strata)

Unit side resistance (f_s) is computed via the FHWA (\alpha)-method:

[ f_s = \alpha \cdot c_u ]

• (\alpha = 0.55) for (c_u / p_a \le 1.5) (where atmospheric pressure (p_a = 101.3\text{ kPa}) or 2,116 psf).
• For (1.5 < c_u / p_a \le 2.5): [ \alpha = 0.55 - 0.10 \left( \frac{c_u}{p_a} - 1.5 \right) ]

Shaft Friction Exclusion Zones (Mandatory FHWA Rules):

1. Top 1.5 m (5.0 ft) of the shaft (subject to soil seasonal shrinkage/swelling and surface disturbance).
2. Bottom length equal to one shaft diameter (D) above the tip (due to stress redistribution near the base).
3. Any section surrounded by temporary casing where slurry or space voids exist.

                      DRILLED SHAFT EXCLUSION ZONES
  Ground Surface  ──────────────────────────────────────  z = 0
  │                                                    │
  │ ▒▒▒▒▒▒▒▒▒▒ EXCLUDED ZONE (Top 1.5 m / 5 ft) ▒▒▒▒▒▒ │  z = 1.5 m
  │                                                    │
  │ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █  │
  │ █                                                █ │
  │ █          EFFECTIVE SHAFT FRICTION              █ │  fs = alpha * cu
  │ █              ZONE (fs active)                  █ │  fs = beta * sig'v
  │ █                                                █ │
  │ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █  │
  │                                                    │  z = L - D
  │ ▒▒▒▒▒▒▒▒▒▒ EXCLUDED ZONE (Bottom 1 Diameter D) ▒▒▒ │
  Shaft Tip       ──────────────────────────────────────  z = L

Unit end bearing (q_b) in cohesive soil:

[ q_b = N_c \cdot c_u ]

Where (N_c = 6.0 \left[ 1 + 0.2 \left(\frac{Z}{D}\right) \right] \le 9.0). If (Z/D \ge 15), (N_c = 9.0). If undrained shear strength (c_u < 96\text{ kPa}) (2,000 psf), total base settlement may govern and (q_b) must be reduced.

2. Cohesionless Soils (Sand Strata)

Unit side resistance in sand utilizes the empirical (\beta)-method:

[ f_s = \beta \cdot \sigma'_v ]

Where (\beta = (1 - \sin\phi') \left( \frac{\sigma'_p}{\sigma'_v} \right)^{0.5}), bounded between (0.25 \le \beta \le 1.20). Alternatively, FHWA GEC 10 provides depth-based expressions for cohesionless soils:

[ \beta = 1.5 - 0.245 \sqrt{z \text{ (m)}} \quad (0.25 \le \beta \le 1.20) ]

Unit end bearing (q_b) in sand based on standard penetration testing (SPT (N_{60})):

[ q_b = 0.057 \cdot N_{60} \quad \text{(in MPa, capped at } 4.8\text{ MPa)} ]

3. Intermediate Geomaterials (IGMs) & Bedrock Sockets

For shafts socketed into weak rock or IGMs (e.g., shale, sandstone, limestone), side resistance is governed by the unconfined compressive strength (q_u) of the intact rock (Horvath & Kenney formulation):

[ f_s = 0.65 \cdot p_a \cdot \sqrt{\frac{q_u}{p_a}} \quad \text{or} \quad f_s = 0.20 \cdot \sqrt{q_u \text{ (MPa)}} \quad \text{(in MPa)} ]

Unit end bearing on competent rock:

[ q_b = 4.83 \cdot (q_u)^{0.51} \quad \text{(in MPa)} ]

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Strain Incompatibility Considerations

A critical factor in drilled shaft engineering is the load-displacement response difference between side friction and end bearing:

• Side Resistance Mobilization: Full shaft friction (f_s) mobilizes at extremely small elastic head displacements: 0.5% to 1.0% of shaft diameter (typically 5 to 10 mm).
• End Bearing Mobilization: Full base bearing (q_b) in sand requires substantial downward displacement: 4.0% to 5.0% of shaft diameter (e.g., 60 mm for a 1.2 m shaft).

If design allowable settlement is capped at 12 mm (0.5 in), full end bearing cannot be mobilized concurrently with shaft friction. Engineers must either apply displacement-matching t-z / q-w curves or ignore end bearing capacity in deep sand shafts.

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PE-Style Worked Example: Drilled Shaft LRFD Design

Problem: A drilled shaft with diameter (D = 1.20\text{ m}) is excavated to a total length (L = 15.0\text{ m}) using polymer slurry. The soil profile consists of:

• 0 to 3.0 m: Unsuitable fill (ignored for capacity).
• 3.0 to 10.0 m: Stiff clay, (c_u = 90\text{ kPa}), (\gamma_{sat} = 18.5\text{ kN/m}^3).
• 10.0 to 15.0 m: Dense sand, (N_{60} = 35), (\gamma_{sat} = 19.5\text{ kN/m}^3).
• Water table is at (z = 3.0\text{ m}).

Using FHWA GEC 10 guidelines and LRFD resistance factors ((\phi_s = 0.45) in clay, (\phi_s = 0.55) in sand, (\phi_b = 0.50) in sand tip):

1. Calculate nominal side resistance (R_s) (applying FHWA clay exclusion zones).
2. Calculate nominal tip resistance (R_b).
3. Determine total factored resistance (R_R = \phi R_n).

Solution Step-by-Step:

1. Geometry & Exclusions:

• Shaft Perimeter (P = \pi \cdot 1.20\text{ m} = 3.7699\text{ m})
• Tip Area (A_b = \frac{\pi}{4} (1.20)^2 = 1.1310\text{ m}^2)
• Top Exclusion Zone: Top 1.5 m of ground (z = 0 to 1.5 m).
• Unsuitable fill covers z = 0 to 3.0 m (no skin friction).

2. Clay Layer Shaft Friction (3.0 m to 10.0 m):

• Clay thickness = 7.0 m.
• Bottom exclusion in clay: The bottom of the clay layer is at z = 10.0 m. Does bottom exclusion apply here? FHWA rules exclude the bottom (1D) (1.2 m) of a shaft if the tip terminates in clay. However, here the clay transitions into sand at 10.0 m. Per FHWA GEC 10, top 1.5 m of the shaft is excluded. Since fill extends to 3.0 m, the top 1.5 m exclusion is contained within the fill. Thus, active clay friction acts from z = 3.0 m to z = 10.0 m (length = 7.0 m).
• Adhesion factor (\alpha): For (c_u = 90\text{ kPa}), (c_u / p_a = 90 / 101.3 = 0.888 \le 1.5), so (\alpha = 0.55).
• Unit Skin Friction: (f_{s,clay} = 0.55 \cdot 90\text{ kPa} = 49.5\text{ kPa})
• Clay Shaft Resistance: (R_{s,clay} = f_{s,clay} \cdot P \cdot \Delta z = 49.5 \cdot 3.7699 \cdot 7.0 = 1306.3\text{ kN})

3. Sand Layer Shaft Friction (10.0 m to 15.0 m):

• Sand thickness = 5.0 m (z = 10 to 15 m).

• Average depth in sand layer (z_{avg} = \frac{10 + 15}{2} = 12.5\text{ m}).

• FHWA (\beta) coefficient: (\beta = 1.5 - 0.245 \sqrt{12.5} = 1.5 - 0.245 \cdot 3.5355 = 1.5 - 0.866 = 0.634).

• Compute effective stress profile:

  • (\sigma'_v(z=3) = 3.0 \cdot 18.5 = 55.5\text{ kPa})
  • (\sigma'_v(z=10) = 55.5 + 7.0 \cdot (18.5 - 9.81) = 55.5 + 60.83 = 116.33\text{ kPa})
  • (\sigma'_v(z=15) = 116.33 + 5.0 \cdot (19.5 - 9.81) = 116.33 + 48.45 = 164.78\text{ kPa})
  • (\bar{\sigma}'_{v,sand} = \frac{116.33 + 164.78}{2} = 140.56\text{ kPa})

• Unit Skin Friction Sand: (f_{s,sand} = \beta \cdot \bar{\sigma}'_{v,sand} = 0.634 \cdot 140.56 = 89.11\text{ kPa})

• Sand Shaft Resistance: (R_{s,sand} = f_{s,sand} \cdot P \cdot \Delta z = 89.11 \cdot 3.7699 \cdot 5.0 = 1679.7\text{ kN})

• Total Nominal Side Resistance: [ R_s = R_{s,clay} + R_{s,sand} = 1306.3 + 1679.7 = 2986.0\text{ kN} ]

4. Nominal Tip Resistance (R_b) at (z = 15.0\text{ m}) (Sand):

• For SPT (N_{60} = 35): [ q_b = 0.057 \cdot N_{60} = 0.057 \cdot 35 = 1.995\text{ MPa} = 1995\text{ kPa} \le 4800\text{ kPa} ]
• Tip Resistance: (R_b = q_b \cdot A_b = 1995 \text{ kPa} \cdot 1.1310\text{ m}^2 = 2256.3\text{ kN})

5. Factored LRFD Resistance (R_R):

• Factored Shaft Resistance: (\phi_s R_s = (0.45 \cdot 1306.3) + (0.55 \cdot 1679.7) = 587.8 + 923.8 = 1511.6\text{ kN})
• Factored Tip Resistance: (\phi_b R_b = 0.50 \cdot 2256.3 = 1128.2\text{ kN})
• Total Factored Resistance: (R_R = 1511.6 + 1128.2 = 2639.8\text{ kN} \approx 2640\text{ kN})

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Specialty Deep Foundation Systems: Micropiles, Helical Piles, and Auger-Cast/ACIP Piles

NCEES explicitly names micropiles, helical screw piles, and auger-cast (ACIP) piles as deep foundation systems distinct from conventional driven piles and drilled shafts, each with a different capacity mechanism, installation method, and typical application.

Micropiles

Micropiles are small-diameter ($100$–$300\text{ mm}$), drilled and grouted deep foundation elements consisting of a high-strength steel casing and/or center bar embedded in cement grout. Axial capacity is developed almost entirely through grout-to-ground bond along the bond length (structural steel casing/bar governs capacity at the cross-section, not soil bearing at the tip): $Q_s = \pi D_{drill} L_b \tau_{bond}$ where $\tau_{bond}$ (typical $\tau_{bond} \approx 200$–$700\text{ kPa}$, higher in rock than soil) is obtained from load testing or presumptive values by ground type per FHWA micropile guidance (FHWA-NHI-05-039). Installation uses small, low-headroom, low-vibration drilling equipment, making micropiles the preferred choice for underpinning existing structures, seismic retrofit, and restricted-access sites. Every micropile installation includes rigorous grouting QC (grout cube strength, volume/pressure verification) since bond capacity cannot be visually confirmed after grouting.

Helical Screw Piles

Helical piles are steel shafts with one or more helical bearing plates welded on, hydraulically torqued into the ground rather than driven or drilled — installation torque is the primary field QC parameter. Capacity is estimated by two independent methods that should be cross-checked: (1) individual bearing method, summing end-bearing on each helix plate area plus shaft friction, and (2) the empirical torque correlation method: $Q_u = K_t \cdot T$ where $T$ is the final installation torque and $K_t$ (empirical, typically $\approx 9$–$10\ \text{ft}^{-1}$ for round-shaft piles under $3.5\text{ in}$ diameter) is a manufacturer- and soil-specific correlation factor requiring site-specific verification for critical structures. Helical piles are common for light-to-moderate loads, tension/uplift applications (solar racking, boardwalks, tower guy anchors), and settlement-sensitive remedial underpinning where installation vibration must be minimized.

Auger-Cast/ACIP Piles

Auger-cast-in-place (ACIP) piles (also called continuous-flight-auger, CFA, piles) are constructed by advancing a continuous-flight hollow-stem auger to depth, then pumping cement grout or concrete through the auger stem under pressure while simultaneously withdrawing it, before placing reinforcement into the fluid concrete column. Capacity develops through combined side friction and end bearing, analogous to a conventional drilled shaft, but with important installation-driven QC distinctions: withdrawal rate and grout/concrete pumping pressure and volume must be continuously monitored and matched (over-withdrawal risks a soil "neck" or void in the shaft; excess pressure/volume can cause hydro-fracturing of the surrounding ground). ACIP piles are attractive where casing or slurry-supported drilled shaft construction is impractical (tight sites, low headroom, no spoil handling for open-hole excavation) but are generally limited to lower-capacity, non-permanent-casing applications compared to conventional drilled shafts.

Worked Example: Micropile Bond Length Capacity

A Type B (pressure-grouted) micropile has a drilled diameter of $D_{drill} = 178\text{ mm}$ ($7\text{ in}$) and a bond length of $L_b = 6.0\text{ m}$ in weathered rock with a presumptive ultimate grout-to-ground bond stress of $\tau_{bond} = 350\text{ kPa}$.

$Q_{s,ult} = \pi D_{drill} L_b \tau_{bond} = \pi (0.178\text{ m})(6.0\text{ m})(350\text{ kPa}) = 1{,}175\text{ kN}$

Applying a factor of safety of $2.0$ (typical for micropile geotechnical capacity per FHWA guidance, pending verification testing): $Q_{s,allow} = \frac{1{,}175}{2.0} \approx 587\text{ kN}\ (\approx 132\text{ kip})$

This allowable capacity would then be checked against the structural (steel casing/bar) capacity of the micropile cross-section, with the lower of the two governing the design load.