Wave Equation Analysis Program Research Articles

Case studies to demonstrate challenges of driven piles on rock

In Wyoming, pile foundations for bridges are often driven on rock materials because of the state’s shallow bedrock stratigraphy. Unfortunately, no static analysis methods are currently available for estimating the resistance of these driven piles. In this paper, two recently completed bridge projects (the Owl Creek and Woods Wardell sites) on steel H-piles in Wyoming are explicitly presented, and data from three past projects are included to highlight the limited knowledge and challenges pertaining to the present design and construction practices. Static analysis methods were used to estimate the geotechnical resistances of these piles. The wave equation analysis program and the case pile wave analysis program were used to verify their performances during construction. Structural capacities of these piles were also calculated. The results of the studies show that the static analysis methods and structural analyses yield inconsistent pile resistance estimations. Recommendations in terms of pile bracing and embedded pile length are proposed to predict better the resistances of piles on soft rock.

An application of wave equation analysis program to pile dynamic formulae

Wave equation analysis programs (WEAP) such as GRLWEAP and TNOWave were primarily developed for pre-driving analysis. They can also be used for post-driving measurement applications with some refinements. In the case of pre-driving analysis, the programs are used for the purpose of selecting the right equipment for a given ground condition and controlling stresses during pile driving processes. Recently, the program is increasingly used for the post-driving measurement application, where an assessment based on a variety of input parameters such as hammer, driving system and dynamic behaviour of soil is carried out. The process of this type of analysis is quite simple and it is performed by matching accurately known parameters, such as from CAPWAP analysis, to the parameters used in GRLWEAP analysis. The parameters that are refined in the typical analysis are pile stresses, hammer energy, capacity, damping and quakes. Matching of these known quantities by adjusting hammer, cushion and soil parameters in the wave equation program results in blow counts or sets and stresses for other hammer energies and capacities and cushion configuration. The result of this analysis is output on a Bearing Graph that establishes a relationship between ultimate capacity and net set per blow. A further application of this refinement method can be applied to the assessment of dynamic formulae, which are extensively used in pile capacity calculation during pile driving process. In this paper, WEAP analysis is carried out to establish the relationship between the ultimate capacities and sets using the various parameters and using this relationship to recalibrate the dynamic formula. The results of this analysis presented show that some of the shortcoming of the dynamic formula can be overcome and the results can be improved by the introduction of a correction factor.

A new approach for time effect analysis in the settlement of single pile in nonlinear viscoelastic soil deposits

A new and simple approach is presented to analyze the time effect in the settlement of single pile and the distributions of pile shaft resistance and pile axial force. First, the viscosity of soil is considered by using a linear damper, and the nonlinear elasticity of pile lateral soil and pile end soil are simulated by using a hyperbola model and idealized elastoplastic model, respectively. Then, the settlement of the pile head, shaft resistance, and axial force along the pile are derived by virtue of a wave equation analysis program based on traveling wave decomposition. Based on the solutions, a parametric study has been undertaken to investigate the influences of the parameters of a pile-soil system on the settlement behavior of a single pile. Finally, the calculated results are compared with the measured results to demonstrate the effectiveness and accuracy of the proposed approach. Note that the presented solution allows for a good prediction of the settlement behavior of a single pile and can provide a reference for the preliminary design of a pile foundation.

Integration of construction control and pile setup into load and resistance factor design of piles

Regionally developed Load and Resistance Factor Design (LRFD) recommendations for bridge pile designs are enhanced by integrating the construction control capability of dynamic analysis methods and the recently developed pile setup quantification method in the calibration process. Using a high quality, electronic Pile LOad Test (PILOT) database and 10 recently completed full-scale pile tests, resistance factors were developed using a reliability theory for a locally calibrated static analysis method and two dynamic analysis methods: the Wave Equation Analysis Program (WEAP) and the CAse Pile Wave Analysis Program (CAPWAP). Pile design efficiency was improved by minimizing the discrepancy between design and field pile resistances through a proposed probability-based construction control method. The efficiency of bridge foundations was further increased by incorporating the economic advantages of pile setup into the LRFD recommendations. Compared with recommendations made by Paikowsky et al. (2004), Canadian Engineering Society (2006) and American Association of State Highway and Transportation Officials (2003), regionally-calibrated resistance factors were improved.

Verification of Recommended Load and Resistance Factor Design and Construction of Piles in Cohesive Soils

To enhance regional design and construction practices for driven piles, FHWA permitted the development of regional resistance factors for the design of foundation piles. By fitting allowable stress design safety factors to the load and resistance factor design (LRFD) framework, several state departments of transportation (DOTs), including the Iowa DOT, have adopted interim procedures. Subsequently, an LRFD procedure that incorporates setup was developed for piles in cohesive soils through comprehensive research in Iowa. The proposed LRFD procedure used an Iowa DOT in-house static analysis method and the wave equation analysis program for construction control. To verify the adequacy of the proposed procedure and investigate its economic implications, differences in pile design between the interim and the proposed LRFD procedures were evaluated on the basis of independent data collected from more than 600 production steel H-piles driven in cohesive soils. This study concluded that the proposed LRFD procedure would not significantly increase the design and construction costs. The incorporation of pile setup into the LRFD procedure was found to provide additional economic benefits. Although the current Iowa DOT policy is to drive piles to the contract length, if a suitable pile termination procedure were used once the desired resistance was achieved, a general saving of 20% in pile length would be anticipated for both procedures. Although the research and findings presented in this paper are specific to a local area, these methods could be adopted nationally to increase the efficiency of bridge foundations for all states.

Measured Soil Setup of Steel HP Piles from Windsor Bypass Project in North Carolina

Restrikes were performed on piles driven for a North Carolina Department of Transportation highway construction project to verify the required bearing capacity, which was not achieved at the end of initial drive (EOID). Driving records of 98 piles with both initial driving and restrike blow counts and hammer stroke were collected. Six of these piles were driven with a pile-driving analyzer, and Case Pile Wave Analysis Program analysis was performed on the collected pile-driving analyzer data. All piles were steel H-pile piles, and the restrikes were done within 144 h after the EOID. The pile bearing capacities of both EOID and restrike were estimated from the blow counts and hammer stroke using the GRL Engineers Inc. Wave Equation Analysis Program, Version 2005. Soil setup ratios of these piles were computed and statistically analyzed to find a reliable setup ratio that can be applied to the bearing capacity obtained at the EOID of the remaining piles in this project to ensure the required bearing without a restrike. The mean soil setup ratio of all piles in this project was estimated at 1.41. However, no setup ratio can be applied to the EOID bearing capacity of an individual pile with a 98% confidence level. Restrike of every pile is required to ensure this level of confidence. A setup ratio of 1.10 can be applied with a 90% confidence level. The setup ratios vary greatly from pile to pile. Soil setup occurs rapidly after EOID in this project. Soil setup is more significant in loose or soft soils than in dense or stiff soils.

Wave equation analyses of tapered FRP–concrete piles in dense sand

Fiber-reinforced polymers (FRP)–concrete composites provide an attractive alternative to conventional pile materials such as steel, concrete and wood by improving the durability of deep foundations. In the current study, FRP tubes with different taper angles are filled with self-consolidating concrete (SCC) and driven into dense sand that is enclosed in a large pressurized soil chamber. Driving tests are conducted on FRP–SCC composite piles to determine how the pile material and geometric configuration affect its driving performance. Dynamic data is employed to determine the soil parameters in the TNO model (i.e., soil quake and damping constant) using the DLTWAVE signal-matching program. The driveability of FRP–SCC and traditional pile materials is compared using the wave equation analysis program PDPWAVE. The experimental data and the wave equation analyses indicate that the taper shape has a favourable effect on the driveability and static resistance of piles. It is also found that the driveability of FRP–SCC composite piles is similar to that of conventional prestressed concrete and steel piles. However, empty FRP tubes required a much higher driving energy. Their low flexural resistance along with risk of buckling can hinder their driveability in different soil conditions.

Value of Methods for Predicting Axial Pile Capacity

The purpose of this paper is to compare the value of predicting capacity using dynamic formulas, wave equation analysis, and dynamic monitoring without load tests. A database of pile load test results is used to quantify the precision associated with predictive methods. These methods are quantified and ranked using a “wasted capacity index” (WCI) to quantify the effect of precision. The WCI is a measure of how inefficiently a method predicts capacity. A precise method will be very efficient and accordingly have a low WCI. On the other hand, a less precise method requires a more conservative design and thus a greater WCI. The value of the wasted capacity index is calculated from the precision of the method and the reliability required for the pile foundation. The WCI is presented for the following methods: Engineering News (EN) formula, Gates formula, wave equation analysis program (WEAP), measured energy (ME) approach, pile driving analyzer (PDA), and CASE Pile Wave Analysis Program (CAPWAP).

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Regionally developed Load and Resistance Factor Design (LRFD) recommendations for bridge pile designs are enhanced by integrating the construction control capability of dynamic analysis methods and the recently developed pile setup quantification method in the calibration process. Using a high quality, electronic Pile LOad Test (PILOT) database and 10 recently completed full-scale pile tests, resistance factors were developed using a reliability theory for a locally calibrated static analysis method and two dynamic analysis methods: the Wave Equation Analysis Program (WEAP) and the CAse Pile Wave Analysis Program (CAPWAP). Pile design efficiency was improved by minimizing the discrepancy between design and field pile resistances through a proposed probability-based construction control method. The efficiency of bridge foundations was further increased by incorporating the economic advantages of pile setup into the LRFD recommendations. Compared with recommendations made by Paikowsky et al. (2004), Canadian Engineering Society (2006) and American Association of State Highway and Transportation Officials (2003), regionally-calibrated resistance factors were improved.

SPT Dynamic Analysis and Measurements

Measurements of force and acceleration on SPT systems are discussed and evaluated using solutions from both wave mechanics and a wave equation analysis program. The results show that acceleration and force can be accurately measured during SPT operations with currently available transducers, and that the force and particle velocity calculated by wave equation analysis agrees well with both measurements and wave mechanics solutions. A study of energy transmission in the SPT system is included. This study was conducted using wave mechanics and wave equation analysis. The results show that to accurately calculate energy transmission, measurements of both force and acceleration must be available. The method that has been specified in ASTM D4633-86 can produce large errors. The wave equation analysis also indicates that the standard penetration test (SPT) blow count is affected by drill rod area for low blow counts.