EVALUATION OF GROUND STRAIN FROM IN SITU DYNAMIC RESPONSE

Transcription

1 13 th World Conference on Earthqake Engineering Vancover, B.C., Canada Agst 1-6, 2004 Paper No EVALUATION OF GROUND STRAIN FROM IN SITU DYNAMIC RESPONSE Ellen M. RATHJE 1, Wen-Jong CHANG 2, Kenneth H. STOKOE, II 3, and Brady R. COX 4 SUMMARY Evalating the in sit strains indced in the soil dring dynamic experiments is a critical aspect of varios seismic field stdies. This paper compares and contrasts for approaches for evalating in sit soil strains from field measrements of dynamic response. These approaches are either based strictly on a displacement field (displacement-based methods) or on an assmed propagating wave type (wave propagation-based methods). The displacement-based (DB) method tilies displacement-time histories at embedded instrmentation points, along with an assmed displacement field between points, to compte shear strain. Wave propagation-methods traditionally tilie the ratio of particle velocity to wave propagation velocity to compte shear strain. An in sit field experiment, which tilied a vertically vibrating vibroseis trck to dynamically load an instrmented test area within a liqefiable soil deposit, was sed to evalate the varios strain comptation methods. Three wave-propagation methods were considered for this experiment: (1) plane shear wave (PSW) propagation, (2) plane Rayleigh wave (PRW) propagation, and (3) apparent wave (AW) propagation. These methods were compared with the DB method at varios loading levels. The comparison shows that the PSW and PRW methods overpredict mean shear strain levels, as compared with the DB method, by 40% to 80%. These wave-propagation methods do not perform well for this experiment becase they do not represent the wave type that is predominantly shearing the soil. The shear strains from the AW and DB methods compare favorably over a large range of shear strain levels (0.0005% to 0.02%). However, the AW method cannot adeqately track the change in shear strain amplitde after significant pore pressre generation nless a cycle-bycycle comptation is performed. This cycle-by-cycle comptation was facilitated in this stdy by a sinsoidal load, which may not always be the case for in sit measrements. Additionally, one mst consider the dominant wave type that is shearing the soil when sing any wave propagation-based method. This isse is critical for experiments that generate stress wave fields that are different than those in this stdy. 1 Assistant Professor, University of Texas, Astin, TX, USA. e.rathje@mail.texas.ed 2 Assistant Professor, National Chi-Nan University, Pli, Taiwan, wjchang@ncn.ed.tw 3 Milton T. and Jennie C. Graves Professor, University of Texas, Astin, TX, USA. k.stokoe@mail.texas.ed 4 Gradate Research Assistant, University of Texas, Astin, TX, USA. brcox@mail.texas.ed

2 INTRODUCTION Evalating the in sit strains indced in the soil dring dynamic field experiments is critical in many seismic field stdies, sch as blast-indced liqefaction [Rollins et al. 1], in sit nonlinear soil property evalation [Stokoe et al. 2, Zeghal et al. 3], and vibroseis-indced liqefaction [Rathje et al. 4]. For these field stdies, the in sit dynamic response (i.e., acceleration, particle velocity) is recorded with embedded instrmentation at varios points in the sbsrface and sed to compte strain. For geotechnical considerations, shear strain is the strain component that often is most critical, althogh some blast stdies have considered compressive strain [e.g., Veyera et al. 5; Rollins et al. 1]. There are two general approaches to compting strain from in sit dynamic measrements: the displacement-based approach and the wave propagation-based approach. The displacement-based approach tilies displacement-time histories at adjacent measrement points, along with an assmed displacement field between points, to compte strain. Depending on the nmber of measrement points and the directional components of vibration measred, it is possible to compte both compressive and shear components of strain. The wave propagation-based approach tilies the ratio of particle velocity to wave propagation velocity to compte strain. Depending on the directional component of vibration that is recorded, as well as the wave propagation type, both compressive and shear components of strain can be compted. Most previos geotechnical investigations that compted strain components from dynamic measrements have sed displacement-based approaches. Zeghal et al. [3] estimated shear strains from downhole measrements of horiontal acceleration at the Lotng large-scale seismic test (LSST) site in Taiwan. This stdy sed an analytical procedre that comptes shear strain at a point sing displacement vales from three adjacent depths and an expression derived from the differential of a second-order Lagrange interpolating polynomial [e.g., Chapra and Canale 6]. This analytical procedre assmes one-dimensional wave propagation and reslts in strain estimates that are second-order accrate. To compte the in sit shear strains in the Zeghal et al. [3] stdy, the recorded acceleration-time histories were nmerically integrated twice with respect to time to obtain displacement-time histories that were sed in the strain comptations. The downhole accelerometer array sed in this investigation consisted of 4 accelerometers in the top 17 m with the vertical spacing between accelerometers eqal to abot 5 m. Shear strains were compted for low to moderate earthqake shaking (peak grond acceleration at the srface of 0.01 to 0.26 g) and the strains ranged from abot 0.001% to 0.1%. Gohl et al. [7] compted both compressive and shear components of strain from downhole measrements of acceleration dring a blast experiment. Three components of acceleration were measred at two locations separated by a horiontal distance of abot 2.5 m. Doble integration of the acceleration-time histories prodced three orthogonal components of displacement-time histories at each measrement point. These displacement-time histories were sed with small-strain mechanics theory and the relative locations of the measrement points to compte the strain components. Compted vales of shear strain ranged from 0.01% to over 1.0%. These strain estimates were first-order accrate and represent average vales between measrement points. This paper compares for approaches for evalating in sit soil strains, one displacement-based (DB) method and three wave propagation-based (WB) methods. The DB method tilies displacements from the corners of the 4-node sqare array to compte strain at the center of the array. The three wave types considered for the WB methods are: (1) plane shear wave (PSW) propagation, (2) plane Rayleigh wave (PRW) propagation, and (3) apparent wave (AW) propagation. These methods are named based on the assmed wave type that is propagating throgh the soil: shear, Rayleigh, or apparent waves. The AW method is so named becase the motion is not assmed to be one specific wave type. Each of these methods tilies the ratio of particle velocity to wave propagation velocity to compte strain. Data from an in sit liqefaction experiment [Rathje et al. 4] were sed to compare the for strain comptation methods. This experiment tilies a vertically vibrating vibroseis to dynamically load a 1.2 m by 1.2 m by

3 1.2 m reconstitted, liqefiable test specimen located 3.3 m (horiontally) from the vibroseis. Geophones were embedded at 5 locations within the test specimen dring constrction to monitor horiontal and vertical particle velocities for se in the strain comptation methods. STRAIN COMPUTATION METHODS Displacement-Based Methods Displacement-based (DB) strain comptation methods are established strictly on solid mechanics definitions of strain, sch as: i ε i = (1) xi i j γ ij = + (2) x j xi where ε represents normal strain, γ represents engineering shear strain, represents displacement, x represents direction, and i and j are direction sbscripts that take on 1, 2 or 3 to represent the three, orthogonal coordinate dimensions. To compte strain, displacements are measred at known, discrete points in the soil and nmerical methods are sed to estimate the derivatives in eqations (1) and (2). For three-dimensional problems, there are six components to strain (three normal and three shear components). For plane strain problems, only three components of strain (two normal and one shear) are relevant, while for strain components (three normal and one shear) are important for axisymmetric problems. When considering one-dimensional shear wave propagation, which is common in geotechnical earthqake engineering, only shear strain is of interest. The experiment condcted in this stdy involved the vertical vibration of a circlar area at the grond srface, a configration that is axially symmetric (Figre 1a). An instrmented test area was placed along one radial ray path from the sorce. Within this instrmented test area, the locations of the in sit measrement points were chosen to create a 4-node rectanglar array (Figre 1b). For this array, the horiontal direction is defined as x, the vertical direction is, and the displacements measred in these Dynamic Sorce 4 3 x 2b x Body Waves Instrmented Test Area Node 1 (a) (b) Figre 1. (a) Experimental test set p and (b) instrmentation array for strain comptations. (0, 0) 2a 2

4 two orthogonal directions are x and, respectively (Figre 1b). The sides of this rectanglar array measre 2a in the x direction and 2b in the direction. Using this coordinate system, the pertinent strain components are ε x, ε, and γ x. To compte the strain components within the rectanglar array, a formlation was developed that is based on the 4-node isoparametric element formlation often sed in finite element analysis [e.g., Cook et al. 9]. For this formlation, the horiontal and vertical displacements ( x and, respectively) are known at the nodal points and a linear variation of displacement is assmed between nodes. The reslting expressions that describe the displacement variation across an element (element sie: 2a by 2b) in terms of the nodal displacements are: 1 x, ) = [ x1(1 x a)(1 b) + x (1 + x a)(1 b) x 3 ( 1 + x a)(1 + b) + x4 (1 x a)(1 + b)] (3) 1 x, ) = [ 1(1 x a)(1 b) + (1 + x a)(1 b) x a)(1 + b) + (1 x a)(1 (4) x ( 2 ( 2 3 ( 4 + b where ij is the displacement in the i direction (i = x or ) at node j (j = 1 to 4), 2a is the sie of the element in the x-direction, and 2b is the sie of the element in the -direction (Figre 1b). Differentiating these expressions with respect to x and, and incorporating them into eqations (1) and (2), reslts in the following expressions for strain at a point (x, ) within the element: 1 ε x ( x, ) = [ x1(1 b) + x2 (1 b) + x3 (1 + b) x4 (1 + b) ] 4a (5) 1 ε ( x, ) = [ 1(1 x a) 2 (1 + x a) + 3 (1 + x a) + 4 (1 x a) ] 4b (6) 1 x1 1 x2 2 γ x ( x, ) = (1 x a) (1 b) (1 + x a) + (1 b) + 4 b a b a x3 3 x4 4 + (1 + x a) + (1 + b) + (1 x a) (1 + b) b a b a These expressions provide strain vales within the rectanglar element at location (x, ) and are first-order accrate. It is important to note that these expressions are only applicable to rectanglar elements. An arbitrary qadrilateral that has variable side dimensions reqires a more complicated transformation. A detailed derivation for these strain eqations, along with a more general derivation that does not reqire that the instrmentation array be rectanglar, can be fond in Chang [8]. The most critical assmption employed in this strain formlation is the linear variation of displacement between nodes. For this assmption to be valid, the wavelength of the waves traveling throgh the instrmentation array shold be mch larger than the element sie. To ensre that the compted strains are not significantly affected by the linear variation assmption, it is recommended that the larger dimension of the instrmentation array be smaller than 1/5 of the wavelength. )] (7)

5 Wave Propagation-Based Methods Wave propagation-based (WB) strain comptation methods tilie particle velocity and wave propagation velocity to compte varios components of strain [e.g., Richart et al. 10]. These methods assme a onedimensional stress wave traveling throgh the system. The general expression for strain based on wave propagation is: & Strain = (8) V where Strain can be either normal (ε) or shear (γ) strain, & is particle velocity, and V is wave propagation velocity. The mins sign in eqation (8) indicates that the strain is 180 degrees ot of phase with the particle velocity. For normal strains indced by compression waves, compression wave velocity (V c ) is sed in eqation (8) along with the particle velocity measred in the same direction as the direction of compression wave propagation. For shear strains indced by shear waves, shear wave velocity (Vs) is sed in eqation (8) along with the particle velocity measred in the direction perpendiclar to the direction of shear wave propagation. These strain comptations reqire a known direction of wave propagation and an assmed wave type. For the experiment condcted, shear strains were of most interest and comptations focsed on compting this strain component. Considering the experimental set p and the location of the instrmented test area (Figre 1a), the waves generated by the dynamic sorce travel horiontally throgh the test area. Therefore, the horiontal wave propagation velocity shold be sed in eqation (8) along with particle velocities measred in the direction perpendiclar to wave propagation (i.e., vertical in this case). The wave field generated by the dynamic sorce is complex, with shear, compression, and Rayleigh-type srface waves traveling throgh the test area. However, Rayleigh waves carry the majority of energy (68%) and attenate less rapidly (1/R 0.5, R = distance from the sorce) than the body waves [Woods 11]. Therefore, Rayleigh waves shold dominate the dynamic loading for the testing program considered. However, for comparison prposes, three potential wave types were considered: plane shear waves (PSW), (2) plane Rayleigh waves (PRW), and (3) plane apparent waves (AW). The simplest assmption wold involve plane shear wave propagation. Shear strain can be easily compted sing the wave velocity for a horiontally propagating, vertically polaried shear wave (V S,hv ) measred prior to testing. The reslting shear strain expression for the PSW method is: & γ x = PSW method (9) V S, hv where & is the vertical particle velocity. Using the wave velocity measred before testing to compte strain assmes that the soil remains relatively linear dring the entire test seqence. However, this assmption is not valid for many problems of engineering interest (e.g., liqefaction, site response nder high levels of shaking). Althogh assming shear wave propagation may be most simple, it ignores that fact that shear waves are not the dominant wave type shearing the soil in this experiment (Figre 1a). Becase of the location of the test area in relation to the dynamic sorce and becase body waves attenate more qickly than srface waves, Rayleigh-type srface waves are the dominant wave type shearing the soil. However, eqation (8) is not valid for Rayleigh waves becase Rayleigh waves generate both vertical and horiontal motion, and the indced displacement field varies with depth (Figre 2). To develop a valid expression for the shear

6 strain indced by a Rayleigh wave, the far field, analytical soltion for the x and displacement fields [Rayleigh 12] were sed and incorporated into the shear strain definition in eqation (2). The reslting PRW expression for shear strain, which is similar in form to eqation (8), is: γ x V & = R α v PRW method (10) where & is the vertical particle velocity, V R is the Rayleigh wave propagation velocity, and α v is the shear strain ratio. The factor α v is a fnction of Rayleigh wave velocity, Poisson s ratio (ν), loading freqency ( f ), and depth [Chang 8]. Figre 3 shows the variation of α v with normalied depth, /λ (where λ = V R / f ), for V R eqal to 150 m/s and ν eqal to The largest vales of α v occr near the grond srface, becase the displacements are varying most in this area (Figre 2). At /λ greater than 1.0, α v takes on a relatively constant vale. Sensitivity analyses on α v indicate that Poisson s ratio does Figre 2. Variation of horiontal and vertical displacement amplitdes with depth for Rayleigh waves [Richart et al. 10]. α v /λ V R = 150 m/s ν = 0.25 Figre 3. Variation of shear strain ratio (α v ) with depth.

7 not have a significant effect on the variation of α v with depth and wave velocity has only a minor effect. Note that for the experiment performed in this stdy, the instrmentation was located within /λ=0.2 of the grond srface. Similar to the PSW shear strain comptation method, the PRW method is simple and easy to se. Theoretically, only one vertically oriented geophone is reqired to evalate shear strain, along with prior Rayleigh wave velocity measrements of the native soil. Conversely, two receivers can be sed to monitor V R dring testing. The last strain comptation method considered is the apparent wave (AW) method. This method ses the same form of the shear strain expression as the PSW (eqation 9), bt ses the wave velocity measred in sit dring dynamic testing. This wave velocity is called the apparent wave velocity becase most likely it represents shearing from mltiple wave types, as well as reflected waves for the test pit analyed in this stdy. The reslting shear strain expression for the AW method is: & γ x = AW method (11) V ah where & is the vertical particle velocity and V ah is the apparent wave velocity propagating in the horiontal direction. The in sit V ah is obtained from the phase difference between two adjacent sensors separated by a horiontal distance. SHEAR STRAIN COMPARISONS Test Set Up Data from an in sit liqefaction experiment [Rathje et al. 4] were sed to compare and contrast the strain comptation methods. This newly developed testing procedre dynamically loads an in sit soil deposit sing a vertically vibrating vibroseis as the loading sorce. The vibroseis dynamically loads a footing at the grond srface, which generates body waves and srface waves that propagate throgh the soil. The experiment sed in this stdy focsed on the dynamic response of a reconstitted, liqefiable test specimen constrcted in the field and located 3.3 m (horiontally) from the vibrating footing. The general set p is shown in Figre 1a, while a more detailed schematic is shown in Figre 4. The experiment took place at an aggregate qarry in Astin, Texas. The test site is located on the flood plain of the Colorado River, where the natral soil consists of poorly-graded sand with abot 5% fines. The grond water table is located 2.1 m below the grond srface and the native soil is somewhat cemented and non-liqefiable within a meter of the grond srface. The liqefiable test specimen was constrcted within an excavation (1.2 m by 1.2 m by 1.2 m) that was lined with an impermeable liner. The specimen consisted of a poorly-graded aggregate sand and was constrcted within the excavation by water sedimentation. The specimen preparation procedre reslted in a very loose sand specimen (relative density ~ 35%) and allowed instrmentation to be placed within the specimen dring constrction. The embedded instrmentation consisted of liqefaction sensors, which integrate two orthogonally-oriented geophones and a pore pressre transdcer in a single acrylic case. Liqefaction sensors were embedded at 5 locations within the test specimen to monitor excess pore pressre generation, as well as horiontal and vertical particle velocities. The instrmentation locations correspond to a 4-node sqare element and a position at the center of the element (Figre 4). This sensor configration facilitates the se of the proposed displacement-based method, as well as the apparent wave method, which reqires the wave velocity be evalated dring dynamic testing.

8 Vibroseis trck Waterproof liner ~0.8 m Fondation 3.3 m Legend Liqefaction sensor Accelerometer 0.3 m Backfill sand m m m 0.3 m 0.3 m 1.2 m 1.2 m Figre 4. Experimental test set p (not to scale). Staged testing was performed with the vibroseis, in which small shaking levels first were applied followed by increasing levels of shaking. The staged loading allowed shear strain levels to be compared over a large range of amplitdes (~ to 0.015%). For each stage of loading, a 20-H sinsoidal load was applied for 1 second reslting in 20 cycles of load. The loads were applied at 20 H becase this is the lowest freqency that prodces a clean, sinsoidal signal with the crrent vibroseis trck. The test specimens were allowed to rest for thirty mintes between load stages to allow any excess pore pressre to dissipate. Mean Shear Strain Amplitdes Data from one series of in sit liqefaction experiments were sed to compare the shear strain comptation methods. The comparisons were made at the center of the instrmentation array. For the DB method, the shear strain was compted at this point sing the eight displacement-time histories from the 4 corner sensor points (one vertical and one horiontal displacement per sensor) and eqation (7). The displacement-time histories were acqired by nmerically integrating the recorded particle velocity-time histories and incorporating a baseline correction. The wave propagation-based (WB) methods compte strain at the sensor locations, where particle velocity is measred. To compare with the DB shear strain compted at the center of the array, the WB shear strains were compted at the for corner sensors locations and arithmetically averaged in the time domain to obtain a shear strain time history at the center of the array. For the PSW method, the V S,hv vales sed in the shear strain calclation were obtained from crosshole shear wave velocity measrements condcted before dynamic loading. At a depth of 0.3 m, V S,hv was measred as 83 m/s, and at a depth of 0.9 m, it was measred as 109 m/s. For the PRW method, the Rayleigh wave velocity (V R ) was taken as 150 m/s for the applied 20 H loading, based on field vibration tests condcted prior to testing. The reason V R is larger than V S,hv in this experiment is that V S,hv represents waves only traveling in the liqefiable soil, while V R represents srface waves traveling throgh both the liqefiable soil and abot 5 m of the nderlying, stiffer soils. The α v vales were calclated based on the depths of the geophones, a V R of 150 m/s, and ν = The corresponding vales of α v for the sensor depths of 0.3 m and 0.9 m are and -1.49, respectively. For the AW method, the apparent phase

9 velocities (V ah ) at the geophone depths (0.3 m, 0.9 m) were compted for each testing stage from the phase difference between the two vertical geophones spaced 0.6 m apart (sensors 4-3 and sensors 1-2 in Figre 4). The measred vales of V ah varied somewhat between testing stages, ranging between 120 m/s and 180 m/s. These vales are larger than the measred crosshole shear wave velocities. Figre 5 is a plot of the mean shear strain amplitdes (averaged over the entire shear strain-time history) at the center of the array compted by the WB methods verss those compted by the DB method. For the WB methods, the shear strains in Figre 5 are the reslt of averaging the strains calclated from the 4 sensor points. The data in Figre 5 represent eight separate testing stages, with over an order of magnitde range in shear strain level. Figre 5 indicates that the AW method matches very well with the DB method, especially for shear strain levels less than 1.0x10-2 %. In general, the difference between the AW method and the DB method is less than 10%. The shear strain amplitdes calclated by the PSW and PRW methods have similar vales and are 40% to 80% larger than the DB method. Becase of the good agreement between the mean shear strains compted by the DB and AW methods, the remainder of this stdy focsed on these two shear strain comptation methods. 2.5 Mean Shear Strain by WB Method (x10-2 %) PRW PSW AW Mean Shear Strain by DB Method (x10-2 %) Figre 5. Comparison of mean shear strains compted by wave propagation-based (WB) and displacement-based (DB) methods Shear Strain-Time Histories For a more complete comparison of the shear strain comptation methods, fll shear strain-time histories were evalated by the DB and AW methods (Figre 6). Two testing stages were chosen for comparison; a small loading level where no excess pore pressre was generated and a large loading level where significant excess pore pressre was generated. In the small loading stage (Figre 6a), the shear straintime histories compted by the DB and AW methods are very similar throghot dynamic loading and the shear strain amplitdes are relatively constant. However, in the large-strain test (Figre 6b) the shear strain-time histories from the DB and AW methods are noticeably different after abot the third loading cycle. The shear strain amplitdes compted by the DB method vary considerably between loading cycles, while the shear strain amplitdes compted by the AW method remain relatively constant. In

10 Shear Strain (x10-3 %) AW DB Time (sec) (a) Shear Strain (x10-3 %) AW DB Time (sec) (b) Figre 6. Shear strain-time histories from the DB and AW methods for a (a) small loading stage and (b) large loading stage. fact, the peak shear strain from the DB method is abot 55% larger than from the AW method. This difference at large loading levels is also seen in Figre 5, where the mean AW shear strain is smaller than the mean DB shear strain for the largest strain level. Conseqently, althogh the mean shear strain amplitdes from the DB and AW methods may be qite similar (Figre 5), the maximm shear strain and the variation in shear strain amplitde between cycles may be different. Several isses were considered to explain the differences in the shear strain-time histories. The AW method ses only vertical particle velocity data to compte shear strain, while the DB method ses both horiontal and vertical particle velocity data. To demonstrate the effect of the horiontal motion on the shear strains compted by the DB method, the shear strain-time history at the center of the array was compted sing both vertical and horiontal displacements, as well as sing only vertical displacements. Figre 7 displays the DB shear strain-time history compted from vertical motion only, along with the shear strain-time history reslting from sing both horiontal and vertical motions. The two time histories are very similar, particlarly dring the first three cycles of motion. After abot 0.5 s, the contribtion from the horiontal component becomes most evident, with the peak shear strain from horiontal and vertical motion abot 15% greater than the peak shear strain from only vertical motion. Horiontal motion contribtes to the indced shear strain for this experiment becase Rayleigh waves are dominating the dynamic loading. The displacement field indced by a Rayleigh wave (Figre 2) incldes a variation of the horiontal displacement with depth which contribtes to the shearing of the soil. Figre

11 20 V and H components V component only Shear Strain (x10-3 %) Time (sec) 1.2 DB Method Figre 7. DB method shear strain-time histories compted sing vertical motion only and sing both vertical and horiontal motions. 7 indicates that sing only the vertical component of motion in a DB strain calclation can reslt in an nderprediction of shear strain as large as 15% when Rayleigh waves are the dominant wave type shearing the soil. However, this does not explain the 55% discrepancy observed between the AW and DB methods (Figre 6b). Another isse to consider when reconciling the shear strains compted by the DB and AW methods is the variation in the apparent wave velocity from loading cycle to loading cycle. For the previos analyses, cross-power spectral analysis was sed to calclate an average V ah for the entire stage of loading, and this wave velocity was then sed in the AW shear strain calclation. However, it is also possible to compte the apparent wave velocity for each harmonic cycle of motion and se these wave velocities in a cycle-bycycle AW shear strain calclation. A change in V ah from cycle to cycle indicates a change in phasing between the recordings, which leads to changes in the relative displacement and strain between points. For the large loading stage analyed in Figres 6b and 7, the apparent wave velocities between sensors 4 and 3 and sensors 1 and 2 (see Figre 4) for each loading cycle were compted and are shown in Figre 8a. Srprisingly, the apparent wave velocity generally increases with each cycle, particlarly after cycle 10. For sensors 4 to 3 (depth 0.3 m), the apparent wave velocity more than dobles dring dynamic loading. For comparison, the vales of V ah compted when sing the entire dration of loading are also shown in Figre 8a. Becase these V ah vales represent the average phase difference between adjacent sensors over the fll dration of loading, they fall in between the minimm and maximm V ah vales compted by the cycle-by-cycle method. The data in Figre 8a also are srprising in that different wave velocities are measred at 0.3 m and 0.9 m depths. If the indced motions were only from a single Rayleigh wave, the wave velocity measred at different depths wold be the same. The data in Figre 8a sggest that other wave types are present and are contribting to the motion in the instrmented test pit. It shold be emphasied that the apparent wave velocity is not eqal to the shear wave velocity between the sensors, especially for the complicated wave field encontered in the developed testing techniqe,

12 300 Apparent wave velocity, V ah (m/s) Case 4 to 3 Case 1 to 2 Avg V ah = 151 m/s Case 4 to 3 Avg V ah = 169 m/s Case 1 to Cycle (a) 20 AW (cycle by cycle) DB (V component only) Shear Strain (x10-3 %) Time (sec) (b) Figre 8. (a) Variation of apparent wave velocity with loading stages, and (b) shear strain-time histories from the DB method and the cycle-by-cycle AW method. which also incldes complications added by the bondary conditions at the edges of the reconstitted test specimen. Therefore, the variation in the apparent wave velocities shown in Figre 8a does not represent the variation in the shear wave velocity or shear stiffness of the test specimen. It is not clear why the apparent wave velocity increases dring dynamic loading. One possible explanation is that after a significant amont of pore pressre is indced the wave propagation behavior changes and it cases an increase in apparent wave velocity and a decrease in phase difference between adjacent sensors. This may be the reslt of the change in the impedance contrast at the edges of the test specimen after significant pore pressre is indced. In contrast to the large loading level where significant pore pressre was indced, the apparent wave velocities did not vary from cycle to cycle in the small stage loading levels where no excess pore pressre was indced. This observation spports the theory that the change in apparent wave velocity is related to pore pressre generation and changes in wave propagation behavior in the test pit. The apparent wave velocities in Figre 8a were sed to compte shear strains on a cycle-by-cycle basis sing the AW method. In this calclation, the shear strain at each sensor point was compted sing the

13 vertical particle velocity and the corresponding apparent wave velocity for that cycle. The AW shear strain at the center of the array was compted by averaging the shear strains at the for nodal points. The shear strain-time history at the center of the array sing the DB method (vertical motion only) and the cycle-by-cycle AW method are shown in Figre 8b. The reslts show excellent agreement between the two methods. Additionally, the AW method now shows a redction in shear strain amplitde dring later loading cycles, similar to the DB method. This decrease in shear strain amplitde is de to the increased apparent wave velocity for these cycles and cannot be tracked by the original AW method becase it ses only one vale of V ah. One final comparison was made to investigate the accracy of a two-node DB method. This method reqires only particle motion at two adjacent points (e.g., sensors 4 and 3 in Figre 4), and for shear strains the motion is measred in the direction perpendiclar to the direction of wave propagation. The two-node DB is most appropriate for one-dimensional wave propagation problems that do not have motion in other directions contribting significantly to the indced strains. For a two-node DB method, the shear strain can be simply evalated from the displacements at two adjacent points. For example, the shear strain between sensors 4 and 3 in Figre 4 can be expressed as: = 3 4 γ x (12) L43 where 3 and 4 are vertical displacements at sensors 3 and 4, respectively, and L 43 is the distance between sensors 3 and 4. Vertical displacements are sed here becase this is the direction perpendiclar to wave propagation for this experiment. Figre 9 compares the two-node DB shear strain-time history from sensors 3 and 4 with the cycle-by-cycle AW shear strain-time history for sensor 4. The shear-strain time histories show excellent agreement, indicating that for one-dimensional wave propagation problems the cycle-by-cycle AW method and the two-node DB method prodce similar reslts. However, it is important to monitor the change in wave propagation velocity in the AW method to ensre that the change in phasing can be taken into accont to prodce accrate shear strain-time histories. This isse is most critical when significant nonlinearity, inclding liqefaction, is indced in the soil. Shear Strain (x10-3 %) Time (sec) Case 4 AW, = 0.3 m 2 Node DB, = 0.3 m Note: cycle-by-cycle apparent wave velocities sed Figre 9. Shear strain-time histories from the two-node DB method and the cycle-by-cycle AW method

14 CONCLUSIONS The evalation of in sit shear strains indced dring dynamic field testing has gained interest recently de to the installation of downhole array instrmentation [e.g., Zeghal et al. 3] and the development of direct in sit liqefaction testing and nonlinear soil property evalation techniqes [e.g., Rollins et al. 1, Rathje et al. 4, Stokoe et al. 2]. The comptation of the shear strains indced in the soil relies on measrements of dynamic response (acceleration and/or particle velocity) at varios locations in the soil. There are two basic approaches to evalating strain from dynamic measrements: the displacement-based (DB) approach and the wave propagation-based (WB) approach. The DB approach nmerically integrates the measred velocity- or acceleration-time histories to obtain displacement-time histories that are sed in conjnction with the solid mechanics definition of strain to compte strain-time histories. When sing this approach, the distance between measrement locations shold be small relative to the wavelength of the waves shearing the soil. The WB approach comptes strain from the ratio of particle velocity to wave velocity. Different directions of particle velocity and types of wave velocities are sed to compte varios components of strain. This stdy focsed on comparing shear strains compted by the DB method and three WB based methods (plane shear wave, plane Rayleigh wave, and apparent wave methods). Dynamic response measrements from an in sit liqefaction experiment were sed for the comparisons. When comparing mean shear strains over a large range of shear strain levels (0.0005% to 0.02%), the plane shear wave and plane Rayleigh wave WB methods predict shear strain levels 40% to 80% larger than the DB method. However, the apparent wave WB method predicts mean shear strains that are very similar to the DB method. This comparison indicates the importance of sing the appropriate wave velocity in a wave propagation-based shear strain evalation method. Althogh mean shear strains compted by the DB and AW methods were similar, details in the fll shear strain-time histories did not always agree as well. These differences arise becase the DB acconts for two isses that the AW method does not: displacements parallel to the direction of wave propagation and changes in phasing (i.e., apparent wave velocity) between measrement points as significant nonlinearity is indced. For the testing configration and wave types considered in this stdy, incorporating the horiontal displacements in the DB strain calclation reslted in a 15% increase in peak strain amplitde. This isse was only significant in this experiment becase Rayleigh waves were employed as the dynamic loading and Rayleigh waves indce a displacement field that involves a variation in horiontal displacement with depth. This isse wold not be significant for one-dimensional shear wave propagation. For loading levels where significant nonlinearity and/or liqefaction is indced, the phase difference between measrement points changes, which reslts in changes in the relative displacement between these points and the compted strain levels. This phenomenon can only be captred by the AW method if the apparent wave velocity is compted on a cycle-by-cycle basis. For this stdy, the cycle-bycycle AW method prodced shear strain-time histories that were in good agreement with the DB method. However, the cycle-by-cycle V ah calclation was facilitated in this stdy by the fact that a sinsoidal load was applied. This comptation wold be more difficlt if a non-sinsoidal load was sed. Conseqently, the DB shear strain comptation method is preferred becase it can best track changes in shear strain amplitde as wave propagation behavior changes. This isse is most important when significant nonlinearity and/or liqefaction are indced. ACKNOWLEDGMENTS Financial spport was provided by the National Science Fondation nder the CAREER award CMS and the U.S. Geological Srvey nder NEHRP grant 00HGGR0015. This spport is grateflly acknowledged. P. Axtell, J.Y. Chen, K. Hairbaba, T.Y. Hsieh, I. Karatas, Y.C. Lin, A. Sharma, and C.

15 Viyanant all graciosly assisted in the field testing. Any opinions, findings and conclsions or recommendations expressed in this material are those of the athors and do not necessarily reflect the views of the National Science Fondation. REFERENCES 1. Rollins, K.M., Lane, J.D., Nicholson, P.G., Rollins, R.E. Liqefaction Haard Assessment sing Controlled-Blasting Techniqes. Proceedings, 11th International Conference on Soil Dynamics & Earthqake Engineering and 3 rd International Conference on Earthqake Geotechnical Engineering, Berkeley, California, USA, 2004, Vol. 2: Stokoe, K.H., Axtell, P.J., and Rathje, E.M. Development of an In Sit Method to Measre Nonlinear Soil Behavior. Third International Conference on Earthqake Resistant Engineering Strctres, Malaga, Spain, Zeghal, M., Elgamal, A.W., Tang, H.T., and Stepp, J.C. Lotng Downhole Array II: Evalation of Soil Nonlinear Properties. ASCE Jornal of Geotechnical Engineering, 1995, 121(4): Rathje, E.M., Chang, W.-J., and Stokoe II, K.H. Development of an In Sit Dynamic Liqefaction Test. sbmitted for pblication in ASTM Geotechnical Testing Jornal. 5. Veyera, G.E., Charlie, W.A., and Hbert, M.E. One-Dimensional Shock-Indced Pore Pressre Response in Satrated Carbonate Sand, Geotechnical Testing Jornal, ASTM, 2002, 25(3), Paper ID GTJ _253, 6. Chapra, S.C. and Canale, R.P. Nmerical Methods for Engineers: with programming and software applications, 3 rd Edition. McGraw Hill, Boston, MA, Gohl, W. B., Howie, J.A., and Rea, C.E. Use of Controlled Detonation of Explosives for Liqefaction Testing. Proceedings, 4 th International Conf. on Recent Advances in Geotechnical Earthqake Engineering and Soil Dynamics, San Diego, CA, Chang, W.-J. Development of an In Sit Dynamic Liqefaction Test, Ph.D. Dissertation, University of Texas at Astin, 316 pp, Cook, R.D., Malks, D.S., and Plesha, M.E. Concepts and Applications of Finite Element Analysis, 3 rd Edition. John Wiley and Sons, New York, NY, Richart, F. E., Hall, J. R., and Woods, R. D. Vibration of Soils and Fondations. Prentice-Hall, Inc., New Jersey, Woods, R. D. Screening of srface waves in soils, Jornal of the Soil Mechanics and Fondations Division, ASCE, 1968, 94(SM4): Rayleigh, L. On waves propagated along the plane srface of an elastic solid. Proceedings of the London Mathematical Society, 1885, 17:4-11.