751.37 Drilled Shafts

751.37.1 General

751.37.1.1 Design Criteria

Drilled shafts can be an economical alternative to spread or pile footings. They can be constructed in a wide variety of soils. Drilled shafts should be considered:

• To accommodate sites where depth to bedrock is too short for pile embedment but too deep for spread footings.
• For high design loads. (Eliminates the need for large quantities of piles)
• To provide resistance against large lateral and uplift loads.
• To eliminate the need of cofferdams
• To provide protection against scour.
• To accommodate site concerns associated with driving process (vibrations or interference with battered piles)

Materials

Concrete used for drilled shaft construction shall be Class B-2, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c} = 4.0 ksi.

Casings

All drilled shafts shall have permanent casings (corrugated metal pipe or steel pipe) unless specific conditions exist and Construction and Materials Division approve the use of temporary casing or uncased. Permanent casing may also be required due to issues such as:

• Required flexural capacity of the drilled shaft
• Located in seismic area
• Unsupported length
• Installation through water
• Insufficient height available for casing recovery

Rock sockets are uncased.

Dimensions

Drilled shafts shall be sized in six inch increments. The minimum diameter shall be 18 in.

The length to diameter ratio of the drilled shaft should be in the following range: 3 ≤ L/D ≤ 30

Initial size and length of drilled shafts shall be estimated by the vertical loads applied to the foundation. The size may have to be adjusted if large lateral loads are present. For shafts rock socketed, length of sockets are usually kept at the minimum length required, to reduce cost.

When rock sockets are used, the diameter of the socket shall be 6 in. less than the inside diameter of casing when casing is used through the overburden soils. For shafts not requiring casing, the rock socket diameter may be the same size as the shaft diameter.

Where there is a column to drilled shaft connection, the drilled shaft diameter shall be a minimum of 6 in. larger than the diameter of column.

When the base is cleaned and inspected, the entire base can be considered effective in transferring load. However, at the present time, typical drilled shaft installation is not cleaning the base sufficiently to utilize end bearing. The Structural Project Manager or Liaison should be contacted prior to designing a drilled shaft with end bearing.

Limit States

The Strength limit states and applicable Extreme Event limit states shall be investigated when calculating the soil and structural capacity of the drilled shaft.

Service I Limit State shall be used when investigating allowable lateral deflection and settlement.

751.37.1.2 Analysis

To analyze laterally loaded drilled shafts, the point of fixity of the drilled shaft must be estimated. This location may be estimated by using a computer program. This is an iterative process that requires you to first assume a point of fixity so that the bent stiffness may be calculated.

The stiffness of the bent may be found by modeling the bent in a structural analysis program, applying a load to the middle of the beam cap and measuring the amount of deflection that load causes. The moment of inertia of the bent is then found by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I = \frac{\big(P/\delta\big)L^3}{3E}}

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I}	= moment of inertia of the bent
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, P}	= load applied to middle of beam cap
$\,\delta$	= deflection caused by load, P
$\,L$	= length from point of fixity of drilled shaft to middle of beam cap
$\,E$	= modulus of elasticity of concrete

When the moment of inertia of the bent is calculated, the longitudinal forces applied to the bent can be calculated. Once loads are obtained, they can be input into computer software to get a point of fixity.

If the point of fixity is different than what was assumed to obtain the original bent stiffness, then the bent stiffness will have to be calculated again with a new assumed point of fixity. This process shall be continued until the point of fixity location converges. Tip: Usually shafts socketed into rock are fixed at approximately the rock elevation.

The location of the point of fixity should be considered only an approximation. Many factors influence the actual location of the point of fixity. The thickness of the casing, scour and actual geotechnical properties could cause different results for the actual location of the point of fixity.

751.37.1.3 Design Considerations

Scour

The possibility of scour and its effect on the bearing and lateral capacity shall be investigated.

Ground Water

Effects of variable ground water levels and buoyancy shall be taken into account with the capacity.

Downdrag

Downdrag shall be considered when bearing resistance and settlement are investigated. For drilled shafts socketed into rock and overlayed with soil that has the potential to settle, downdrag shall be considered as an applied load. Downward movements of 0.1 to 0.5 in. are enough to mobilize full downdrag. The top 5 ft. and a bottom length equal to the shaft diameter shall not be included in calculating downdrag. Allowance shall be given for an increase in the undrained shear strength as consolidation of the soil occurs.

Uplift

Shafts in cohesive soils, not socketed into rock shall be investigated for the affects of uplift.

Movement

Settlements and lateral movements shall be designed at the Service I Limit State.

Design lateral movements should not exceed approximately 1.5 in. at the top of the shaft.

For shafts not socketed into rock, settlement shall be investigated. For cohesionless soils, all loads specified in the Service I Load combination shall be used. For cohesive soils, transient (live load) loads may be omitted. See Structural Project Manager or Liaison for allowable settlement.

Settlement for cohesive soils can be estimated with the same procedure for calculating settlement for shallow foundations.

Settlement for cohesionless soils can be estimated by the following equations.

For SPT:

$\,\rho =qI{\frac {\sqrt {B}}{NI_{60}}}$

For CPT:

$\,\rho ={\frac {qBI}{2q_{c}}}$

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, I}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 1 - 0.125 D' / B \ge 0.5}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N_{corr}}	= $\,{\Bigg [}0.77log_{10}{\Bigg (}{\frac {40}{\sigma _{v}^{'}}}{\Bigg )}{\Bigg ]}N\leq 2.0$
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \rho}	= settlement of pile group (in.)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q}	= applied load divided by equivalent area of footing
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, B}	= width or smallest dimension of pile group
$\,D'$	= effective depth = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 2D_b/3}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D_b}	= depth of embedment of piles in layer that provides support
$\,NI_{60}$	= SPT blow count corrected for both overburden and hammer efficiency effects (blows/ft.)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \sigma^'_v}	= effective vertical stress
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_c}	= average static cone resistance over a depth of X below the equivalent footing

Group Effects

Drilled shafts shall not have a center-to-center spacing closer than 2.5D. Shafts in cohesive and cohesionless soils, having center-to-center spacing in between 2.5D and 4D, shall be multiplied by an axial load reduction factor, $\,\eta$.

For shafts spaced at 2.5D:

$\,\eta$ = 0.65

For shafts spaced at 4.0D:

$\,\eta$ = 1.0

An intermediate spacing shall be linearly interpolated from the above h values.

For cohesive soils, the capacity shall be determined from the lesser of the group capacity of drilled shafts or from the capacity of an equivalent pier which includes the block of soil within the area bounded by the drilled shafts.

751.37.2 Geotechnical Resistance

Drilled shafts typically are founded on rock. Axial capacity is developed using side shear of a rock socket. End bearing capacity is neglected in shale and weak rock material. The Structural Project Manager or Materials Division shall be consulted before assuming another design approach to calculate the Geotechnical Resistance of a drilled shaft. Side resistance must be neglected or reduced according to the AASHTO specifications and/or Materials Divisions in locations where permanent casing exists.

751.37.2.1 Rock

Resistance in Rock

Side resistance from overlying soils may be neglected if drilled shafts are socketed into rock. Where permanent casing extends into the rock socket, the length of socket where casing protrudes shall be ignored when calculating the capacity in side resistance. If the Geotechnical Resistance is not provided in the Soils Report or provided by the Materials Division, the information may be calculated from the following:

Side Resistance

$\,q_{s}$	= $\,0.65\alpha _{E}p_{a}(q_{u}/p_{a})^{0.5}<7.8p_{a}(f'_{c}/p_{a})^{0.5}$, ksf
$\,Q_{r}$	= $\,\phi q_{s}(H_{s}\pi D_{s})$, kips

Where:

$\,q_{s}$	= side resistance, ksf
$\,q_{u}$	= uniaxial compressive strength of the rock, ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \alpha_E}	= determined from LRFD Table 10.8.3.5.4b-1
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, p_a}	= atmospheric pressure = 2.12 ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, f'_c}	= concrete strength of drilled shaft, ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, H_s}	= height of rock socket, ft
$\,D_{s}$	= diameter of rock socket, ft
$\,\phi$	= 0.55

Tip Resistance

If it is determined by the geotechnical report that tip resistance may be utilized for calculating capacity then:

$\,q_{p}=2.5q_{u}$, ksf for shales

Otherwise,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_p = \Big[ s^{0.5} + {(m \times s^{0.5} + s)}^{0.5} \Big] q_u} , ksf for limestone and dolomite

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q_r = \phi q_p(\pi D^2_s /4)} , kips

Where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi}	= 0.50
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_p}	= tip resistance, ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, m, s}	= fractured rock properties determined from LRFD Table 10.4.6.4-4

751.37.2.2 Cohesive Soils

If the drilled shaft resistance is determined by load test, then the $\,\phi$ factor applied shall be as follows regardless of the soil conditions: $\,\phi$ = 0.7

Resistance in Cohesive Soils

Ignore top five feet of shaft and bottom of shaft length equal to shaft diameter.

Shaft Resistance using $\,\alpha$-method

$\,q_{r}$	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi q_s} , ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q_r}	= $\,\phi q_{s}\pi D(L-5'-D)$, kips
Where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi}	= 0.45
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_s}	= $\,\alpha S_{u}$, ksf
$\,\alpha$	= adhesion factor
For $\,S_{u}/p_{a}\leq 1.5$
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \alpha}	= 0.55
Otherwise, for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 1.5 < S_u / p_a \le 2.5}
$\,\alpha$	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 0.55 - 0.1 (S_u / p_a - 1.5)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, S_u}	= undrained shear strength, ksf
$\,p_{a}$	= atmospheric pressure = 2.12 ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L}	= length of shaft in soil, ft
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D}	= diameter of shaft, ft
Tip Resistance
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_r}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi q_p} , ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q_r}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi q_p \pi d^2 / 4} , kips
Where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi}	= 0.40
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_p}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N_c S_u \le 80.0} ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N_c}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 6[1+0.2 \times(Z/D)] \le 9}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Z}	= penetration of shaft, ft

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, S_u} is determined from undisturbed samples obtained within a depth of 2 diameters below the tip of the shaft.

For Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, S_u < 0.50} ksf, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N_c} shall be multiplied by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 0.67} .

751.37.2.3 Cohesionless Soils

If the drilled shaft resistance is determined by load test, then the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi} factor applied shall be as follows regardless of the soil conditions: $\,\phi$ = 0.7

Resistance in Cohesionless Soils

Side Resistance

$\,Q_{r}$	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi q_s \pi DL} , kips
Where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi}	= 0.55
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, D}	= diameter of drilled shaft, ft
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, L}	= length of drilled shaft contributing to side resistance, ft
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_s}	= nominal side resistance of soil, ksf
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_s}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \beta \sigma'_v \le 4.0}   ksf for   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 0.25 \le \beta \le 1.2}
Where:
$\,\beta$	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 1.5 - 0.135 \sqrt{z}}   for   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N_{60} \ge 15}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \beta}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, (N_{60} / 15) \times (1.5 - 0.135 \sqrt{z})}   for   Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, N_{60} < 15}

If permanent casing is used, the side resistance shall be adjusted with consideration of type and length of casing used.

Tip Resistance

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, Q_r}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi q_p \pi D_2/4} , kips
Where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, \phi}	= 0.50
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_p}	= nominal tip resistance of soil
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, q_p}	= Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \, 0.6 N_{60} \le 60}   ksf for   $\,N_{60}\leq 50$
Tip Resistance Reduction
For drilled shaft diameters greater than approximately > 4 ft, qp should be reduced.
$\,q_{pr}$	= $\,4.17q_{p}/D_{p}$
Intermediate Geomaterial (IGM) SPT-N60 blow counts greater than 50
$\,q_{p}$	= $\,0.59\sigma '_{v}{(N_{60}(p_{a}/\sigma '_{v}))}^{0.8}$
$\,\phi$	= 0.65 for Side Resistance
$\,\phi$	= 0.55 for Tip Resistance

751.37.3 Structural Resistance

751.37.3.1 Reinforcement Design

Drilled shaft structural resistance shall be designed similarly to reinforced concrete columns. Strength Limit State load combinations shall be used in the reinforcement design.

Reinforcing steel shall extend 10 ft. below the point of fixity of the drilled shaft.

If permanent casing is used, and the shell consists of smooth pipe greater than 0.12 in. thick, it may be considered load carrying. An 1/8" shall be subtracted off of the shell thickness to account for corrosion. Casing could also be corrugated metal pipe.

If casing is assumed to contribute to the structural capacity, the plans should indicate the minimum thickness and of type of casing required.

Longitudinal Reinforcement

Longitudinal Reinforcement shall be designed to resist bending in the shaft due to lateral loads.

The limits for the longitudinal reinforcement are as follows:

$\,0.135A_{g}f'_{c}/f_{y}\leq A_{s}\leq 0.08A_{g}$

Where:

$\,A_{g}$	= gross cross-sectional area of drilled shaft
$\,f'_{c}$	= concrete compressive strength of drilled shaft
$\,f_{y}$	= yield strength of reinforcement
$\,A_{s}$	= area of reinforcement in drilled shaft

In most cases, the minimum amount of longitudinal reinforcement will be required.

A suggested range for spacing longitudinal reinforcement is 6" to 9" (center to center) to insure concrete flow around reinforcement cage.

Axial Capacity

The axial capacity of a drilled shaft shall be determined by the following equations:

$\,P_{r}$	= $\,\phi P_{n}$
Where:
$\,\phi$	= 0.75

Shafts w/ Spiral Reinforcement:

$\,P_{n}=0.85[0.85f'_{c}(A_{g}-A_{s})+A_{s}f_{y}]$

Shafts w/ Tie Reinforcement:

$\,P_{n}=0.80[0.85f'_{c}(A_{g}-A_{s})+A_{s}f_{y}]$

Shear Capacity

Shear reinforcement will need to be designed if:

$\,V_{u}>0.5\phi V_{c}$

Where:

$\,\phi$	= resistance factor for shear, 0.9
$\,V_{u}$	= factored shear force
$\,V_{c}$	= $\,0.0316\beta {\sqrt {f'_{c}b_{v}D_{v}}}$

|Where:

$\,\beta$	= 2.0
$\,b_{v}$	= $\,D$, diameter of shaft
$\,d_{v}$	= $0.9(D/2+D_{r}/\pi )$
$D_{r}$	= diameter of the circle passing through the centers of the longitudinal reinforcement. See commentary LRFD C5.8.2.9-2.

Minimum Reinforcement

The minimum amount of reinforcement must satisfy the following equation:

$\,A_{v}\geq 0.0316{\sqrt {f'_{c}}}{\frac {b_{v}s}{f_{y}}}$

Where:

$\,A_{v}$	= area of transverse reinforcement within distance, s
$\,s$	= spacing of transverse reinforcement
$\,f_{y}$	= yield strength of reinforcement

Maximum Spacing

The maximum spacing of transverse reinforcement shall meet the following criteria:

If $\,v_{u}<0.125f'_{c}:$

$\,s_{max}=0.8d_{v}\leq 24.0\ in.$

If $\,v_{u}\geq 0.125f'_{c}:$

$\,s_{max}=0.4d_{v}\leq 12.0\ in.$

Where:

$\,v_{u}$

= factored shear stress

Shear Resistance

When shear reinforcement design is required, the following equation applies:

$\,V_{r}=\phi (V_{c}+V_{s})$

Where:

$\,\phi$	= 0.9
$\,V_{s}$	= ${\frac {A_{v}f_{y}d_{v}cot\theta }{s}}$
$\,\theta$	= angle of inclination of diagonal compressive stresses = 45°