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By Gustavo Armijo

Slippery and unstable working platforms spoiled not only by natural weather conditions but also by the effects of the construction process (drilling mud, grout slurry) are among the main sources of hazards. Due to this fact a set of recommendations for execution and maintenance of working platforms are presented in this paper, which is based on a study on this subject that is being carried out by AETESS, the Spanish Federation of Geotechnical Contractors. The main objective of this paper is to establish the basis for the right execution and maintenance of working platforms for geotechnical jobs with the idea of increasing safety and productivity. All the aspects involved in working platform safety are analyzed: ground and equipment characteristics, geometric conditions and working platform maintenance. From this analysis a set of general requirements is proposed together with the necessary specific controls before and after the equipment arrival to the job site. In order to facilitate this analysis some flow charts and tables and specific appendixes for each geotechnical technique are included.

Jan 1, 2006

By Trevor L. L. Orr

"AbstractThe background to the harmonization of geotechnical standards that has taken place in recent years in Europe has been the move to more economic and political integration following World War II that has led to the formation of the European Union. Prior to 2010 the standards used in the European countries for geotechnical design, investigation and testing and for the carrying out geotechnical work, such as the installation of piles, were the different national standards, which were not harmonized. The harmonization of geotechnical standards in Europe started in 1981 with work on a model Eurocode 7 for geotechnical design that led eventually to publication by CEN, the European Committee for Standardization, of the European Standard version of Eurocode 7 in 2004. In parallel with the work on Eurocode 7, a large number of associated harmonized standards have been, and are being, prepared by CEN and by the International Standards Organization (ISO) for geotechnical investigation and testing and for the execution of geotechnical works. Standards published by CEN must be adopted by the CEN member countries and all conflicting standards withdrawn. Hence all the CEN countries have adopted the same the harmonized text of Eurocode 7, but with National Annexes that allow national choice with regard to Design Approach and partial factor values. The adoption of Eurocode 7 and its associated geotechnical standards has removed the barriers to geotechnical activity in Europe due to the presence of different national standards. It has also enhanced the ability of EU firms to compete in the global market.Background to harmonization of geotechnical standards in EuropeThe initial moves towards the harmonization of geotechnical standards in Europe can be related to the economic and political developments that took place in the period immediately following World War II to revive the economies of Western Europe. Europe at that time was divided by a political and, in many places, a physical barrier, known as the Iron Curtain, into two very different and separate zones: communist in the east and non-communist in the west. In 1952 the European Coal and Steel Community (ECSC) was formed, linking 6 countries: Belgium, West Germany, France, Italy, Luxembourg and the Netherlands, and establishing a common market in coal and steel. The ECSC was the first international organization to be established on the basis of supranational principles whereby negotiated power is delegated to an authority by the governments of the member states. In 1957 the ECSC became the European Economic Community (EEC), also known as the Common Market in the English-speaking world, with the aim to bring about economic integration. With the addition of Denmark, Ireland and the UK in 1973 and Greece in 1981, followed by Portugal and Spain in 1986, this led to the formation of the European Union (EU) in 1993. East and West Germany were reunified in 1990, following the fall of the Iron Curtain in 1989. In 1995, Austria, Finland and Sweden joined the EU, and since then the numbers of countries in the EU has increased to 28, many of which are countries that were formerly behind the Iron Curtain."

Jan 1, 2014

By Tianfei Liao

Extensive site investigations revealed that abandoned shallow mine workings exist under a site planned for construction of a major new facility. Since the mine voids were susceptible to collapse, they were stabilized by grouting. After completion of the mine remediation, three types of deep foundations (micro-piles, auger-cast piles, and drilled piers) were considered for this site. Micro-piles spread the load via the bond between the pile and the bedrock. Without significant length socketed in rock, the axial load of auger-cast piles and drilled piers has to be concentrated on end bearing. Although spreading the load is preferable in this environment, economic consideration dictated the choice of drilled piers for construction.

Jan 1, 2009

By Chu E. Ho

Jet grout column formation at large depths are prone to several uncertainties, such as inaccuracy in setting out boreholes, drilling deviation, soil variability and reduced jetting energy at the nozzle. This would result in shorter cutting distance of the jet, with potential lack of interlock between grouted columns. A design strategy for mitigating the risk should include a soil investigation program aimed at discovering potential variability in soil conditions at the locations of jetting. Determination of soil strength profiles with depth would be useful for evaluation of jetting parameters and prediction of the achievable cutting distance at any depth. Selection of design column spacing should include allowance for setting out accuracy, verticality of the boreholes and the achievable jet cutting distance. For deep jet grouting operations, it would be necessary to take into account the energy losses at the nozzle inlet; however the increase in the presiding pressure at the nozzle outlet at depth is small relative to the range of jetting pressures commonly employed and would not affect the cutting distance to any significant degree. Design column spacing should not be so close as to cause problems with ?masking? which may lead to localized ungrouted zones of soil. For effective field control, boreholes should be cased up to the top elevation of the grouted zone so that the orientation of the borehole can be measured prior to grout injection. An analytical equation for calculating the cutting distance is proposed for adjusting jetting parameters where necessary to compensate for drilling deviation and changes in soil conditions. It is preferable that jet grouting trials be executed at elevations that correspond to the actual production jet grouting depths for accurate evaluation of jet cutting performance.

Jan 1, 2008

By J. Wennerstrand

Slender steel piles have found an increased use in Sweden in resent years. These piles are often driven throw soft normally consolidated clay to refusal in till or at the rock surface. In contrast to most other piles the bearing capacity with regard to failure of the shaft is in many cases smaller than the bearing capacity with regard to failure of the soil or rock at the lower end of the pile. Imperfections such as deviations from a straight line of the pile centerline and residual stresses in rolled and welded profiles are important for the capacity of the pile shaft. Even thow the second order moment caused by initial deviations in piles is only half of that in a column with the same slenderness, imperfections can and should be accounted for in much the same way as for columns.

Jan 1, 1989

By Nabil F. Ismael, Khalid Farraj

"The axial load transfer along large diameter bored piles in very dense silty sand was examined by field tests. Two instrumented piles 1.2 m diameter and with embedded length of 18 m and 25 m were load tested in axial compression to failure in connection with the construction of a big tower building in Kuwait City, Kuwait. Instrumentation included vibrating wire strain gages at various levels, displacement transducers and extensometers. The purpose being to measure the axial load distribution, skin friction, and base resistance at various load levels. In addition the settlement of the piles and the elastic compression were monitored. The ultimate pile capacity, side friction, and base resistance were determined and correlated with the Standard Penetration Resistance values as determined from the boreholes. Most of the load was transferred as side friction and the pile settlements at the maximum loads ranged from 1.6% to 2.2% of the pile diameter.INTRODUCTIONLarge diameter bored piles are used with increasing frequency for heavy structures in Kuwait and the Gulf region in calcareous sand. The behavior of short piles ranging in depth from 8 m to 15 m was examined by field test (Ismael 2012). However, larger diameter and deeper piles are being used more frequently, including the project described in this paper which included piles with 1.2 m diameter and 18 m to 25 m depth. The design of these piles requires knowledge of the skin friction and point resistance in these soils. While field tests on driven piles are available (Ismael 1989, Ismael 1999), field test data on long large diameter piles installed through very dense sands or silty sands are very limited at present. The results of two load tests carried out recently on instrumented bored piles at one site in downtown Kuwait City have become available. In these tests the failure load was extrapolated from the test results. It is important to examine and analyze the test results for the benefit of the geotechnical research and design engineers."

Jan 1, 2017

By Jean J. Abiassi

The Boston Marine Industrial Park (BMIP) VENT 6 project is a cut and cover tunnel, part of the Central Artery / Tunnel (CA/T) in the city of Boston. The BMIP job will serve as the south approach to the Third Harbor Tunnel crossing. The alignment is approximately 2500 Ft long and is made up of four sections starting from west to east: 1. West Tunnel 2. Boat Section 3. East Tunnel 4. Tunnel inside Vent 6 Cofferdam and connection to the Third Harbor Tunnel. The support of excavation (SOE) system for the West Tunnel, Boat Section, and East Tunnel are all a part of this project whereas the SOE for Tunnel inside the Vent 6 Cofferdam was a part of the contract for the Third Harbor Tunnel.

Jan 1, 1994

By Yu Zhenquan

At the construction site of Bao Shan Iron &. Steel Mill in Shanghai, lots of RC driven piles with length of 50 to 60m were applied. The most unfavourable distribution of stress along the pile shaft was known by measuring the compressive and tensive stresses. With analysing the test results a phenomenon of impact fatigue of RC pile was discovered, the range of impact fatigue and its critical zone can be distinguished. Finally some countermeasures are presented to avoid the impact fatigue of RC long pile.

Jan 1, 1991

By Siavash Mahvelati, Alireza Kordjazi, Joseph Thomas Coe

Deep foundations are often constructed as end bearing members with a significant amount of their capacity derived from bedrock. Sites with highly variable bedrock conditions therefore present a unique challenge when attempting to estimate the design elevation of deep foundations. Typical subsurface characterization techniques such as drilling, standard penetration testing (SPT), and cone-penetration testing (CPT) may fail to adequately establish top-of-rock elevation in geologic settings prone to karst and/or significant amounts of residuum, saprolite, and deformed bedrock. Seismic surface wave geophysical methods have been increasingly used to map bedrock topography in such settings. However, the current standard of practice for these methods introduces resolution limitations in spatially variable subsurface conditions due to averaging effects from the analytical framework used to process the acquired data. This study explores the use of a tomographic approach with full waveform inversion (FWI) to map top-of-rock elevations at a numerically simulated site representative of highly variable bedrock topography. Comparisons are made with seismic refraction (SR) and a dispersion-based multichannel analysis of surface waves (MASW) approach as more commonly used in geophysical subsurface investigations. The results highlight that FWI provides a superior estimate of top-of-rock topography than SR and MASW at a cost of a significant increase in the required computational resources and time.

Sep 8, 2021

By Siavash Mahvelati, Alireza Kordjazi, Joseph Thomas Coe

Deep foundations are often constructed as end bearing members with a significant amount of their capacity derived from bedrock. Sites with highly variable bedrock conditions therefore present a unique challenge when attempting to estimate the design elevation of deep foundations. Typical subsurface characterization techniques such as drilling, standard penetration testing (SPT), and cone-penetration testing (CPT) may fail to adequately establish top-of-rock elevation in geologic settings prone to karst and/or significant amounts of residuum, saprolite, and deformed bedrock. Seismic surface wave geophysical methods have been increasingly used to map bedrock topography in such settings. However, the current standard of practice for these methods introduces resolution limitations in spatially variable subsurface conditions due to averaging effects from the analytical framework used to process the acquired data. This study explores the use of a tomographic approach with full waveform inversion (FWI) to map top-of-rock elevations at a numerically simulated site representative of highly variable bedrock topography. Comparisons are made with seismic refraction (SR) and a dispersion-based multichannel analysis of surface waves (MASW) approach as more commonly used in geophysical subsurface investigations. The results highlight that FWI provides a superior estimate of top-of-rock topography than SR and MASW at a cost of a significant increase in the required computational resources and time.

Oct 1, 2021

By Jean-Louis Briaud

The following is a summary of a very recent report prepared at Texas A&M University for the National Cooperative Highway Research Program and entitled "Downdrag on Bitumen Coated Piles". Anytime the soil settles more than the pile, downdrag or negative skin friction will develop. The load in the pile increases with depth up to a certain point and then decreases down to the pile point. This phenomenon has been quoted as being the number one culprit for deep foundation failures. In Chapter 1, an introduction to downdrag is given. The most common criterion for downdrag is to consider it in design as soon as the settlement of the soil surface after pile driving exceeds 0.5 in. Coating piles with bitumen is an effective way of reducing downdrag forces and therefore allows to use smaller piles for the same load. This results in cost savings. Coating piles with bitumen increase the cost of piles by about 33% and therefore the decision to use bitumen is generally based on economic considerations.

Jan 1, 1989

By Kent C. Werle

This brief discusses the installation and application of sleeved piles of two different types for two different projects, the W, Seattle to Harbor Island Swing Bridge Project and the Seattle Access Project. A description of these relatively novel piling systems is given, as well as some notes on their installation and application. As implied by the term "sleeved" these are piles which consist of two piles, an inner pile combined with an outer concentric sleeve pile. Background, Swing Bridge The Swing Bridge project is virtually unique in the world in that it is a "lift and turn" swing bridge. It is also a concrete, cast -in-place segmental bridge which is designed to be moveable.

Jan 1, 1990

By Antonio Marinucci, Robin Mao

The new Hangzhou West Railway Station, which is currently in the early stages of construction, will be located in the city of Hangzhou, China. To accomplish the ambitious goals of the project, the construction work and station building was divided into three project areas. The original design utilizes 1,580 drilled shafts with diameters of either 800 mm or 1000 mm (32 or 40 inch) to support the new Station and its various ancillary structures. The drilled shafts will be tipped into the moderately weathered argillaceous siltstone a distance between 5 and 15 m (16.5 and 49 ft), resulting in an effective pile length ranging from 35 to 43 m (115 to 141 ft), respectively. For the first phase, approximately 550 production drilled shafts will be installed. Eight (8) sacrificial drilled shafts each with a diameter of 1000 mm (40 inch) were installed to a depth ranging from 50 to 57 m (164 to 187 ft), and were tested to confirm the design parameters used for the first phase, to evaluate the contractor’s installation means-and-methods, and to provide guidance whether redesign is warranted for the subsequent two phases. Bi-directional static load testing was performed using a donut-shaped Super Cell to apply unidirectional axial loads up to 13,200 kN (2,970 kip). This paper will describe the bi-directional testing and select results obtained therefrom. The axial compressive and uplift resistances determined from the testing verified that the available axial resistance of a single drilled shaft exceeded the minimum design requirements.

By Seth H. Hamblin, Leo J. Hart, John E. Regan

The Route 6 /10 10 Interchange Design/Build project, located in Providence, Rhode Island, involves the design and construction of five (5) new elevated bridge structures to replace and reconfigure the existing interchange and to provide a link between Route 10 northbound and Route 6 westbound. Due to site logistics, headroom restrictions, and depth to bedrock, 50 ton drilled micropiles installed in the deep medium dense sand strata were initially proposed as the deep foundation solution. Post project award, Geosciences Testing and Research, Inc. (GTR) performed various analyses and developed an alternate driven pile solution using steel Tapertube. The results of these analyses indicated that driven steel taper tube and steel pipe piles could develop greater capacities than the drilled micropiles in the granular soil layer, thereby reducing the number of foundation elements, decreasing construction schedule and providing a more cost effective foundation alternative. A comprehensive driven pile load test program was subsequently executed by GTR and the Design Build Team led by Barletta Heavy Division of Canton, Massachusetts, to assess the performance of Tapertube and steel pipe piles, including pile drivability, load-deformation characteristics under static and dynamic loading, and to develop site-specific design parameters in two (2) distinct test areas. The test pile program included dynamic, static compression, tension and lateral load tests on each test pile. Load test measurements were automated with embedded Vibrating Wire Strain Gages (VWSG) to measure load transfer with depth. The execution and results of the successful pile load test program are presented and offer unique case study and valuable data for the use of Tapertube piles on deep foundation projects in the New England region INTRODUCTION The Rhode Island Department of Transportation (RIDOT) Route 6 / Route 10 Interchange is located west of downtown Providence. Originally constructed in the 1950’s as a highway bypass around the historic Olneyville neighborhood, the interchange consists of a series of nine (9) bridges and ramps that serve as a vital east-west link between Interstate 295, 95 and 195. Based on recent bridge rating assessments, seven of the nine bridge structures are rated “structurally deficient”. With many bridge structures shored with temporary supports as many as 15 years ago, the interchange is in critical need of replacement. In 2018, RIDOT awarded the Route 6/10 Reconstruction Design-Build Project to 6/10 Constructors, Joint Venture. Led by Barletta Heavy Division of Canton, Massachusetts, the Design Build team includes O&G Industries, DW White Construction, Aetna Bridge Co. and AECOM. The scope of work includes the replacement of the bridges and ramps, and will provide direct access from Route 10 northbound to Route 6 westbound. Valued at over $400M (US), this is currently the largest project awarded in RIDOT history.

Jan 1, 2019

By Dino Kartofilis, Rick Deschamps, Giovanni (John) Bonita

"Anew condominium complex in Arlington, Va., presented some formidable constraints. One was the requirement for a permanent retaining wall to support a 48.5-ft (15-m) cut and an existing 16- story building on top of the slope. Another was the adjacent property owners’ refusal to allow tieback anchors to encroach on their property. The General Contractor (GC) proposed an innovative design incorporating vertical concrete load-bearing elements (LBEs) supported by post-tensioned tiedowns. The owner accepted and the project was successfully completed in 2007.The original designer had proposed a system that included a temporary, raked soldier pile and lagging wall and a permanent cantilever retaining wall with a large piled footing. The system was potentially costly and its constructability questionable.The GC then asked for a design-build alternative to reduce costs and enhance the schedule. The first idea was a diaphragm wall with vertically anchored T-sections. However, configuring a crane to excavate perpendicular sections using grab equipment seemed impossible. There were also utilities approximately 25 ft (9 m) from the existing building, two tiered retaining walls down the slope and a large swimming pool at the base. However, the GC was committed to providing a stable bench 20 ft (6 m) wide along the wall alignment to support the crane.The design evolved to single bite panels using diaphragm wall technology, commonly called LBEs, or barrettes, when they carry vertical loads. For this project, 44 LBEs were horizontally spaced at 9 ft (2.75 m) on center, oriented perpendicular to the wall, extending into bedrock and anchored vertically on the upslope side to resist overturning moments. They were essentially large soldier piles that provided both temporary and permanent support of excavation.An unusual formal agreement was established with the GC to complete the work based on pricing, and prior to completion of final design. This arrangement allowed for an exchange of ideas that increased project efficiencies and lowered costs — without the fear that design concepts would be “shopped” to competitors."

Jan 1, 2009

By Tomohiro Yamasaki

"At the pre-construction foundations of the controlled waste disposal site built at the Port of Kinuura, the clayey soil account for the most, and with lesser amounts of sand compaction piles and sand mat. The cement deep mixing method (CDM) was used to improve ground impermeability and to reinforce the foundations on the seawall. Laboratory mixing and testing was performed to determine the appropriate quantities of cement additive for clayey soil, SCP sand, and sand mat. The test results indicated that maintaining the design strength of qu = 1,550 kN/m2 would require C = 100 kg/m3 of cement additive for all three soil types (clayey soil, SCP sand, sand mat). The permeability performance needed to improve ground impermeability assumes a permeability coefficient of K = 1.0×10-6cm/s. And the clayey soil satisfied the performance requirements at C = 100 kg/m3. However, to improve grand impermeability of the SCP sand and sand mat required more than 5% of particles having diameters of less than 75 µm. Thus, in the latter two cases, the required cement adding quantity was C = 250 kg/m3. The test specimens at one to two weeks after the created with a permeability coefficient of K = 10-6cm/s became permeability coefficient of K = 10-7cm/s six week later due to the effects of cement solidification. So the permeability coefficient declined about one order. The permeability coefficient three months later tends to decline continued with a somewhat lower.INTRODUCTIONBetween 2008 and 2011, the Aichi Seaside Environment Center constructed the Kinuura No. 3 offshore controlled waste final disposal site at Taketoyo in Aichi prefecture. (see Figure 1). The disposal site offers a landfill capacity of 5.21 million m3 and measures 472,000 m2 in area, of which some 344,000 m2 is a managed controlled sector enclosed within an impermeable seawall."

Jan 1, 2015

The pile inspector is a critical element in the quality control process necessary for a successful pile installation project. This guide is intended to provide the inspector with a basic understanding of only one of the many components of this process - the pile driving hammer. Pile driving hammers are used to install both bearing piles for structure foundations and sheet piles (and soldier piles) as used in retaining structures. In a single document, this guide offers a general presentation of the operation of the more common types of hammers the inspector is likely to encounter. It should make the information in the contractor's hammer submittal for the project more understandable. It should also provide an appreciation for the importance of a properly operating pile hammer. Prior to the start of most pile driving operations, the contractor will normally furnish a submittal to the engineer giving the specific pile driving equipment that he intends to use on the job. This submittal should include the make, model, and type of the intended pile driving hammer or hammers and their operating characteristics such as ram weight, rated energy, operating speed, external power requirements and, other pertinent information. Frequently, the operating characteristics are provided in the form of the manufacturer's specification sheet. The engineer will review this information and when he is satisfied, approve it and pass it on to the inspector. The driving criteria will have been determined by the engineer or others (the geotechnical engineer, consulting engineer, contractor, etc.) from the results of static analysis (for minimum penetration), driving during a test pile installation, Wave Equation analysis, dynamic formula, pile instrumentation during driving, static load test, or a combination of these or other appropriate analyses. The driving criteria can be a minimum penetration of driven pile length (embedded length), or a minimum (or maximum) blow count per unit of penetration. The pile inspector should become familiar with this information prior to the start of the job and should understand or seek help to comprehend the terminology and intent of each specification.

Jan 1, 1995

By Lorie M. Dilley

Alaska Village Electric Cooperative (AVEC), an electric utility cooperative providing power to 51 Alaska villages, has made a concerted effort to install wind turbines in the villages they serve in an effort to mitigate the growing costs of electrical power generation. The subsurface soils in several of these villages consist of sands and silts with ground temperatures of between 30°F and 32°F. The presence of warm, degrading permafrost in three of the villages has required innovative foundation designs, including the use of helical piers and piles to support steel and concrete wind turbine foundations. The design of the deep foundations had to account for the effects of degrading permafrost likely resulting from observed climate change patterns. Uplift forces imposed on the foundations were approximately 100 kips per pile. Uplift pile load testing was conducted on the installed piers and piles in order to determine the actual working load that each pier or pile could sustain. In addition, pile driving analyzer testing was conducted on several piles installed in the permafrost and compared to pile load tests. Results indicated that the installed piers and piles achieved the necessary capacity with sufficient factors of safety. Thermosyphons were installed near the foundations in order to limit the effects of climate change on the permafrost. The two to four wind turbines in each of the three villages are currently operational. Refinement of the design based on the pile testing from the first village to the third has decreased the cost of the tower foundations and improved our understanding of designing for warm, degrading permafrost.

Jan 1, 2010

By Adriaan van Seters

"Abstract The content of Eurocode 7 – Part 1 and Part 2 – with respect to piled foundations is outlined. The important role of pile testing is presented and the derivation of the characteristic value of pile bearing resistance is explained. Recommendations for the use of correlation factors are given. The ongoing work of the Evolution Groups on piling is to prepare a revision of Eurocode 7 after 2019. Future topics and changes are highlighted.General outline of pile design by Eurocode 7In his paper for this conference Frank (2014) outlined the various aspects of standardisation for pile foundations, which involves Eurocode 7 as leading for pile construction in Europe. Standards for pile testing and execution of piling works were established in the last 15 years.This paper focuses on the design of piled foundations according to the design code Eurocode 7, which consists of 2 parts:EN 1997-1 Geotechnical design - Part 1: General Rules (CEN, 2004);EN 1997-2 Geotechnical design – Part 2: Ground investigation and testing (CEN, 2007) In Eurocode 7-1, Section 7 – Pile Foundations - deals with the design of piles. The safety concept for pile design is given in Section 2 – Basis of Geotechnical Design - for the three Design Approaches.In Section 7 presents the design of piles according to four methods:1. Results of static load tests2. Empirical or analytical calculation methods3. Results of dynamic load tests4. Observed performance of a comparable pile foundation.Guidelines for the ground investigation for piles is provided in Eurocode 7-2, Annex B.3. In the Annexes of Eurocode 7-2 examples of analytical methods to determine the bearing resistance of a single pile based on the results of various ground investigation techniques are given. Thus calculation models are presented based on design using the results of Cone Penetration Tests (D.6 and D.7) and Pressuremeter Tests (E.3). The Annexes of Eurocode 7-2 are informative.For the interpretation of Eurocode 7, reference is made to Frank et al (2004) and Bond and Harris(2008)."

Jan 1, 2014

By David M. Rempe

The purpose of this standard is to provide a method for testing of cushion materials that leads to uniform results when employed by various organizations and laboratories. The load-deflection characteristics measured using this method are intended to provide input data for analysis of pile driving, as in wave equation analysis of pile driving. It should be recognized, however, that there are several factors which may cause a difference in performance between the test samples under laboratory conditions and actual cushion materials under pile driving conditions. These factors include variations in material properties from sample to sample, compaction and/or deterioration of the materials with use, eccentric loading due to misalignment, confinement effects or the cushion container or inter layered materials, head buildup, rate of loading, etc. In order to obtain representative load-deflection characteristics, therefore, testing of cushion specimens which have been subjected to actual pile driving conditions is encouraged 1 such specimen should be tested at various stages of the useful life of the cushion. The users of the data are cautioned to determine if the particular wave equation program they are using requires either the secant or tangent definition of the stiffness and modulus of elasticity.

Dec 1, 1984