10.5 Dynamic Load Testing & Pile Integrity Evaluation

10.5 Dynamic Load Testing & Pile Integrity Evaluation

Geotechnical design of deep foundations relies heavily on field verification. While static load tests (ASTM D1143) provide the ultimate standard for capacity determination, they are expensive and time-consuming. Dynamic load testing, wave equation analysis, and non-destructive integrity testing provide rapid, cost-effective quality assurance for driven piles and drilled shafts.

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Wave Equation Analysis & WEAP Modeling

Historical empirical driving formulas (such as the Engineering News-Record [ENR] formula (Q_{all} = \frac{W_h h}{F (s + c)})) possess severe error margins (sometimes overestimating capacity by 300% or underestimating by 50%) because they model the pile as a rigid body undergoing simple energy conservation.

Modern analysis employs One-Dimensional Wave Equation Analysis (WEAP), based on Saint-Venant's dynamic wave equation for stress wave propagation in elastic rods:

[ \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial z^2} ]

Where:

• (u) = axial displacement at depth (z) and time (t)
• (c = \sqrt{\frac{E}{\rho}}) = stress wave propagation speed in the pile material (m/s or ft/s)
  • Steel wave speed: (c \approx 5,120\text{ m/s}) (16,800 ft/s)
  • Concrete wave speed: (c \approx 3,800 - 4,000\text{ m/s}) (12,500 - 13,000 ft/s)
  • Timber wave speed: (c \approx 3,600\text{ m/s}) (12,000 ft/s)

Smith Soil Model in WEAP

In WEAP software (e.g., GRLWEAP), the pile hammer, helmet, pile stem, and soil are modeled as a series of discrete masses, springs, and dashpots. The dynamic soil resistance (R_{dyn}) during hammer impact includes static soil resistance (R_{stat}) and viscous damping:

[ R_{total} = R_{stat} \left( 1 + J \cdot v \right) ]

Where (v) is instantaneous pile segment velocity, (J) is the Smith damping factor (s/m or s/ft), and static resistance activates up to an elastic limit called the quake ((q), typically 2.5 mm / 0.10 in for soil).

                    WEAP DISCRETE MASS-SPRING SOIL MODEL

     [ Hammer Mass ]
           │  Spring (Hammer Cushion)
     [ Helmet Mass ]
           │  Spring (Pile Cushion)
     [ Pile Segment 1 ] ─── Static Spring (Quake q) & Dashpot (Damping J)
           │
     [ Pile Segment 2 ] ─── Static Spring (Quake q) & Dashpot (Damping J)
           │
     [ Pile Segment n ] ─── Tip Spring (qb) & Tip Dashpot (Jb)

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High-Strain Dynamic Testing (PDA) & Case Method

High-strain dynamic testing is performed during pile driving using a Pile Driving Analyzer (PDA) in accordance with ASTM D4945.

Instrumentation Setup

Two paired strain transducers and two accelerometers are bolted on opposite sides of the pile stem at a distance of at least (2B) below the pile head (to avoid localized impact stress concentrations).

                   PDA FIELD TEST INSTRUMENTATION
           Impact Hammer
               │
               ▼
       ┌───────────────┐
       │   Pile Head   │
       │               │
 z=2B  ├─(S)───────(A)─┤  (S) Strain Transducer -> Force F(t) = A * E * eps(t)
       │               │  (A) Accelerometer      -> Velocity v(t) = Integral a(t)dt
       │   Pile Stem   │
       │               │  Pile Impedance Z = E * A / c

Primary Calculations & Case Method Equation

• Force Trace: (F(t) = E \cdot A \cdot \epsilon(t))
• Velocity Trace: (v(t) = \int a(t) dt)
• Pile Impedance ((Z)): The mechanical resistance of the pile section to dynamic change: [ Z = \frac{E \cdot A}{c} = \rho \cdot A \cdot c ]

Under ideal uniform conditions, prior to wave reflections from soil or pile tip (at time (t < 2L/c)), force and velocity traces overlay perfectly: (F(t) = Z \cdot v(t)).

Case Method Static Capacity Equation

The total dynamic resistance (R_{TL}) measured at wave impact time (t_1) and tip reflection return time (t_2 = t_1 + 2L/c) is:

[ R_{TL} = \frac{1}{2} \left[ F(t_1) + F(t_2) \right] + \frac{1}{2} Z \left[ v(t_1) - v(t_2) \right] ]

To extract static resistance (R_{static}), dynamic viscous damping force (R_{dyn} = j_c \cdot Z \cdot v_{toe}) is subtracted via the Case Method Equation:

[ R_{Case} = \frac{1 - j_c}{2} \left[ F(t_1) + Z v(t_1) \right] + \frac{1 + j_c}{2} \left[ F(t_2) - Z v(t_2) \right] ]

Where (j_c) is the dimensionless Case Damping Factor (ranging from 0.05-0.20 for sand to 0.40-1.00 for clay).

CAPWAP Signal Matching

To separate shaft resistance along each individual layer from tip bearing, field PDA data is processed using CAPWAP (Case Pile Wave Analysis Program). CAPWAP performs numerical iterations, adjusting modeled soil parameters along the pile shaft until the calculated force wave trace matches the measured field velocity wave trace with high precision.

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Time-Dependent Soil-Pile Phenomena: Setup & Relaxation

Pile static capacity measured immediately at End of Initial Driving (EOID) often differs significantly from capacity measured days or weeks later.

1. Soil Setup (Soil Freeze / Capacity Gain)

• Mechanism: Driving piles into fine-grained saturated cohesive soils (clays/silts) generates high positive excess pore water pressures ((\Delta u)), drastically reducing effective stress and shear strength during driving. As excess pore pressure dissipates over time, soil reconsolidates, and thixotropic bonds reform, causing static shaft capacity to increase substantially.
• Capacity Gain Ratio: Restrike capacity (Q_{BOR}) (Beginning of Restrike) can be 2 to 5 times higher than (Q_{EOID}).
• (Q(t) = Q_o + A \cdot \log_{10}\left(\frac{t}{t_o}\right))

2. Soil Relaxation (Capacity Loss)

• Mechanism: In dense fine sands, non-plastic silts, or weathered soft shales, rapid driving dilated soil matrix creates negative excess pore pressures or crushes grains. Over time, negative pore pressures dissipate to hydrostatic equilibrium or rock stress relaxes, causing static tip bearing or shaft capacity to decrease post-driving.
• Design Precaution: Restrike testing (BOR) must be performed 24 to 72 hours after initial driving in dense silts or weak rock to verify that relaxation has not compromised foundation safety.

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Low-Strain Non-Destructive Integrity Testing

Non-destructive integrity methods evaluate concrete quality, shaft continuity, defects (honeycombing, necking, soil inclusions), and unknown pile depths.

1. Low-Strain Impact Integrity Testing (PIT / Sonic Echo Method)

• Method (ASTM D5882): A small hand-held hammer taps the pile top, sending a low-strain compression wave down the shaft. An accelerometer records reflected waves.
• Defect Identification: Reflectivity changes occur at changes in impedance (Z = \frac{E A}{c}):
  • Necking / Void / Crack (Impedance Decrease): Reflects a compression wave with the same polarity as the input impact.
  • Bulge / Hard Rock Entry (Impedance Increase): Reflects a compression wave with opposite polarity.
• Depth to Defect ((x)): (x = \frac{c \cdot \Delta t}{2}), where (\Delta t) is reflection arrival time.

                 LOW-STRAIN PIT WAVE REFLECTION TRACES

   (A) UNIFORM PILE                          (B) PILE WITH NECKING DEFECT
   Impact                                    Impact    Necking Defect Reflection
     │                                         │       (Same Polarity)
     ▼   Tip Reflection                        ▼   │
   ──┼─────────────┼──                       ──┼───┼─────────┼──
     │            ╱                            │  ╱         ╱   Tip Reflection
     │           ╱                             │ ╱         ╱

2. Crosshole Sonic Logging (CSL) in Drilled Shafts

• Method (ASTM D6760): Steel or PVC access tubes (typically 38-50 mm diameter) are tied to the rebar cage prior to concreting (1 tube per 0.25 to 0.30 m of shaft diameter, minimum 3 tubes). Tubes are filled with clean water. An ultrasonic transmitter probe and receiver probe are pulled simultaneously up logging tube pairs.
• Measurements: First Arrival Time (FAT) of the ultrasonic wave and signal energy/amplitude.
• FHWA Evaluation & Defect Classification:

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PE-Style Worked Example: Case Method & CSL Integrity Analysis

Problem:

Part A (PDA Dynamic Capacity): A 450 mm square precast concrete pile ((A = 0.2025\text{ m}^2), (E = 35\text{ GPa} = 35 \times 10^6\text{ kPa}), concrete density (\rho = 2400\text{ kg/m}^3)) of length (L = 20.0\text{ m}) is tested using a PDA during restrike.

• Wave propagation speed (c = \sqrt{E/\rho} = \sqrt{\frac{35 \times 10^9}{2400}} = 3819\text{ m/s}).
• Impedance (Z = \frac{E A}{c} = \frac{(35 \times 10^6)(0.2025)}{3819} = 1858.5\text{ kN}/(\text{m/s})).
• Wave return time (2L/c = \frac{2(20.0)}{3819} = 0.01047\text{ s} = 10.47\text{ ms}).
• PDA sensor readings during restrike:
  • At peak force time (t_1 = 2.0\text{ ms}): (F(t_1) = 1900\text{ kN}), (v(t_1) = 2.1\text{ m/s}).
  • At return time (t_2 = t_1 + 2L/c = 12.47\text{ ms}): (F(t_2) = 450\text{ kN}), (v(t_2) = -0.4\text{ m/s}).
• Case Damping Factor (j_c = 0.35).

Calculate the static pile capacity (R_{Case}).

Part B (CSL Defect Evaluation): A 1.2 m diameter drilled shaft has 4 CSL tubes spaced (1.0\text{ m}) apart. In sound concrete, the ultrasonic First Arrival Time (FAT_{sound} = 0.250\text{ ms}) (wave velocity (v_c = 1.0\text{ m} / 0.000250\text{ s} = 4000\text{ m/s})). At depth (z = 8.5\text{ m}), between Tubes 1 and 3, (FAT) increases to (0.330\text{ ms}).

Calculate the wave velocity drop percentage and determine the FHWA defect classification.

Solution Step-by-Step:

Part A Solution:

1. Apply Case Method Static Capacity Equation: [ R_{Case} = \frac{1 - j_c}{2} \left[ F(t_1) + Z v(t_1) \right] + \frac{1 + j_c}{2} \left[ F(t_2) - Z v(t_2) \right] ]
2. Evaluate Term 1 at (t_1): [ F(t_1) + Z v(t_1) = 1900 + (1858.5 \cdot 2.1) = 1900 + 3902.85 = 5802.85\text{ kN} ] [ \frac{1 - 0.35}{2} (5802.85) = 0.325 \cdot 5802.85 = 1885.93\text{ kN} ]
3. Evaluate Term 2 at (t_2): [ F(t_2) - Z v(t_2) = 450 - (1858.5 \cdot -0.4) = 450 + 743.4 = 1193.4\text{ kN} ] [ \frac{1 + 0.35}{2} (1193.4) = 0.675 \cdot 1193.4 = 805.55\text{ kN} ]
4. Sum static capacity: [ R_{Case} = 1885.93 + 805.55 = 2691.48\text{ kN} \approx 2691\text{ kN} ]

Part B Solution:

1. Measured wave velocity at depth 8.5 m: [ v_{measured} = \frac{1.0\text{ m}}{0.000330\text{ s}} = 3030.3\text{ m/s} ]
2. Velocity Drop Percentage: [ \text{Velocity Drop} = \frac{v_{sound} - v_{measured}}{v_{sound}} \times 100% = \frac{4000 - 3030.3}{4000} \times 100% = \frac{969.7}{4000} \times 100% = 24.24% ]
3. FAT Increase Percentage: [ \text{FAT Increase} = \frac{0.330 - 0.250}{0.250} \times 100% = \frac{0.080}{0.250} \times 100% = 32.0% ]
4. Classification: Since the wave velocity drop is 24.2% (> 20%) and FAT increase is 32.0% (> 20%), FHWA criteria classifies this zone as a Severe Defect (P/D), indicating poor concrete, honeycomb, or soil inclusion requiring core drilling or remedial grouting.

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Static Load Test Interpretation: Davisson's Offset Method

Static axial load tests provide the most direct measurement of deep foundation capacity, but the resulting load-settlement curve rarely shows an abrupt "plunging" failure — an objective, repeatable failure-load definition is needed, which is the role of graphical interpretation methods.

Davisson's Offset Method

Davisson's method (the most widely specified criterion in U.S. practice, including many state DOT and FHWA specifications) defines failure load as the load at which the measured gross pile-head settlement exceeds the theoretical elastic compression line of the pile acting as a free-standing column, offset by a fixed movement to account for a small, acceptable amount of plastic tip movement at working load:

$s_{offset} = \frac{PL}{AE} + \left(0.15\text{ in} + \frac{D}{120}\right)$

(in SI: offset $= 4\text{ mm} + D/120$), where $P$ is the applied test load, $L$/$A$/$E$ are the pile's embedded length, cross-sectional area, and elastic modulus, and $D$ is the pile diameter (in the same units as the $0.15$-in term). The Davisson failure load is the load at which the measured load-settlement curve intersects this offset line. Because the criterion is purely geometric and requires no engineering judgment about curve shape, it is favored for specifications and code compliance.

Other Common Interpretation Methods (Brief)

• Chin's method extrapolates the full load-settlement curve using a hyperbolic fit (settlement/load vs. settlement plotted as a straight line), estimating an asymptotic ultimate load even from a test that was not carried to failure — useful for high-capacity shafts where testing to plunging failure is impractical.
• 80% Criterion (Brinch Hansen) defines failure at the load where the settlement is 4 times the settlement at $80%$ of that load, also via extrapolation of an incomplete curve.
• Butler-Hoy method uses the intersection of two tangent lines (initial near-elastic slope and a specified secondary slope, typically $0.05\text{ in per ton}$) and is frequently applied to large-diameter drilled shafts where Davisson's fixed offset (calibrated originally for smaller driven piles) is considered overly conservative.

Worked Example: Davisson Failure Load

A steel pipe pile ($16\text{ in}$ OD, $0.5\text{ in}$ wall, $A = 24.35\text{ in}^2$, $E = 29{,}000\text{ ksi}$) is driven to an embedded length $L = 80\text{ ft} = 960\text{ in}$ and static load tested. Measured gross head settlements are:

Step 1 — Compute the elastic-compression term at, e.g., $P = 480\text{ kip}$: $\frac{PL}{AE} = \frac{480 \times 960}{24.35 \times 29{,}000} = \frac{460{,}800}{706{,}150} = 0.653\text{ in}$

Step 2 — Add the Davisson offset ($D = 16\text{ in}$): $s_{offset} = 0.653 + \left(0.15 + \frac{16}{120}\right) = 0.653 + 0.283 = 0.936 \approx 0.94\text{ in}$

Repeating this calculation at each load builds the offset-line column above.

Step 3 — Locate the intersection: comparing the measured settlement column against the offset-line column, the two curves cross at $P \approx 480\text{ kip}$ (measured $= 0.94\text{ in}$, offset line $= 0.94\text{ in}$) — for loads below $480\text{ kip}$ the pile settles less than the offset line predicts, and above $480\text{ kip}$ the measured curve rapidly diverges above it (settlement nearly doubling between $500$ and $600$ kip). The Davisson failure load is $480\text{ kip}$ ($2{,}135\text{ kN}$), and an allowable geotechnical capacity would typically be taken as this value divided by the project's specified factor of safety (e.g., $FS = 2.0 \Rightarrow Q_{allow} = 240\text{ kip}$).

Static vs. Dynamic (PDA/CAPWAP) Comparison

High-strain dynamic testing (PDA with CAPWAP signal-matching analysis) estimates capacity indirectly from stress-wave measurements during a hammer blow and is far faster/cheaper per pile than a static load test, making it practical for testing a large fraction of a pile population. However, PDA/CAPWAP results are a model-fit estimate, sensitive to soil damping/quake parameter assumptions and set-up/relaxation effects, and are conventionally calibrated against a static test (or Davisson-interpreted result) on a representative pile at the same site before being relied upon as the primary acceptance criterion for the remaining production piles.