What Is WEAP Analysis? A Complete Guide to Wave Equation Analysis of Piles

WEAP (Wave Equation Analysis Program) is a computer simulation that predicts pile driving performance by modeling stress wave propagation through the pile-hammer-soil system. This analysis helps contractors select the correct hammer, estimate blow counts, predict driving stresses, and verify that piles will achieve design capacity without damage—all before mobilizing equipment to the jobsite.^[1]

Wave equation analysis of piles has become a standard engineering tool in foundation construction, particularly for projects where pile integrity, cost control, and schedule certainty are critical. The Federal Highway Administration (FHWA) recommends WEAP for driven pile design, and many state DOTs require it for bridge foundations.^[2] At PVE Equipment USA, we provide WEAP analysis as a pre-project service to help contractors optimize hammer selection and avoid costly field surprises.

How Does WEAP Analysis Work?

WEAP uses one-dimensional wave propagation theory to simulate the impact or vibration of a pile hammer, tracking stress waves as they travel through the pile and into the soil. The software divides the pile into discrete segments and calculates forces, velocities, and stresses at each segment during driving. Soil resistance is modeled using spring and damper elements that represent static and dynamic skin friction along the shaft, plus end bearing at the toe.^[3]

The analysis runs hundreds or thousands of simulated hammer blows, varying parameters like hammer energy, cushion stiffness, and soil resistance. Results show predicted blow counts (blows per foot), maximum compressive and tensile stresses in the pile, and the relationship between driving resistance and ultimate pile capacity. Engineers compare these predictions against allowable stress limits and capacity requirements to verify drivability before construction begins.^[4]

What Does WEAP Predict for Pile Driving Projects?

WEAP analysis predicts four critical performance metrics: required hammer energy or frequency, driving stresses, blow count at final depth, and ultimate pile capacity based on dynamic resistance. These outputs guide equipment selection, construction sequencing, and acceptance criteria for driven pile foundations.

Hammer Size and Energy Requirements

The analysis identifies the minimum hammer size needed to drive the pile to design depth and achieve target capacity. For impact hammers, WEAP calculates required rated energy (foot-pounds or joules) and stroke. For vibratory hammers like PVE’s Variable Moment systems, the software models eccentric moment and operating frequency to predict penetration rates. Undersized hammers lead to refusal before reaching bearing strata; oversized hammers cause pile damage and waste fuel.^[5]

Driving Stresses and Pile Integrity

WEAP calculates maximum compressive and tensile stresses during driving, comparing them to allowable limits based on pile material. For concrete piles, tensile stress is the limiting factor—excessive tension causes cracking. For steel piles, compressive stress and local buckling govern. The analysis helps engineers specify hammer cushions, pile cushions, and driving systems that keep stresses within safe limits throughout installation.^[6]

Blow Count Predictions

Blow count—the number of hammer impacts required to advance the pile one foot—is a primary field acceptance criterion. WEAP predicts blow count at various depths based on soil resistance profiles from geotechnical borings. Contractors use these predictions to estimate production rates, schedule equipment, and set acceptance criteria. Significant deviations between predicted and observed blow counts in the field may indicate changed soil conditions or pile damage requiring investigation.^[7]

Ultimate Pile Capacity Correlation

While static load tests provide the most reliable capacity measurements, WEAP correlates dynamic driving resistance to ultimate capacity using damping coefficients and soil models. This relationship—often expressed as a bearing graph—allows field engineers to confirm that driven piles meet design loads. Many specifications require that observed driving resistance fall within a predicted range at final depth.^[8]

When Is WEAP Analysis Required?

WEAP analysis is required by most state transportation departments for bridge foundations, recommended by FHWA for all driven pile projects, and increasingly specified for commercial and industrial deep foundations where performance and cost control are priorities. The analysis is particularly valuable when driving conditions are challenging or pile performance is critical to structural safety.

State DOTs across the U.S. mandate wave equation analysis for bridge piles, with specifications varying by jurisdiction. AASHTO LRFD Bridge Design Specifications reference WEAP as a standard tool for driven pile design.^[9] Beyond regulatory requirements, contractors use WEAP voluntarily to reduce risk on projects involving hard driving, high-capacity piles, or tight construction schedules where equipment downtime is costly.

Projects that benefit most from WEAP include: deep foundations in mixed soil profiles with dense layers or bedrock, high-capacity piles where driving stresses approach material limits, projects using new or unfamiliar hammer types, installations where pile damage would compromise structural performance, and contracts with strict acceptance criteria or liquidated damages for delays. PVE provides WEAP analysis services for contractors planning these types of installations.

What Inputs Are Needed for Wave Equation Analysis?

Accurate WEAP analysis requires detailed information about the pile, hammer system, and soil conditions—including pile dimensions and material properties, complete hammer specifications, driving system components, and geotechnical boring logs with soil resistance parameters. Missing or inaccurate inputs lead to unreliable predictions.

Input Category	Required Data	Source
Pile Properties	Type, length, cross-section, material grade, weight per foot, elastic modulus	Structural drawings, manufacturer specs
Hammer Specifications	Type (impact/vibratory), rated energy or eccentric moment, ram weight, stroke, frequency	Manufacturer data, equipment rental specs
Driving System	Cushion materials and thickness, helmet weight, lead dimensions	Field setup plans, contractor standards
Soil Conditions	Boring logs, SPT N-values, soil layers, unit weights, strength parameters, setup factors	Geotechnical report

Soil resistance parameters are the most uncertain inputs. WEAP uses empirical correlations between static soil properties (SPT blow count, CPT tip resistance, shear strength) and dynamic resistance during driving. Geotechnical engineers select damping coefficients and quake values based on soil type—cohesive or cohesionless—and project-specific data. When available, dynamic load test results from similar projects improve prediction accuracy.^[10]

For vibratory hammer analysis, additional inputs include operating frequency ranges, eccentric moment settings, and power unit specifications. PVE’s Variable Moment technology allows continuous adjustment of eccentric moment during driving, which can be modeled in advanced WEAP variants to optimize penetration in layered soils.^[11]

How Are WEAP Results Used in the Field?

WEAP results guide pre-construction planning and provide real-time acceptance criteria during pile installation—contractors use bearing graphs to confirm capacity, compare observed blow counts to predictions, and adjust driving procedures if field conditions differ from design assumptions. The analysis output becomes part of the project quality control documentation.

Before mobilization, contractors review WEAP output to confirm that specified hammers will drive piles to design depth without exceeding stress limits. If analysis shows refusal risk or overstress, engineers may revise pile lengths, specify different hammer models, or adjust cushion systems. This pre-planning avoids costly jobsite delays when equipment proves inadequate.^[12]

During installation, field engineers plot real-time blow count versus depth and compare it to WEAP predictions. Close agreement confirms that soil conditions match boring logs and the pile is performing as designed. Significant deviations trigger investigation—sudden increases in blow count may indicate obstructions or denser-than-expected strata, while lower-than-predicted resistance suggests softer soils or pile damage. Some projects require dynamic load testing (PDA) on indicator piles to validate WEAP assumptions before production driving begins.^[13]

Need help interpreting WEAP results or selecting the right hammer for challenging soil conditions? Contact PVE Equipment USA at 888-571-9131 or visit https://pveusa.com/contact-us/ to discuss your project requirements.

What Software Tools Perform Wave Equation Analysis?

The most widely used WEAP software in the U.S. is GRLWEAP, developed by Pile Dynamics Inc. and endorsed by FHWA, though other programs include TNOWAVE and proprietary tools from equipment manufacturers. Most state DOTs reference GRLWEAP specifically in their driven pile specifications.

GRLWEAP (Ground Response to Lateral Wave Equation Analysis of Piles) has been the industry standard since the 1980s, with regular updates to include new hammer models, pile types, and soil resistance algorithms. The software includes databases of commercially available impact and vibratory hammers, allowing engineers to compare performance of different equipment on the same pile-soil system. Version 2010 and later support Windows environments and produce graphical bearing graphs that simplify field interpretation.^[14]

European projects may use TNOWAVE, developed by TNO in the Netherlands (the same country where PVE’s parent company, Dieseko Group B.V., was founded in 1974). Some pile driving equipment manufacturers offer proprietary analysis tools optimized for their specific hammer lines, though these are less commonly accepted by agencies than GRLWEAP.^[15]

How Does PVE Equipment USA Support WEAP Analysis?

PVE Equipment USA provides complimentary WEAP analysis for contractors renting or purchasing equipment, leveraging 50+ years of foundation engineering expertise from our parent company Dieseko Group to optimize hammer selection and installation procedures. Our engineers work directly with project teams to interpret results and troubleshoot field challenges.

When you contact PVE for equipment rental or field services, our technical team reviews your project drawings, geotechnical reports, and pile specifications to perform site-specific WEAP analysis. We model your exact soil profile and pile configuration with our full range of Variable Moment vibratory hammers, standard frequency units, and hydraulic impact hammers to identify the optimal equipment package. This analysis is included as part of our project support—no separate engineering fee.^[16]

Our three U.S. divisions in Jacksonville FL, Houston TX, and Norfolk VA maintain in-house WEAP capability to provide rapid turnaround on analysis requests. We also offer on-site support during critical installations, with field engineers who can compare real-time driving data to WEAP predictions and recommend adjustments if conditions change. For projects where dynamic load testing is specified, we coordinate with testing firms to validate analysis assumptions and refine soil parameters based on measured pile response.

What Are the Limitations of WEAP Analysis?

WEAP is a predictive tool with inherent uncertainties—accuracy depends on soil parameter assumptions, the one-dimensional wave equation simplifies complex three-dimensional behavior, and results cannot replace load testing for final capacity verification. Engineers must understand these limitations when specifying acceptance criteria and interpreting field data.

The largest source of uncertainty in WEAP is soil resistance modeling. Empirical correlations between SPT values or CPT data and dynamic driving resistance include significant scatter, especially in mixed soil profiles or when soil setup (strength gain after driving) is significant. Conservative practice includes sensitivity analyses with upper and lower bound soil parameters to bracket expected field performance.^[17]

One-dimensional wave theory assumes axial symmetry and neglects bending, torsion, and three-dimensional stress states that occur in real piles, particularly during vibratory driving or when piles encounter obstructions. For highly irregular pile cross-sections or complex driving systems, finite element analysis may provide more accurate stress predictions, though WEAP remains the standard for routine design due to its computational efficiency and regulatory acceptance.^[18]

WEAP predicts capacity based on dynamic resistance during installation, but ultimate static capacity depends on soil consolidation, pore pressure dissipation, and time-dependent setup effects that the analysis cannot fully capture. For this reason, building codes and AASHTO specifications require static load tests or dynamic testing with signal matching (CAPWAP analysis) on a percentage of production piles to verify design assumptions.^[19]

Ready to discuss your project requirements? Contact PVE Equipment USA at 888-571-9131 or request a quote online.

Frequently Asked Questions

What does WEAP stand for in pile driving?

WEAP stands for Wave Equation Analysis Program. It refers to computer software that simulates pile driving by modeling stress wave propagation through the pile-hammer-soil system to predict driving stresses, blow counts, and pile capacity.

Is WEAP analysis required for all driven pile projects?

WEAP is mandatory for most state DOT bridge projects and recommended by FHWA for all driven piles. Commercial projects may not legally require it, but contractors increasingly use WEAP voluntarily to reduce risk, optimize equipment selection, and avoid costly field problems.

How much does WEAP analysis cost?

Commercial engineering firms typically charge $1,500-$5,000 per analysis depending on project complexity. PVE Equipment USA provides complimentary WEAP analysis when you rent or purchase equipment from our fleet, as part of our technical support services.

Can WEAP be used for vibratory pile driving?

Yes, modern WEAP software includes models for vibratory hammers that simulate continuous sinusoidal excitation rather than impact blows. The analysis predicts penetration rate, required eccentric moment, and operating frequency for vibratory installation in various soil types.

What is the difference between WEAP and dynamic load testing?

WEAP is a pre-construction predictive analysis based on assumed soil parameters. Dynamic load testing (PDA/CAPWAP) measures actual pile response during driving using strain gauges and accelerometers, providing real-time capacity verification and more accurate soil resistance data.

How accurate are WEAP predictions?

WEAP typically predicts blow counts within 25-50% of observed field values when soil parameters are well-characterized. Accuracy improves when geotechnical data includes dynamic testing from similar nearby projects. Predictions are less reliable in highly variable soils or when soil setup is significant.

Do I need a geotechnical engineer to perform WEAP analysis?

WEAP analysis requires engineering judgment to select appropriate soil models and interpret results, so it should be performed by a licensed professional engineer with foundation design experience. At PVE, our in-house engineers handle this analysis as part of equipment rental and project support services.

Can WEAP help avoid pile damage during driving?

Yes—one of WEAP’s primary functions is predicting driving stresses and comparing them to allowable limits. The analysis identifies combinations of hammer energy, cushion stiffness, and driving resistance that could cause pile cracking or buckling, allowing engineers to modify the driving system before installation begins.

Optimizing pile driving performance starts with accurate analysis and the right equipment. PVE Equipment USA combines wave equation expertise with the industry’s most advanced vibratory hammer technology to help you drive piles safely, efficiently, and on schedule. Contact PVE Equipment USA at 888-571-9131 or visit https://pveusa.com/contact-us/ to discuss your project requirements.

Contact PVE Equipment USA at 888-571-9131 or visit our contact page to discuss your project requirements.

Written by The Team at PVE USA — North American subsidiary of Dieseko Group B.V. | 50+ years of foundation equipment engineering | Largest vibratory hammer rental fleet worldwide | U.S. divisions in Jacksonville FL, Houston TX, Norfolk VA. Updated January 2026.

References

1. Pile Dynamics, Inc. (2010). GRLWEAP Wave Equation Analysis Software Manual. Cleveland, OH.
2. Federal Highway Administration. (2006). Design and Construction of Driven Pile Foundations (Publication No. FHWA-NHI-05-042). U.S. Department of Transportation.
3. Smith, E.A.L. (1960). “Pile Driving Analysis by the Wave Equation.” Journal of the Soil Mechanics and Foundations Division, ASCE, 86(4), 35-61.
4. Rausche, F., Goble, G.G., & Likins, G.E. (1985). “Dynamic Determination of Pile Capacity.” Journal of Geotechnical Engineering, ASCE, 111(3), 367-383.
5. Hannigan, P.J., et al. (2016). Design and Construction of Driven Pile Foundations (Publication No. FHWA-NHI-16-009). Federal Highway Administration.
6. American Concrete Institute. (2014). Building Code Requirements for Structural Concrete (ACI 318-14). Farmington Hills, MI.
7. American Association of State Highway and Transportation Officials. (2020). AASHTO LRFD Bridge Design Specifications (9th ed.). Washington, DC.
8. Davisson, M.T. (1972). “High Capacity Piles.” Proceedings, Soil Mechanics Lecture Series on Innovations in Foundation Construction, ASCE Illinois Section, 81-112.
9. AASHTO. (2020). LRFD Bridge Design Specifications, Section 10: Foundations (9th ed.). Washington, DC.
10. Paikowsky, S.G., et al. (2004). Load and Resistance Factor Design (LRFD) for Deep Foundations (NCHRP Report 507). Transportation Research Board.
11. Viking, K. (2002). Vibro-Driveability: A Field Study of Vibratory Driven Sheet Piles in Non-Cohesive Soils. Royal Institute of Technology, Stockholm.
12. Fellenius, B.H. (2020). Basics of Foundation Design (Electronic Edition). www.Fellenius.net.
13. Likins, G., Rausche, F., & Goble, G. (2000). “High Strain Dynamic Testing and Analysis of Drilled Shafts.” New Technological and Design Developments in Deep Foundations, ASCE, 227-240.
14. Pile Dynamics, Inc. (2020). GRLWEAP Background Report. Cleveland, OH.
15. TNO. (1996). TNOWAVE: Wave Propagation Analysis for Pile Driving. Delft, Netherlands.
16. Dieseko Group B.V. (2024). Technical Services and Engineering Support. Company technical documentation.
17. Paikowsky, S.G. (2002). “Load and Resistance Factor Design for Deep Foundations: Analysis and Recommendations.” Deep Foundations 2002, ASCE, 1242-1256.
18. Hussein, M., & Rausche, F. (2005). “Pile Driveability: Analysis and Assessment.” Contemporary Issues in Deep Foundations, ASCE, 1-13.
19. International Building Code. (2021). IBC 2021: Section 1810 Deep Foundations. International Code Council.