for reliable prediction ofpile capacity after the end of

PILE-SOIL DYNAMIC SYSTEM WITH VARIABLE DAMPING M.R. Svinkin* *Gable Rausche Likins and Associates, Inc. 4535 Emery Industrial Parkway Cleveland, Ohio 44128 U.S.A. ABSTRACT. Thtipaper deals with application of the wave equation to pile driving analysis. It is shown that changes of the pile-soil system related to soil remolding around pile should be taken into account for reliable prediction ofpile capacity after the end of initial driving. Soil damping is the basic parameter for adjustment of wave equation solution with timedependent soil properties. Experimental data was acquired for three piles, one in clay and two in sand. Adjusted wave equation solutions yield an increase of soil damping with elapsed time after the end of driving with laker intensity in clay. A linear relationship between the skin damping coef&ient and time elapsed after driving was approximately found for piles in clay and sand. NOMENCLATURE J, : Skin damping coefficient Jse Skin damping coefficient at EOID J sr : Skin damping coefficient at RSTR Jt : Toe damping coefficient EOID : End of initial driving RSTR : Restrike T : Period of the first mode t : Elapsed time after EOID D : Nominal pile toe diameter RU : Pile capacity LINTRODUCTION Most of piles are driven into the ground by dynamic means such as impact or vibration. Therefore, it is reasonable to use measurements made during driving and computed dynamic methods to predict pile capacity. The traditional method for assessment of pile capacity has been dynamic pile formulas which employ energy approach and permanent pile set per hammer blow. New methods, namely CAPWAP and Case Method, have been derived on the basis of measurements of force and velocity at the pile head [l-2]. Case Pile Wave Analysis Program (CAPWAP) is post-driving analysis, signal matching technique, for determining pile capacity. The Case Method is a closed form solution based on a few simple assumptions and correlation to static pile test results. Wave equation analysis of driven piles is widespread used during both the design and construction stages of many projects. The wave equation is an indispensable tool in the analysis of driven piles for the selection of proper driving equipment to ensure pile installation in satisfied grade keeping stresses in the pile allowable and to determine the penetration rate corresponding to the required capacity. Application of the wave 240

equation to pile driving analysis is based on Smith s mathematical model of hammer-pile-soil system [3]. The wave equation method has been the subject of numerous research papers vastly referenced in [4]. The survey and analyzing of different studies for the wave equation method were performed in paper [5]. The wave equation method is used for pile-driving calculations and for determination and prediction of pile capacity as a function of pile penetration set or blow count per 0.3 m, so-called bearing graph. A number of researchers, for example [6,7], have performed parametric study of sensitivity and accuracy of pile capacity computed by the wave equation method. However, they considered soil parameters as some constant quantities. This paper shows that the pile-soil system changes its characteristics after completion of pile driving and damping is time-dependent property of soil surrounding the pile. It is recommended in the GRLWEAP that damping under the pile tip, J,, of 0.50 s/m be applied Values for skin damping, J,, are related to the soil conditions and range bchveen 0.16 and 0.66 s/m for non-cohesive and cohesive soils, respectively. The pile is penetrated in soil under each hammer blow and oscillated relatively of a new position of the static equilibrium. For that reason, the total resistance of the pile-soil system developed under each hammer blow is a sum of the ultimate static (pile capacity) and dynamic pile-soil resistance. There is some uncertainty in wave equation analysis before pile driving because actual efficiency of the entire hammer assembly is unknown. Dynamic measurements during driving yield force, energy and velocity as functions of ACTUAL SYSTEM DILSEL r-l MODEL Tr- 2. EXISTING MODEL The first computer program for pile driving analysis was dcvcloped by Smith. In spite of some modifications and improvements of original model, results obtained by many researchers confirmed the soundness of the basic approach. Today, the most commonly used wave equation programs are based on either WEAP [8,10] or TIT [9]. The most recently released GRLWEAP is a WEAF - based program with a number of special options and enhancements for personal computer. Mathematical model simulates the dynamic behavior of the real hammer-pile-soil system. The hammer and pile model consists of a series of discrete masses and springs. Soil resistance to pile penetration is represented by both a displacement and a velocity dependent parts. At each pile segment below ground level a soil resistance model is assigned, as illustrated in Figure 1. The displacement dependent component is shown as an elastic-plastic spring. The deformation at which the plastic behavior starts is called quake. The velocity dependent dynamic soil resistance (soil Smith damping) is represented by a linear dashpot. Fig. 1 The analysis model (after [S]) time. Adjustment of WEAF input with maximum values of those quantities, which phases almost coincide, improves WEAF solutions. However, computed pile capacity is not often equal to results of static and dynamic tests. It is necessary to make second adjustment of WEAF input data with soil parameters. 241

MODIFICATION OF PILE-SOIL SYSTEM Pile capacity determined at the end of initial driving in various soils as a rule changes with time. During pile installation, soil around the pile experiences plastic deformations and pore pressure changes. Excess pore water pressure reduces the soil shear strength and ultimate pile capacity during driving. After the completion of pile driving, soil remolding and reconsolidation, related to a certain degree to the dissipation of excess pore pressure at the soil-pile interface zone, are usually accompanied with an increase in pile capacity (soil setup). The amount of increase in pile capacity depends on soil properties and pile characteristics. In saturated sandy soils, ultimate pile capacity may decrease (soil relaxation) after initial driving or acquisition of certain strength gain. The phenomenon of time-dependent strength gain and loss in soils related to pile driving has been studied and published in some papers [ll-131. easily observed in pile displacement records obtained by integration of velocity. The measured pile displacements at EOID and RSTR are displayed in Figures 2 and 3 for concrete and steel piles, respectively. Prestressed concrete pile 457x4.57 mm has length of 23.5 m. Steel H-pile 14x73 has length of 22.9 m. The half-period of the fundamental mode is determined using the intersection of displacement curve and a line drawn through the final pile head displacement. Analyzing of observed curves has shown that the frequency of the pile fundamental mode at RSTR is somewhat higher as compared with EOID. So, this frequency increased from 13.3 to 16.3 Hz for prestressed concrete pile and from 25.0 to 30.4 Hz for a steel H-pile. Besides change of excess pore pressure induced by pile driving, two more vital and substantial causes may influence the soil strength vs. time characteristics. The first is age hardening, the phenomena of time-dependent strength gain in soil [14]. The second is thixotropy defined as an isothermal, reversible, time-dependent process occurring under conditions of constant composition and volume whereby a material stiffens while at rest and softens or liquifies upon remolding, [15]. The phenomenon of thixotropy is moistly observed in fine-grained materials. Assessment of pile capacity as a function of time is, of course, important in the design of pile foundations. Changes of strength in soil after driving and the time required for return of equilibrium conditions is highly variable and depends mainly on soil type. Fortunately, soil setup is observed in most cases. Changes of the pile-soil system with elapsed time after EOID are reflected in measured vibrations at the pile head in the moment of hammer blow. The fundamental mode of pile vibrations is the distinctive feature of each record. This mode is Fig. 2 Measured displacements at the head of prestressed concrete pile, a EOID, b RSTR, (After P51) Obviously, at each RSTR the pile-soil system has various soil stiffness, damping and involved in vibration soil mass. Changes of soil properties with elapsed time after EOID can be taking into account via quake and damping which represent the soil in the existing model. 242

LCD, fn.50. -I- * [171. Interesting example about the quake influence on WEAP solution was reported in paper [18] which yields better prediction with the small quake in spite of the large quake developed during driving. Soil damping is the basic parameter for adjustment of WEAP solution. Though Smith permitted all parameters in analysis to be treated separately, a better way to receive the best pile capacity match is to pick out only damping coefficient while keeping the rest of model parameters in certain range. Search of a damping-time relationship from measured pile capacity during EOID, RSTR and static test (ST) was undertaken for three piles (Table 1)..m. -. 50 1 D. S Fig. 3 Measured displacements at the head of steel H-pile, a EOID, b RSTR, (After [16]) VARIATION OF SOIL DAMPING Smith model is the certain idealization of loaddeformation characteristics for the soil without conjunction of those with soil constants from usual geotechnical in-situ or laboratory testing. There arc numerous experimental investigations of Smith damping coefficient for driveability analysis. However, successful laboratory test of damping parameters does not necessarily guarantee the prediction of accurate and reliable pile capacity. For idealized Smith model, it is desirable to find a suitable combination of parameter values, mainly paying attention to soil variables, in order to receive the reliable prediction of pile capacity, Moreover, some artificial quantities of damping and quake may not coincide with their values from laboratory tests. One approach among others to determine proper soil parameters for computing pile capacity is the evaluation of damping and quake changes with time after EOID. The effect of the quake developed during dynamic testing on computed pile capacity is relatively complicated, but it is clear that the toe quake affect weakly on pile capacity for low blow count Analysis was performed in the following manner. Percentage of skin friction and friction distribution along the pile shaft was taken from CAPWAP results. According to GRLWEAP recommendations, the quake was chosen as 2.54 mm for a skin and D/120 mm for a toe where D is the effective toe diameter of the displacement pile. These recommendations are based on Smith original suggestion and the accumulated experience of using wave equation analysis for many years. For each dynamic testing, WEAP was run repeatedly to match computed and measured values of force, energy and velocity. Then adjustment of Smith damping was made to correlate pile capacity and blow count per 0.3 m for the best match of WEAP solution and measured pile capacity from dynamic and static testing. WEAP details for case study are presented in Table 2. Ultimate pile capacity from ST was defined in accordance with the Davisson criterion and WEAP was performed to find expected blow count per 0.3 m for that pile capacity. Case 1 (after [17]). The prestressed concrete pile (Table 1, pile 1) was dynamically tested during EOID and three restrikes. The soil consisted of about 25.6 m of mainly grey clays followed layer of silty sand. Pile toe elevation was 23.2 m. The water table was at a ground surface level. It can be seen in Table 2 that the side damping coefficient, J,, has high value of 3.609 s/m for EOID and drops out from the row of J, quantities for restrikes. For this reason and because at 243

Time after EOID (days) Fig. 4 Variable Smith damping from adjusted WEAP EOID clayey soil remolding just begins and pore pressure is unstable that value has not taken into account. The skin damping coefficient obtained from WEAP solutions is shown in Figure 4. High initial damping value of 0.984 s/m for the first restrike (1 day after EOID) increased in 2.5 times when 18 days have elapsed after EOID. A total enhancement is 150.0 % with rate of 8.82 % per day. For the considered pile in clay a relationship between the side damping coefficient and elapsed time is very well approximated with a straight line (Figure 5) Js = Jsc (1 + 0.075t) (1) where J,,=O.984 s/m (RSTR-I), t=time in days after EOID for any test following RSTK1. For WEAP solution adjusted to pile capacity from ST, percentage of skin friction and friction distribution along the pile shaft was taken from RSTR-3 results and J, was set by extrapolation using equation 1. WEAP solution with derived J, gave reasonable blow count of 187 b110.3 m. Case 2 (after [17]). Prestressed concrete and closed end pipe piles (Table 2, piles 2 and 3) were dynamically tested during EOID and RSTR-1. They were driven in sand with natural moisture. Percentage of skin friction during ST was calculated by static analysis. Skin friction distribution was taken from results of RSTR-1. The skin damping coefficient obtained from Time after EOID (days) Fig. 5 Variable Smith damping in clay WEAP solutions is shown in Figure 4 as well. Initial damping value of 0.164 s/m for EOID was the same for both piles and increased in 1.4 and 1.1 times for pile 2 and 3, respectively, when 7 days have elapsed after EOID. A total damping enhancement is 40.2 % with a daily rate of 5.75 % for pile 2 and 9.8 % with a daily rate of 1.40 % for pile 3. Taking into account that pile capacity for both pile 2 and 3 varies almost linearly with time [12], a linear damping(time relationship was approximately assumed for both piles (Figure 6). However, J,, from EOID instead of J,, and different coefficient before t is used in the equation 2. For pile 2 Js = JsG (1 + 0.057t) (2) 5 0.P -- 0 4.!? 3 Pile 2 1 -Adjusted WEAP E 5 II- 2.l*=.lse,, +0.057,, D Pile 3 2 3. Jr=Jae,, 4 Adjuded WEAP +0~0,4,, VI 0, 0 5 $0 15 20 Time after EOID (days) Fig. 6 Variable Smith damping in sand 244

For pile 3 Js = J_ (1 + 0.014t) (3) can strongly improve reliability of WEAP solutions. where t=time in days after EOID. WEAP solution for correlation of pile capacity from the static load test showed refusal driving for both piles (Table 2). It is obviously, the rated energy of hammer Vulcan 80~ is not sufficient to mobilize pile capacity developed during the static test. 5. CONCLUDING REMARKS (i) Wave equation analysis enable engineers to predict pile capacity for EOID and restrikes. Adjustment of WEAP solution with the actual force, energy and velocity measured during driving may improve WEAP solution but not enough to receive actual pile capacity at any time after EOID. (ii) For reliable prediction of pile capacity at any elapsed time after EOID, it is necessary to take into account the changes of the pile-soil system with time. (iii) Soil damping is the basic parameter for adjustment WEAP solution with time-dependent soil properties. Suggested procedure was applied for three piles. Obtained adjusted WEAP solutions have demonstrated the enhancement of Smith skin damping constant for clay and sand but the initiai damping value and daily enhancement rate is substantially larger for clay. The initial damping value was taken from the first restrike for clay and from EOID for sand. (iv) On the basis of three tested piles, a linear relationship approximately assumed between the skin damping coefficient and elapsed time after EOID. (v) It is necessary to continue research and collection experimental and computed data for the damping-time relationship because derived results 6. REFERENCES [l] Rausche, F., Gable, G.G., and Likins, G.E. Dynamic Detemzination of Pile Capacity, J. of Geotechnical Engineering, ASCE, Vol. 111, No. 3, pp. 367.387, 1985. [Z] GRL and Associates, Inc. CAPWAP - Case Pile Wave Analysis Program, Continuous Model, Manual, Cleveland, Ohio 1993. [3] Smith, E.A.L. Pile Driving Analyses by the Wave Equation, J. of the Soil Mechanics and Foundation Division, ASCE, Vol. 86, pp. 35-61, 1960. [4] Rausche, F., Hussein, M., Svinkin, M.R. Application of the Wave Equation to Pile Driving Analysis, Proc. of the IV Inter. Conf. on Problem of Pile Foundation Engineering, Saratov, Russia, 1994. [S] Goble, G.G., Rausche, F., and Likins, G. The Analysis of Pile Driving. A State-of-the-art, Proc. of the First Inter. Conf. on the Application of Stress-Wave Theory on Piles, Stockholm, pp. 131.161, 1980. [6] Forehand, P.W. and Reese, J.L. Prediction of Capacity by the Wave Equation, J. of the Soil Mechanics and Foundation Division, ASCE, Vol. 90(2), pp. l-25, 1964. [7] Ramey, G.E. and Hudgins, A.P. Sensitivity and Accwaq of the Pile Wave Equation, Ground Engineering, 10(7), pp. 45-47, 1977. [t?] Gable, G.G. and Rausche, F. Wave Equation Analysis of Pile Driving. WEAP PlOgiYVn, Vol. l-3, U.S. Dept. of Trans. FHWA, Off. of Res. and Dev., Washington, 1976. [9] Hirsch, T.J., Carr, L., and Lowry, L.L. 245

Pile Driving Analysis. Wave Equation User s manual. TTI Program, Vol. 1-3, U.S. Dept. of Trans. FHWA, Off. of Res. and Dev., Washington, 1976. [lo] GRL and Associates, Inc. GRLWEAP Wave equation Analysis of Pile Driving, Manual, Cleveland, Ohio, 1993. [ll] Fellenius, B.H., Riker, R.E., O Brien, A.J., and Tracy, G.R. Dynamic and Static testing in Soil Exhibiting Set-up, J. of Geotechnical Engineering, ASCE, Vol. 115, No. 7, pp. 984-1001, 1989. [12] Svinkin, M.R., Morgano, C.M., and Morvant, M. Pile Capacity as a Function of Time in Clayey and Sandy Soils, Proc., of the Fifth Inter. Conf. and Exhibition on Piling and Deep Foundations, Bruges, Belgium, pp. 1.11.1-1.11.8, 1994. [13] York, D.L., Brusey, W.G., Clemente, F.M., Law, S.K. Setup and Relaxation in Glacial Sand, J. of Geotechnical Engineering, ASCE, Vol. 120, No. 9, pp. 1498-1513, 1994. [14] Schmertmann, J. The Mechanical Aging of Soils. The 25th Tenagi Lecture, J. of Geotechnical Engineering, AXE, Vol. 117, No. 9, pp. 1288-1303, 1991. 1151 Mitchell, J.K. Fundamental Aspects of Thixotropy in Soils, J. of Soil Mechanics and Foundations Division, ASCE, Vol. 86, No. SM3, pp. 19-52, 1960. [I61 Svinkin, M.R. Pile Driving Induced Vibrations as n Source of Industrial Seismology, Proc. of the Fourth Inter. Conf. on the Application of Stress-Wave Theory to Piles, The Hague, The Netherlands, pp. 167-174, 1994. [17] Svinkin, M.R. and Teferra, W. Some Aspects of Determination of Pile Capacity by the Wave Equation, ASCE Structural Congress 94, Session on Application of Stress Wave Theory to Piles, Atlanta, USA, pp. 946-951, 1994. [18] Thompson, C.D. Discussion of quake values determined from dynamic measurements, Proc. of the Third Inter. Conf. on the Application of Stress Wave Theory to Piles, Stockholm, Sweden, pp. 319-322, 1980, No. Description Pile LC gth (4 Depth of pile toe (mm) II 1 I Prestressed concrete I 25.6 I 24.8 610 I[ 610 nlm (305 mm D. hohv center) Hammer Model A--- &, I 46~13 Prestressed concrefe 356 x 356 mm 324 mm O.D. by 6.4 mm thick closed end steel pipe 35.1 27.4 1265 VULCAN Kc 30.5 25.3 64 VUICAN ROC Table 1 Pile and hammer data 246

Table 2 WEAP details of case study 247