Data Extrapolation Method for The Dynamic Increasing Energy Test: SEM-CASE

Transcription

1 ata Extrapolation Method for The ynami Inreasing Energy Test: SEM-CASE E.C. Alves, M.M. Sales, P.M.F. iana Abstrat. The dynami inreasing energy test has been widely sed in pile load tests in Brazil in reent years. However, the ltimate strength of the single-fondation system is not mobilized in most of the tests bease of varios fators. In some ases, the eqipment available annot attain the neessary kineti energy, or the strtral element presents initial imperfetions/rptres. In this stdy, the athors present a method for extrapolating the mobilized stati resistane vs. maximm displaement rve, whih is obtained sing the dynami inreasing energy test (IET. Using the fore and veloity signals olleted by the PA (Pile riving Analyzer system, it is possible to allate the resistane and displaement by applying the Simplified CASE Method. An extrapolation method, the Simplified Extrapolation Method of the CASE Method (SEM-CASE, is presented based on the reslts of twenty-one preast onrete pile load tests that have been arried ot in different soils. The estimated vales of the ltimate omplementary energy and ltimate strength were very lose to the measred vales in the presented load tests. Keywords: extrapolation method; dynami load test; driven pile; omplementary energy; strain energy. 1. Introdtion The first methods sed to estimate the bearing apaity of a driven pile were based on data obtained dring the pile installation. Alternatively, the wave eqation was initially applied to piles in the 1930s to estimate bearing apaity (Warrington, 1997; Hssein & Goble 004. Smith (1960 presented a model that sed a grop of eqations and allation rotines to desribe the stress-wave displaement and its effets along the pile after a hammer blow. With the development of more powerfl sensors and ompters, Smith s model an now be applied and has beome the fndamental basis for the methods employed in dynami load test analysis. In this ontext, onsidering the need to estimate the ltimate apaity of the pile based on the dynami load test, this paper presents a method for extrapolating the mobilized stati resistane ( vs. maximm displaement ( rve to obtain the behavior and ltimate strength apaity of the dynami inreasing energy test (dynami load test. The method is sed for driven preast onrete piles, whih mobilize the shaft and toe resistane dring loading. The giding priniple of this method is the omplementary energy riterion first presented by Aoki (1997, whih ses the expression mobilized stati resistane to indiate the resistane of the stati portion that is mobilized after a hammer blow dring the dynami load test, as allated by the simplified CASE method.. ynami Test and Nmerial Analysis.1. ynami load test The prpose of the dynami load test is to estimate the ltimate stati resistane of the pile-soil system and propose a load vs. virtal-settlement rve. By applying a hammer blow to the head of the pile, generally throgh a pile driver, fore and veloity signals are obtained at the pile head with deformation and aeleration sensors, respetively (Teferra et al., 1996; Likins et al., 008. The signals obtained from the sensors are transferred to and stored in a portable ompter, known as PA (Pile riving Analyzer. After the data have been olleted by the sensors, the PA transodes and proesses the data to obtain the fore and veloity signals, and the CASE nmerial method provides the stati resistane in eah hammer blow at the moment of impat dring the pile driving... ynami inreasing energy test - IET Two types of dynami load tests an be sed to obtain the pile-bearing apaity: onstant or inreasing energy. The dynami onstant energy test is the most traditional and widely sed test worldwide. Aording to Aoki (1989a, the dynami onstant energy test is similar to a yli stati load test in whih the same load is always applied, and the same settlement is always obtained for the same strain energy. Eder Chaveiro Alves, M.S., Civil Engineering, Agênia Goiana de Transporte e Obras, AGETOP. Av. Gov. José Ldovio de Almeida, n o 0, Goiânia, GO, Brazil. ederhaveiro@yahoo.om.br. Maríio Martines Sales, Ph.., Assoiate Professor, Esola de Engenharia Civil e Ambiental, Universidade Federal de Goiás, UFG. Praça Universitária, 1488, Goiânia, GO, Brazil. sales.mariio@gmail.om. Palo Mário Fernandes iana, Ph.., Assoiate Professor, epartamento de Engenharia Civil, Universidade Estadal de Goiás, UEG. B-153, Qadra área, km 99, Anápolis, GO, Brazil. pmfviana@gmail.om. Sbmitted on Jly 15, 015; Final Aeptane on Marh 3, 016; isssion open ntil eember 30, 016. Soils and oks, São Palo, 39(: , May-Agst,

2 Alves et al. The inreasing energy test onsists in the appliation of blows with variable and inreasing fall heights, based on a level of energy that is lower than that of the driving end (free-fall impat system (Aoki, 000. Crrently, the inreasing energy method is the most freqently sed method for performing the dynami load test in Brazilian bilding fondations. Aoki (1989a presents the appliation of the dynami inreasing energy test to obtain a rve similar to the load vs. settlement rve obtained in the stati load test, whih is the mobilized stati resistane vs. displaement rve..3. Simplified CASE method eveloped by the Case Institte of Tehnology (rrently Case Western eserve University, the main objetive of this method is to allate the stati resistane in real time and at the test site for eah hammer blow. It was impliit that eah blow was enogh to mobilize the ltimate soil resistane. This method is a losed-form soltion of the wave eqation, in whih the signals of fore and veloity are sed and reorded in a partilar pile setion, jst as the blow reahes its highest intensity in the setion of the sensors (t 1 and jst as the wave refleted at the end of the pile retrns to the instrmented setion (t. Stati resistane ( is allated by the differene between total resistane and dynami resistane. Linkins & ashe (1981 presented the start point of Case Method and in following paper, ashe et al. (1985 expanded the formlation of stati resistane as EA J Ft vt J Ft EA ( ( 1 vt (1 where Ft 1, Ft, vt 1, and vt are, respetively, the vales of fore and veloity allated by means of the data obtained throgh the speifi deformation and aeleration sensors at times t 1 and t. J is a dimensionless onstant alled the dynami damping oeffiient of the CASE method and is determined based on experienes of orrelations with stati load test reslts, E is the elasti modls of pile material, A is the ross-setional area of pile and is the veloity of wave propagation. The relation (EA/ is also known as the pile impedane. 3. Complementary Energy Presented by Aoki (1989b, this riterion allows the pile-soil system to be in a state of dynami eqilibrim (elasti-perfetly plasti behavior dring the hammer impat, with the appearane of non-onservative inertial and damping fores, and the appliation of Hamilton s energy onservation priniple is valid. It is also assmed that the system retrns to its original state after eah blow, i.e., there is no signifiant hange in the initial ondition of the system. Clogh & Penzien (1975 stated the priniple as: t t1 t ( T dt ( W dt 0 ( t1 n where is the variation in the time interval (t - t 1 ; T is the total kineti energy in the system; is the potential energy in the system; W n is the work done by non onservatives fores. Soil rptre is haraterized in the dynami inreasing energy test when a partilar impat, orresponding to a point on the idealized mobilized stati resistane-displaement rve, shows that a the mobilized stati bearing apaity ( passes throgh a maximm ; b the omplementary kineti energy (T of the impat passes throgh a maximm T ; and the omplementary potential energy ( passes throgh a maximm. Hamilton s priniple, as applied to the maximm impat energy T, also an be expressed by {[ T ( K ] [( S Wa]} 0 (3 where T is the maximm kineti energy; S is the maximm permanent portion (penetration; and W a is the work done by the non onservative fores. The omplementary energy tends towards a onstant vale when the total strain energy and the settlement S tend towards infinity, i.e., the analysis of the variation of the omplementary strain energy with loading shows how lose rptre is bease the rate of variation of this parameter is anelled ot when the reation or resistane apaity of the system reahes an extreme, as shown in Fig. 1. Aoki (000 presented the new formlations for determining the vales of potential energy s, omplementary energy, and work W done by the stati portion of the fores. These made it possible to allate area vales that are more onsistent with the mobilized stati resistane ( vs. displaement ( rve. The expressions are given below for allating the potential energy (Eq. 4, omplementary energy (Eq. 5, and work (Eq. 6: Figre 1 - The strain energies that form part of the mobilized stati resistane ( vs. maximm displaement ( rve of IET. 178 Soils and oks, São Palo, 39(: , May-Agst, 016.

3 ata Extrapolation Method for The ynami Inreasing Energy Test: SEM-CASE n i i1 s ( i i 1 i1 (4 n i i1 ( i i 1 i1 (5 W ( s e (6 where e is the portion of elasti strain energy (Fig Fit Eqations for vs. Crve This setion presents the se of the exponential, hyperboli, and paraboli fntions as possible models to represent the mobilized stati resistane ( vs. isplaement ( rve, as shown in Fig.. Moreover, the eqations for the allation of omplementary energy ( were deded by means of Eqs. 7 to 15 (see all detailing in the appendix, whih present different approahes to represent the mobilized stati resistane ( vs. displaement rve, the omplementary energy (, and the ltimate omplementary energy (, sing the ltimate stati resistane and displaement ( at the moment that the test mobilizes the ltimate stati resistane. The other variables presented in this figre are: 1 and are displaements before and after the ltimate stati resistane, respetively; 1 and are displaement variations; 1 is the stati resistane orresponding to a displaement 1 ; is a stati resistane variation; is the potential energy; 1 and are energy variations; 1 is the orresponding variation in the omplementary energy. Exponential rve ( ( 1exp (7 [ 1( 1 exp ] (8. (9 Figre - Mobilized stati resistane ( vs. maximm displaement( rve of IET (modified from Aoki, 000. Hyperboli rve 1 1 ( arsen (10 (11 0, 15. (1 Paraboli rve 3 3 ( SEM-CASE Method (13 (14 (15 A new method is presented here for extrapolating the trajetory of the mobilized stati resistane ( vs. maximm displaement ( rve, obtained by analyzing the CASE nmerial method based on the omplementary energy riterion. This methodology is hereafter alled the Simplified Extrapolation Method of the Simplified CASE Method (SEM-CASE. This method is appliable to preast onrete piles driven by a pile driver with a free-fall hammer and tested by the dynami inreasing energy test. In addition, the pile mst have been designed to bear the working load sing the portions of shaft and toe resistane, where the rptre is haraterized by onstant mobilized stati resistane nder the ation of inreasing kineti energy with a well-defined vertial asymptote. Some pile tests an present different forms of resistane vs. displaement rves. Sometimes the tests do not present an evident mobilization of stati resistane. In others, the reslts are initially represented by an almost linear behavior in the graph x and then ors an abrpt failre. Both ases are onseqenes of partilar pile-soil systems and an not be extrapolated or predited by any method. Aoki (000 disssed some examples of pile tests in sh ases. The SEM-CASE method will not be able to extrapolate the maximm stati resistane in sh rves. The data from a dynami inreasing energy test presented by Aoki (000 were sed to demonstrate the se of the method (Fig. 3. The onrete pile had a total length of 1 m, a driven length of 10.1 m, a diameter of 0.4 m, and a hollow ylindrial form with a setion area of 0.09 m. Soils and oks, São Palo, 39(: , May-Agst,

4 Alves et al. Figre 3 -vs. graph of a driven pile (modified from Aoki, 000. This pile reahed the ltimate resistane dring the test, aording to the omplementary energy riterion. However, to simlate a dynami load test that did not mobilize the ltimate stati resistane, Fig. 3 represents only part of the test as if it had been interrpted when the resistane reahed 1790 kn (the other points beyond 1790 kn are not presented in Fig. 3. The appliation of the method an be divided into three (3 steps: Step 01: The variation ratio of the mobilized stati resistane (ar. to the variation of kineti energy (ar. T is allated in eah blow of the dynami load test. The vales obtained for the pile are shown in Table 1. The vales for the ratio of ar. to ar. T are plotted in Fig. 4, with the vales of the mobilized stati resistane plotted on the absissa sing a logarithmi sale. The graph in Fig. 4 has three (3 stages: Stage 1, Stage, and Stage 3. Stage 1 has an almost 90 slope in relation to the x-axis. The first blows, with a lower fall height, i.e., lower kineti energy, generally form part of this stage. Stage has a slope tending from 90 to 0, in relation to the x-axis, depending on the analyzed pile. Stage 3 tends to a 90 slope, regardless of the analyzed pile geometry. The slope of the three stages of the vs. ar. / ar. T graph varies aording to the following harateristis of the pile fondation: a Loal srronding soil; b Pile geometry; Length of the strtral element driven into the srronding soil; and d Pile age (time interval between the end of the driving and the start of the test. From analyses of the 1 dynami inreasing energy tests stdied by Alves (010, it was observed that in stage 1, the test pratially mobilizes only the lateral resistane. In stage, the test mobilizes the lateral and tip resistane of the pile, and in stage 3, the lateral resistane dring the test is exhasted (remains onstant, and only the tip resistane inreases ontinosly and is mobilized ntil rptre (when the ratio of the variation of the mobilized stati resistane - ar. to the variation in applied kineti energy - ar. T is eqal to zero, indiating similarities with the reslts presented by Aoki (1989b. Figre 5 ses the last five points, whih are in stage 3 of Fig. 4, to present a simple linear regression. It shows good agreement between the points and the linear regression. This good agreement ors when the portion of tip resistane of the pile is signifiantly mobilized. The priniple of extrapolation of the ltimate stati resistane stems from the onept that when the ratio (ar. /ar. T is eqal to zero, the pile reahes the ltimate resistane, i.e., when the variation of the mobilized stati resistane in two blows with inreasing kineti energy is eqal to zero, the pile is sbjet to the mobilization of the ltimate stati resistane. As stated by Aoki (000, this kind of approah wold be the pper bondary limit of the ltimate stati resistane. Figre 5 shows the linear regression of the points that is sed to extrapolate the ltimate stati resistane (. This ors when the straight line interepts the x-axis. Table 1 - ales of,, T, ar., ar. T, and ar. /ar. T. (m (kn T (knm ar. (kn ar. T (knm ar. /ar. T (1/m Soils and oks, São Palo, 39(: , May-Agst, 016.

5 ata Extrapolation Method for The ynami Inreasing Energy Test: SEM-CASE Figre 4 - vs. ar. / ar.t graph of a driven pile. Figre 5 - Linear regression of the last five points of the vs. ar. /ar. T graph of a driven pile. The linear regression expression is desribed below y ax b (16 b. (17 a Note that the orrelation oeffiient ( had a vale of Aording to the stdies of Alves (010, vales greater than 0.8 were fond in all tests. Solving the linear regression expression in Fig. 5, an estimated ltimate stati resistane vale of kn an be obtained. Therefore, the extrapolated ltimate mobilized stati resistane is determined by Eq. 17. Step 0: The x rve in Fig. 3 is divided into eqal maximm displaement segments (Fig. 6. The reommended division vale is 1 mm, as sed in this example. The vales of mobilized stati resistane n are allated by means of interpolation. This task prodes a smoother rve in the segments where it has sdden variations in trajetory. The omplementary energy vales are allated in eah segment as i n n 1 n ( n n 1. (18 n 1 Table presents the vales for maximm displaement adopted ( n for the interpolated mobilized stati resistane ( n and the allated vales, with Eq. 18, and for the omplementary energy in the analyzed segment ( n of the test. The vales of n vs. n-1, presented in Table, are plotted in Fig. 7. After the qadrati regression of the plotted points, this regression was extrapolated ntil it inter- Soils and oks, São Palo, 39(: , May-Agst,

6 Alves et al. Figre 6 - vs. graph divided into eqal maximm displaement segments. Table - Interpolated and vales and the allated. (m n (kn n-1 (kn n (knm n-1 (knm epted the dotted line. The dotted line represents the points at whih the vales of n are eqal to those of n-1, i.e., a sitation in whih, nder the omplementary energy riterion, the test wold mobilize the ltimate stati resistane. The qadrati eqation, aording to Eq. 19, is sed to determine the ltimate omplementary energy ( when the pile reahes its rptre point. ax ( b 1 x 0. (19 The vales of a, b, and, as fond in the qadrati regression (Fig. 7, are sbstitted into Eq. 19. The nknown qantity b is reded by 1 to arrive at the ondition where both axis vales are eqal, i.e., n is eqal to n-1. Solving the qadrati eqation, 1 and are fond, disarding any vale that eventally is negative or has no physial signifiane. In the example presented here, by solving the eqation shown in Fig. 7, a vale of kn is fond. Step 03: Using the vales obtained for the ltimate mobilized stati resistane and for the ltimate omplementary energy of the test, it is possible to extrapolate the remaining segment of the mobilized stati resistane ( vs. maximm displaement ( rve. Eqs. 7 to 15 an be sed for this prpose. Finally, by sbstitting the vales = kj and = kn into Eq. 9, Eq. 1 and Eq. 15, the parameters for the exponential, hyperboli, and paraboli eqations, respetively ( , m, and m, an be obtained. Figre 8 shows the omparison of the mobilized stati resistane ( x maximm displaement ( rve measred in the dynami inreasing energy test with the rves allated by the exponential, hyperboli, and paraboli eqations. 6. eslts and isssions 6.1. Analyzed tests The dynami load tests were arried ot starting with the appliation of inreasing dynami axial loads, sing a free fall hammer, in different Brazilian states. 18 Soils and oks, São Palo, 39(: , May-Agst, 016.

7 ata Extrapolation Method for The ynami Inreasing Energy Test: SEM-CASE Figre 7 - n-1 vs. n graph of a driven pile with qadrati regression. transferred to the pile, sing the vale of EMX given by the dynami load test, an be fond in Alves (010. All of the piles were made from preast reinfored onrete with metal splies at the ends. The onrete presented harateristi resistane (f k of 35 MPa. When neessary, the splies of the elements were welded. Table 3 shows the vales for total length (L total, driven length (L, diameter, setion area, and dynami modls of elastiity of the strtral elements of the stdied piles. The 1 tested piles were part of 1 different works in 7 Brazilian ities. Free-fall pile drivers were sed in all tests, with steel hammers weighting from 18.5 to 50 kn. The driving systems were eqipped with a damping system that was omposed of a metal helmet with a hardwood blok and plywood shion. 6.. Comparison of different fit eqations for extrapolation of the vs. rve Table 4 shows the orrelation oeffiient vales ( of the three fntions: exponential, hyperboli, and para- Table 3 - Geometri data of the piles. Figre 8 - Comparison of the measred and allated vs. rves. The data aptred by the sensors fastened onto the piles were proessed by the simplified CASE method and so obtaining. The vales of the soil damping oeffiients of the CASE method (J were obtained with the greater energy blow in eah test, by a nmerial analysis sing the CAPWAP (Case Pile Wave Analysis Program method. This J vale was sed to all blows of that test. Complementary details, sh as the vales of the weights of the pile-driving hammers sed in the test, the PA (Pile riving Analyzer model sed, the pile age (time elapsed from pile installation and test date, the J vales adopted in the test analyses, the vales for fall heights (H fall of the hammer dring the test, the maximm displaement in eah hammer blow ( measred in the test, the vales for mobilized stati resistanes ( allated by the CASE method, and the vales of maximm kineti energy (T Pile L total (m L (m iam. (m Setion area (m ynami Pile Elast. Modls (GPa * * * * * * (* = dimension of the side of the piles of sqare setions. Soils and oks, São Palo, 39(: , May-Agst,

8 Alves et al. Table 4 - vales of the exponential, hyperboli, and paraboli fntions. Pile ales of Exponential Hyperboli Paraboli Mean Standard eviation boli rves targeting the best fit for all of the pile load tests. The vales in bold fae are the ones that presented, among the three fntions, the vale losest to 1, i.e., the fntion that presented the best fit in a partilar pile. It was observed that in 13 of the 1 stdied piles, the best fit fntion for the vs. rve was the exponential fntion. Only five piles had the best fit for the paraboli fntion, and three piles had the best fit for the hyperboli fntion. Three tests all the attention in Table 4 by the lowest vales of. Test 10 presented a sdden rptre and tests 16 and 17 still presented a very linear behavior in the last stage of the test. As said before, in this sitations any extrapolation method is not effiient in prediting the ltimate stati resistane, and this the reason for lower vales. Among the three stdied fntions, the mean of the vales that presented the vale losest to one was also the exponential fntion. Moreover, this fntion was shown to have the lowest standard deviation of the stdied fntions ifferent ltimate load riteria applied in the vs. rves The dynami inreasing energy tests were sed in this analysis. The tests were ondted ntil the point of pilesoil rptre, however, to se the rptre riteria to estimate the, only the reslts obtained after one hammer blow before pile rptre were onsidered. The piles (listed in Table 3 sed in the present omparison were 0, 10, 11, 18, 0, and 1 bease they mobilized the ltimate stati resistane. To ompare the proposed method (SEM-CASE method, Table 5 presents the ratio of allated to measred for the onventional methods that are sally applied for stati load testing SLT. All preditions were made sing the same vs. rve measred in the dynami inreasing energy test. Table 5 - ales of the ratio of allated to measred for the extrapolation riteria of for SLT and the SEM-CASE method of Piles, 10, 11, 18, 0,and 1. Criterion/Pile Callated/ Measred an der een ( % Brinh Hansen ( N/A N/A N/A 90% Brinh Hansen ( N/A N/A N/A Chin ( N/A Mazrkiewiz ( N/A Massad ( éort ( N/A.483 N/A SEM-CASE N/A = not available. 184 Soils and oks, São Palo, 39(: , May-Agst, 016.

9 ata Extrapolation Method for The ynami Inreasing Energy Test: SEM-CASE Figre 9 shows a 3 bar graph omparing all of the riteria shown in Table 5. It shows that the SEM-CASE method had the lower variation in the ratio of allated to measred. The SEM-CASE presented a better predition to all piles with relations allated/measred very lose to one. The preditions sing the riteria of an der een (1953, Brinh Hansen (1963 and Mazrkiewiz (197 had a good behavior to this set of piles. The methods of Chin (1970, Massad (1986 and éort (1996 presented a higher variability, overprediting in most of the ases. 7. Conlsions This paper presents a new method, the Simplified Extrapolation Method of the Simplified CASE Method (SEM-CASE, to extrapolate the mobilized stati resistane ( vs. maximm displaement ( behavior based on the omplementary energy riterion. This method is mainly appliable to preast onrete piles and was alibrated with dynami inreasing energy tests. With respet to the presented analyses, the following shold be noted: The SEM-CASE method an be easily sed and has an aeptable theoretial basis. The estimated vales of the ltimate stati resistane, obtained by the SEM-CASE method, were similar to the measred vales, with an error below 10%. By evalating three different fntions (exponential, hyperboli, and paraboli fntions to reah the best fit with the test, it was noted that the exponential fntion obtained better reslts in more than 60% of analyzed ases. Figre 9 - Bargraph of the ratios of allated to measred for all ompared methods. The ability of lassial methods to predit the ltimate load in stati load tests was ompared with the proposed SEM-CASE method. In the six presented dynami load tests, the SEM-CASE reslted in better preditions that were loser to the ltimate measred resistane. The presented method was tested with a set of onrete driven piles. However, the same onept is srely valid for steel piles, sine load tests on these piles normally present a well defined stati resistane (. As any other extrapolation method, the SEM-CASE method is appliable to tests that are gradally onverging to the ltimate stati resistane with a well-defined vertial asymptote. Aknowledgments The athors of this paper wold like to thank the ompany SETE, Serviços Ténios de Engenharia Ltd. for sharing the dynami load tests sed in this stdy, AGETOP, Agênia Goiana de Transporte e Obras for its spport, and CNPq, Conselho Naional de esenvolvimento Científio e Tenológio for the finanial spport. eferenes Alves, E.C. (010. A New Extrapolation Method of ynami Load Tests: SEM-CASE. MS issertation, Shool of Civil and Environmental Engineering. Federal University of Goias, Brazil, 50 p. (in Portgese. Aoki, N. (1989a. A new dynami load test onept. Pro. 1 th Int. Conf. on Soil Mehanis and Fondation Eng., ISSMFE, io de Janeiro, Session 14, rivability of Piles. Japanese Soiety for Soil Mehanis and Fondation Engineering, Tokyo, v. 1, pp Aoki, N. (1989b. Predition of the behavior of vertial driven piles nder stati and dynami onditions. Pro. 1 th Int. Conf. on Soil Mehanis and Fondation Eng., ISSMFE, io de Janeiro, v., pp Aoki, N. (1997. eformation of Ultimate Load Capaity of riven Piles in ynami Inreasing Energy Test. Ph Thesis, Shool of Civil Engineering, University of São Palo, Brazil, (in portgese. Aoki, N. (000. Improving the reliability of pile bearing apaity predition by the dynami inreasing energy test (IET. Pro. 6 th Int. Conf. on the Appliation of Stress Wave Theory to Piles, São Palo, pp Brinh Hansen, J. (1963. isssion: Hyperboli stressstrain response: ohesive soils. Amerian Soiety of Civil Engineers, J. of the Soil Mehanis and Fondation iv., 89(4:41-4. Chin, F.K. (1970. Estimation of the ltimate load of piles not arried to failre. Pro. nd Sotheast Asian Conferene on Soil Engineering, pp Clogh,.W. & Penzien, J. (1975. ynamis of Strtres. MGraw-Hill, New York. Soils and oks, São Palo, 39(: , May-Agst,

10 Alves et al. éort, L. (1996. Evalation of fondation rptre based on the onept of stiffness. Pro. III Seminário de Fndações Espeiais, São Palo-SP, Anais. ABMS, v., pp. 15-4, (in Portgese. Hssein, M.H. & Goble, G.G. (004. A brief history of the appliation of stress-wave. Theory to piles. Crrent Praties and Ftre Trends in eep Fondations, Geotehnial Speial Pbliation N. 15, ASCE, eston, pp Likins, G.E. & ashe, F. (1981. Case method. The Seond Seminar on the ynamis of Pile riving in Bolder, CO, Pile ynamis, In., Cleveland, OH. Likins, G.E.; Pissalko, G.; oppel, S. & ashe, F. (008. PA testing: State of the art. Pro. 8 th Int. Conf. on the Appliation of Stress Wave Theory to Piles, pp Massad, F. (1986. Notes on the interpretation of failre load from rotine pile loads tests. Soils and oks, 9(1: Mazrkiewiz, B.K. (197. Test Loading of Piles Aording to Polish eglations. oyal Swedish Aademy of Eng. Sienes, Committee on Pile esearh, eport n. 35, Stokholm, 0 p. ashe, F., Goble, G.G. & Likins, G.E. (1985. ynami determination of pile apaity. ASCE Jornal of Geotehnial Engineering, 111(3: Smith, E.A.L. (1960. Pile driving analysis by the wave eqation. J. Soil Meh. Fond. Eng. iv., ASCE, 86(4: Teferra, W.; Thendean, G. & Likins, G.E. (1996. riving stress ontrol dring the installation of preast prestressed ylindrial onrete piles. Pro. 5 th Int. Conf. on the Appliation of Stress-wave Theory to Piles, pp an der een, C. (1953. The bearing apaity of a pile. Pro. 3 rd Int. Conf. on Soil Mehanis and Fondation Eng., Zrih, v., pp Warrington,.C. (1997. Closed Form Soltion of the Wave Eqation for Piles. MS Thesis, University of Tennessee at Chattanooga. List of Symbols a, b, : parameters of regressions A: ross-setional area of pile : veloity of wave propagation CAPWAP: Case Pile Wave Analysis Program, 1, : displaement : maximm displaement IET: dynami inreasing energy test E: elasti modls of pile material Ft 1, Ft : vales of fores H fall : fall heights of the hammer J : dynami damping oeffiient L: pile driven length L total : pile total length PA: Pile riving Analyzer, 1 : mobilized stati resistane : maximm resistane : vales of orrelation oeffiient S : maximm permanent penetration t 1, t : time T: total kineti energy in the system T : omplementary kineti energy T : maximm omplementary kineti energy T : maximm kineti energy vt 1, vt : vales of veloity : potential energy in the system : omplementary potential energy : maximm omplementary potential energy e : elasti strain energy s : potential energy W: work W a : work of the final damping fores W n : work done by non onservatives fores rve shape oeffiient : variation in the time interval (t -t 1, 1, : displaement inrement or variation : resistane variation, 1, : energy variation Appendix: Callation of Complementary Energy When Using ifferent Fit Eqations As different fit eqations old be sed to represent the mobilized stati resistane ( vs. isplaement ( rve, as shown in Fig., this appendix explain how the omplementary energy ( is allated in the three sed fntions in this paper: exponential, hyperboli, and paraboli fntions. A Exponential fntion Based in an der een (1953, Aoki (000 proposed to express x relationship as: ( e ( 1 (0 where is the maximm resistane and is a rve shape oeffiient. The potential energy ( s wold be the integral of Eq. 0 from the origin to a generi vale of : ( ( ( 1e d d ( e d s (1 1 s e 1 ( (. ( The omplementary energy an be allated as:. (3 s Using the reslt of Eq. in Eq. 3, reslts: 186 Soils and oks, São Palo, 39(: , May-Agst, 016.

11 ata Extrapolation Method for The ynami Inreasing Energy Test: SEM-CASE e ( ( 1 a and hanging the vale of by Eq. 0, reslts: (4 e 1( 1. (5 When tends to large vales of displaement, the limit omplementary energy ( an be expressed as:. (6 B Hyperboli fntion Using a hyperboli relation between x : 1 1 (7 where is the maximm resistane and is maximm displaement This eqation old be rewritten in different form: 1 1. (8 In this form, the omplementary energy ( wold be the integral of Eq. 7 from the origin p to a generi vale of resistane (: d d d (9 or arsin. (30 eplaing by, the limit omplementary energy ( an be expressed as: 1 1 arsin( 1 (31 or approximately: (3 C Paraboli fntion Using a paraboli fntion where wold be proportional to the sqare of, the relationship old be expressed as. (33 The omplementary energy ( wold be the integral of Eq. 33 from the origin p to a generi vale of resistane (: 0 d 3 3. (34 eplaing by, the limit omplementary energy ( an be approximately expressed as: 3. (35 Soils and oks, São Palo, 39(: , May-Agst,