Geotechnical Testing Journal

Geotechnical Testing Journal Andhika Sahadewa,1 Dimitrios Zekkos,2 Richard D. Woods,2 and Kenneth, H., Stokoe II3

DOI: 10.1520/GTJ20140016

Field Testing Method for Evaluating the Small-Strain Shear Modulus and Shear Modulus Nonlinearity of Solid Waste VOL. 38

/ NO. 4 / JULY 2015

Copyright by ASTM Int'l (all rights reserved); Wed Jun 10 10:57:19 EDT 2015 Downloaded/printed by University of Michigan (University of Michigan) pursuant to License Agreement. No further reproductions authorized.

Geotechnical Testing Journal

doi:10.1520/GTJ20140016

/

Vol. 38

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No. 4

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July 2015

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available online at www.astm.org

Andhika Sahadewa,1 Dimitrios Zekkos,2 Richard D. Woods,2 and Kenneth, H., Stokoe II3

Field Testing Method for Evaluating the Small-Strain Shear Modulus and Shear Modulus Nonlinearity of Solid Waste Reference Sahadewa, Andhika, Zekkos, Dimitrios, Woods, Richard D., and Stokoe, Kenneth, H., II, “Field Testing Method for Evaluating the Small-Strain Shear Modulus and Shear Modulus Nonlinearity of Solid Waste,” Geotechnical Testing Journal, Vol. 38, No. 4, 2015, pp. 1–15, doi:10.1520/GTJ20140016. ISSN 0149-6115

ABSTRACT Manuscript received January 28, 2014; accepted for publication April 2, 2015; published online May 26, 2015.

Dynamic properties of solid waste are needed to reliably evaluate the seismic response of landfills. A testing method for investigating the dynamic properties of solid waste in situ has been implemented at various landfills. The field method is primarily aimed at evaluating

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Department of Civil and Environmental Engineering, Univ. of Michigan, Ann Arbor, MI 48109 (Corresponding author), e-mail: [email protected]

shear wave and compression wave velocities at small strains as well as the shear modulus

Department of Civil and Environmental Engineering, Univ. of Michigan, Ann Arbor, MI 48109.

relationship between shear modulus and shearing strain was investigated by applying

Department of Civil, Architectural and Environmental Engineering, Univ. of Texas, Austin, TX 78712.

component geophones. The testing method also permitted in situ assessment of the effect

reduction versus shearing strain relationship of solid waste. In this study, shear modulus nonlinearity was successfully evaluated for shearing strains ranging from 10–4 to 0.2 %. The dynamic horizontal loads applied by a mobile field shaker at the waste surface in a stagedloading sequence. The solid waste response was measured with a buried array of threeof confining stress and waste variability on the dynamic properties of solid waste. Loadsettlement measurements and in situ unit weight measurements were also made. Testing equipment, field setup, testing procedure, data analysis, and examples of test results are presented. Keywords dynamic properties, compression wave velocity, shear wave velocity, field testing, nonlinear shear modulus, shearing strain, solid waste

Copyright V 2015 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. Copyright by ASTM Int'l (all rights reserved); Wed Jun 10 10:57:19 EDT 2015 Downloaded/printed by University of Michigan (University of Michigan) pursuant to License Agreement. No further reproductions authorized. C

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Introduction The 1994 Northridge Earthquake demonstrated that landfills are seismically sensitive infrastructure systems (Augello et al. 1995; Matasovic et al. 1995). Excessive displacement of the waste during an earthquake may result in slope instability or damage to the landfill containment or cover system. Landfill failures impact the environment, public health, and may lead to financial losses or loss of life (e.g., Eid et al. 2000; Koelsch et al. 2005; Merry et al. 2005; Zekkos et al. 2013). Subtitle D regulations (U.S. EPA 1995) require the seismic design and analysis of landfills in areas of modest to high seismicity. Dynamic properties of solid waste are important input parameters in assessing the seismic performance of landfills. Seismic site response analysis requires dynamic properties in the linear and nonlinear shearing strain range. In the smallstrain range (i.e., the linear range), properties include shear wave velocity (Vs), the associated small-strain shear modulus (Gmax), and small-strain material damping ratio (kmin). These linear dynamic properties of solid waste were investigated in the laboratory and in situ (e.g., Kavazanjian et al. 1996; Rix et al. 1998; Zekkos et al. 2008; Sahadewa et al. 2011; Stokoe et al. 2011; Zekkos et al. 2014). In the nonlinear range, properties include the normalized shear modulus reduction and material damping increase as a function of shearing strain. The nonlinear dynamic properties of solid waste have been historically studied using two approaches: back-calculation analysis of the seismic response of instrumented landfills (e.g., Augello et al. 1998; Matasovic and Kavazanjian 1998; Elgamal et al. 2004) and large-specimen laboratory testing (e.g., Lee 2007; Zekkos et al. 2008; Yuan et al. 2011). Back-calculation analysis was performed using ground motion records from the Operating Industries, Inc. (OII) landfill, in Monterey Park, CA. Although this landfill was studied extensively, different back-calculation approaches implemented by researchers resulted in significant differences in the developed nonlinear shear modulus reduction and material damping curves (Kavazanjian 2006). In addition, the OII landfill included a mix of municipal solid waste (MSW), large quantities of soils, and liquid hazardous waste (Matasovic et al. 1995), so it may not necessarily be considered a typical modern MSW landfill. Large-specimen laboratory testing methods, in particular cyclic triaxial, resonant column, and cyclic simple shear, have also been used to evaluate the nonlinear dynamic properties of solid waste. Laboratory testing always involves reconstitution of solid waste specimens since recovering “undisturbed” samples of solid waste has proven to be not feasible. In addition, the testing apparatus and specimens must be relatively large in size to accommodate the larger waste particles (Zekkos et al. 2008). The use of mobile field shakers on instrumented ground was successfully applied to evaluate nonlinear dynamic properties, as well as liquefaction potential, in a variety of geomaterials

(e.g., Phillips 2000; Axtell et al. 2002; Stokoe et al. 2001; Rathje et al. 2001; Rathje et al. 2005; Kurtulus 2006; Cox et al. 2009; Park 2010; Stokoe et al. 2011). Nevertheless, in situ evaluation of nonlinear dynamic properties of solid waste using mobile field shakers has not been performed before this study and the associated work in Stokoe et al. (2011). Mobile field shakers provide an unprecedented opportunity to evaluate nonlinear dynamic properties of solid waste in situ without the limitations mentioned from either back-calculation analysis or large-specimen laboratory testing. In this paper, the implementation of a field testing program for in situ evaluation of dynamic properties of solid waste is described. The work expands on previous relevant studies (Stokoe et al. 2006,2011; Park 2010). In addition, complimentary seismic wave propagation velocities in different propagation and polarization directions and their in situ stress dependency are studied using crosshole and downhole testing at small-strains. Shear modulus reduction curves are developed in situ by applying a dynamic load using mobile field shakers on a landfill site. The response of solid waste during testing is measured using an array of embedded geophones. This field testing program was conducted in three Subtitle D landfills in Texas, California, and Arizona, as well as a Class I hazardous waste landfill in an undisclosed location in the US. Zalachoris (2010) tested solid waste at a pre-Subtitle D site in a Texas landfill using a simpler experimental setup as part of a proof-of-concept test for this study.

General Testing Procedure Dynamic field testing in the small-strain (linear) range employs small-scale crosshole and downhole seismic testing using source rods and a hand-held hammer. The nonlinear dynamic testing consists of steady-state small to large strain testing in a stagedloading sequence using mobile field shakers. Embedded threecomponent geophone sensors are used to measure particle velocity time-histories in the solid waste. The general testing configuration is illustrated in Fig. 1. The dimensions shown are for testing executed at the Los Reales landfill in Arizona. At each instrumented site, these dimensions were varied, tailoring the test to the existing conditions and the testing objective. Overall, the sensors are located in the vicinity of the footing, where the shearing strains are largest, so that the nonlinear response of the waste can be captured. The collected data are used to calculate Vs, compression wave velocity (Vp), shear modulus (G), and shearing strain (c) at each instrumented site. A load–settlement curve for the footing is also generated by monitoring the vertical displacement during application of static vertical loads by jacking against the dead weight of the mobile shaker. Unit weight is also evaluated in situ as described by Zekkos et al. (2006).


SAHADEWA ET AL. ON DYNAMIC PROPERTIES OF SOLID WASTE

FIG. 1 Field testing setup: (a) plan view and (b) cross-section (dimensions in meters).

EQUIPMENT AND INSTRUMENTATION

Mobile Field Shakers Steady-state dynamic testing requires a well-controlled dynamic loading source. Thumper and T-Rex, two mobile field shakers of the George E. Brown, Jr. Network for Earthquake Engineering Simulation at the University of Texas at Austin (NEES@UTexas), are used. These mobile field shakers are equipped with a mounted servo-hydraulic vibrator that applies dynamic loads to a rigid plate with adjustable frequency, amplitude, number of loading cycles, and shaking direction. Thumper and T-Rex are capable of generating dynamic loads up to 27 kN (6 kips) and 133 kN (30 kips), respectively. In addition, Thumper and T-Rex can be used to apply vertical hold-down forces up to 36 kN (8 kips) and 178 kN (40 kips), respectively. Thumper is equipped with a crane for heavy-load lifting that is used for field test preparation. T-Rex has a hydraulic cylinder at the rear of the machine that can be used to push a sampler, or sensors, into the ground. Detailed technical specifications on these mobile field shakers can be found in Stokoe et al. (2004,2008) and Menq et al. (2008). 3D Geophone Sensor Triaxial motion transducers are installed in the receiver boreholes at preselected elevations. These sensors must be selected

for appropriate sensitivity and frequency response. The 3D geophone sensor that is used in these tests, Fig. 2, is 7.62 cm (3 in.) in diameter and 3.81 cm (1.5 in.) thick, made of acrylic, and containing three independent single-degree-of-freedom geophones in a triaxial array. Slow-set epoxy resin is used to fill the acrylic case and to hold the geophones in place. A counterweight is installed so that the center of gravity (c.g.) of the whole unit coincides with the c.g. of the cylindrical acrylic case to minimize rocking along the horizontal axis. A square shaped acrylic neck is also installed at the top of the case for attaching a guide rod to ensure proper sensor orientation during installation in a borehole. The use of geophones has several advantages. First, the coil–magnet sensor portion of a geophone requires no external power, reducing the required wiring and embedded instrumentation relative to other sensors. In addition, a geophone is a rugged and economical transducer. Geophones with a natural frequency lower than the frequencies of interest in the field testing are selected. Specifically, 28-Hz geophones (GS-14-L9 of Geospace Technologies Corp.) are used as the sensing element. A 1.870 kilo-Ohm resistor, equivalent to 50 % critical damping in the geophone, is installed to create a well-damped output response curve. Each geophone is calibrated independently to obtain its individual calibration response curve. Other sensors,


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FIG. 2 3D geophone sensor: (a) top view and (b) side view.

such as microelectromechanical system (MEMS) accelerometers, could be used as well (e.g., Cox 2009). Load Cell, Linear Potentiometer, and Power Supply A load cell and three identical linear potentiometers are used to measure load and surface settlement, respectively, during application of vertical static loads. Two 1020-series Interface load cells with maximum capacities of 111 kN (25 kips) and 222 kN (50 kips) are used. The larger capacity load cell is used in vertical load applications up to 133 kN (30 kips). Linear potentiometers are used as the displacement transducer and have a full-scale capacity of 0 to 5.1 cm (0–2 in.) with a measurement precision of 60.005 cm (0.002 in.). The load cells and potentiometers are powered by a 10-VDC Agilent E3620 power supply. Function Generator and Data Acquisition System An Agilent 33120A function generator is used to drive the shaking mechanism of Thumper and T-Rex with a sinusoidal signal at a specified amplitude and frequency for a given number of cycles. A VXI-technology multichannel dynamic signal analyzer (DSA) is used to record output signals from the 3D geophones, load cell, linear potentiometers, driving signal from the function generator, and ground force acceleration from the loading plate of the mobile shakers. This DSA is equipped with 16-bit A/D modules that are capable of recording up to 72 channels with a maximum sampling frequency of 51.2 kHz per channel. This DSA has high resolution and high sampling frequency and is needed to ensure adequate sensor output recording. TESTING PROCEDURE

The in situ testing procedure involves site preparation, geophone installation, placement of precast concrete footing, and load–settlement testing in conjunction with crosshole and downhole seismic testing, steady-state linear and nonlinear dynamic testing, solid waste sampling, and in situ unit weight measurements. Each step is discussed in detail below.

Site Preparation and Geophone Installation Field testing is performed on locations where solid waste is typically covered by daily soil cover. Because shearing strains attenuate with depth during dynamic loading, removing the soil cover entirely and working directly on top of solid waste would be ideal. However, this approach is generally impractical because of uncertainties in waste support capacity and odor concerns. The site is graded so that sufficient soil cover remains to bridge uneven solid waste and to minimize odor concerns. A 2.5 cm (1 in.) soil cover has been found sufficient. A thin soil cover permits generation of the largest shearing strains in the solid waste; hence inducing pronounced nonlinear behavior. After the excess soil cover is removed, ropes and nails are used to create grid lines on the ground as references and markers to designate the locations of key elements, boreholes, concrete footing or shaker load plate, and crosshole source rods. In addition, an elevation reference is established for borehole drilling and sensor installation. The contact area of the concrete footing or mobile field shaker load plate is leveled manually. In the steady-state dynamic testing, a flat horizontal contact between the loading mechanism and ground is important to generate strong wave propagation, reduce the amount of footing rocking, and ensure axisymmetric mean confining stress and uniform axial strain distributions under the contact area. Two boreholes are prepared for geophone installation. A core barrel with an o.d. of 10.2 cm (4 in.) and length of 60.9 cm (24 in.) is used to excavate the boreholes. The core barrel is pushed into the solid waste using the hydraulic cylinder attached to T-Rex. Important considerations in creating the geophone boreholes are: (1) minimizing disturbance in the solid waste; and (2) maintaining verticality. The solid waste recovered from inside the core barrel is visually assessed and collected in sealed bags. After the target depth is reached, a thin-walled PVC pipe is inserted as a casing in each borehole to prevent the boreholes from collapsing. During geophone installation, a portable gas detector is used to assure that landfill gas levels remain below a safety limit.



Geophone units are installed using an aluminum hollow rod with a square cross-section. This rod is attached to the square neck on the geophone case (Fig. 2). A compass and a mark on the square rod are used as references to properly orient the geophones and to place them at the desired depth. Correct orientation and depth of the geophones are essential in the sensor installation stage. The rod and geophone are lowered into the borehole by hand to the desired depth. The PVC pipe is then retracted from the borehole. Subsequently, a small amount of soil is used to fill the gap between the geophone and borehole wall so that good coupling is obtained. Additional soil is also used to bury the geophones. The soil is lightly compacted using 1-cm (0.4-in.) and 2-cm (0.8-in.) diameter steel rods. Two 1-cm (0.4-in.) diameter steel rods are pushed against the sensor top cap to hold the sensor in place, while the square hollow rod is carefully decoupled from the sensor so that there is no change in its orientation. The steel rods are then retracted from the borehole. The finer fraction of the solid waste is used to fill the borehole in lifts and the waste is compacted by tamping with a 2.5-cm (1-in.) diameter wooden rod. In this fashion, the geophone at the lowest elevation is installed. Subsequently, the deepest geophone in the second borehole is placed using the same procedure. After the two deepest geophones have been installed, two more geophones at each of the shallower depths are similarly installed. After all geophones have been installed, the precast concrete footing is placed on the ground using Thumper’s crane. If the concrete footing is not used, the loading plates of the mobile shaker are used. Use of the footing permits the load to be applied over a smaller contact area, inducing higher stresses at the surface. The concrete footing has a diameter of 91.4 cm (36 in.) and thickness of 22.9 cm (9 in.), and is designed based on recommendations from Park (2010). The footprint of the concrete footing needs to be large enough relative to the instrumented waste volume so that plane wave propagation over the instrumented ground is reasonably approximated. The footing needs to be thick enough so that it is considered rigid, but not too thick so that rocking motions during steady-state horizontal shaking are reduced. A circular footing shape is selected so that axisymmetry can be assumed in analyzing mean confining stress and axial strain distributions beneath the footing. Geophone wires are routed through cable access holes in the footing. Hammer impact locations on the footing for downhole testing are shown in Fig. 1, with vertical impacts for compression wave (P-wave) generation and horizontal impacts for shear wave (S-wave) generation. Three crosshole source rods are installed outside the test pad using the hydraulic cylinder at the back of T-Rex. The distance between the source rods and the footing is selected to be as short as possible, but also long enough to allow the mobile field shakers to straddle the footing and not interfere with the rods (see Fig. 1).

Staged Load Testing Field testing is performed in a staged loading sequence as illustrated in Fig. 3. First, crosshole and downhole seismic testing are performed without application of a static vertical load on the footing. Subsequently, a predetermined static vertical load is applied to the footing using a hydraulic jack reacting against the mobile shaker to perform load–settlement testing. Crosshole and downhole seismic testing are performed again at this vertical static load. The vertical static load is released and then reapplied using the mobile shaker actuator. Then a steady-state horizontal excitation is applied to the footing using the mobile field shaker actuators. These steps are repeated for different static vertical loads in an increasing load sequence as illustrated in Fig. 3.

Crosshole and Downhole Seismic Testing Crosshole and downhole seismic testing are performed to investigate the velocities of small-strain compression and shear waves. These tests are performed at different levels of static vertical load so that the effect of confining stress on these properties can be evaluated. The source for the crosshole seismic tests consists of tapping the crosshole source rods vertically using a hand-held hammer. Horizontally propagating compression waves (PX) and horizontally propagating shear waves with vertical particle motion (SXZ) are simultaneously generated. The seismic waves generated by this impact are captured by a pair of 3D sensors that are located at the same depth as the corresponding source rod tip. The hand-held hammer is instrumented with an accelerometer that is used to trigger the time record and also determine time “zero” on the record using a pre-trigger capture mode. Ten taps are stacked to increase the signal-to-noise ratio of the recorded waveforms. Data are recorded at a sampling frequency of 51.2 kHz and a pre-trigger time of 7.5 ms. The resulting wave velocities are designated as Vp-X and Vs-XZ for the PX and SXZ, respectively. Small-scale downhole testing is performed by tapping several impact points on concrete footing (shown in Fig. 1). Vertically propagating compression waves (PZ) are generated by tapping the top surface of the concrete footing with the hand-

FIG. 3

General testing sequence.


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held hammer. Compression wave propagation is captured by the vertically oriented geophones. The resulting compression wave velocity is designated as Vp-Z. Vertically propagating shear waves with horizontal particle motion in the X (SZX) and Y (SZY) axes are generated by tapping the sides of the concrete footing. The horizontally oriented geophones capture these shear waves. The resulting wave velocities are designated as Vs-ZX and Vs-ZY for the SZX and SZY waves, respectively. Tentap stacking with a sampling frequency of 51.2 kHz and a pretrigger time of 7.5 ms is also used in downhole testing. Load–Settlement Testing Load–settlement testing is performed to record footing settlement due to static vertical load application. A T-shaped frame is used to distribute the vertical load from the hydraulic jack uniformly across the concrete footing as shown in Fig. 4(a). Reference beams spanning the footing support the linear potentiometers at three equilaterally positioned locations on the footing. The hydraulic jack, reacting against the weight of T-Rex, is used to apply a vertical force through the load cell to the footing, while load cell and potentiometers are monitored continuously by the recording system. The jack is hand pumped to a predetermined load, then the load is maintained while small-

FIG. 4 (a) Load application and displacement measuring equipment in place for static vertical loading and (b) steady-state dynamic testing with T-Rex on top of the footing at the Los Reales landfill.

strain crosshole and downhole seismic tests are conducted. Additional stages of loading are added to complete the testing sequence. The static loading and displacement measuring equipment is removed from the footing before the execution of steady-state dynamic testing. Steady-State Dynamic Testing Low-to-high-amplitude steady-state dynamic testing is performed to investigate the nonlinear shear modulus of solid waste. Testing is initiated by placing the vibrator plate of the mobile field shaker on top of the concrete footing. The hydraulic pressure system of the shaker is used to impose a hold-down static force. Then the servo-hydraulic vibrator is used to apply a sinusoidal horizontal dynamic force at a specified amplitude, frequency, and number of cycles. This sinusoidal horizontal load generates vertically propagating shear waves that induce dynamic shearing strain in the solid waste. The geophones measure particle velocity time-histories at various depths in the solid waste. At a constant static hold-down force, the amplitude of dynamic horizontal loads is incrementally increased so that larger shearing strains are induced in the solid waste. This procedure is then repeated at increasing levels of static hold-down force so that the effect of confining stress on nonlinear shear modulus and normalized shear modulus can be investigated. Prior to initiating the dynamic staged loading, a frequency sweep is performed at a low load level to find frequencies of dynamic horizontal loads that yield the most regular sinusoidal waveforms recorded by the geophones. Frequencies of 30 and 50 Hz generally result in good sinusoidal output signals. However, the optimum excitation frequency is site-dependent. For example, a frequency of 100 Hz yielded the best sinusoidal waveforms at an unsaturated silty sand site (Stokoe et al. 2011). The number of dynamic horizontal load cycles is generally selected to be from 8 to 10. This number of cycles is considered sufficient to achieve steady-state motion while minimizing any degradation of the solid waste material. Steady-state testing is usually performed with a sampling frequency of 20.5 kHz. Solid Waste Sampling and In Situ Unit Weight Measurement After completion of staged load testing, the test location is excavated to characterize in situ the solid waste, perform in situ unit weight measurements, collect bulk solid waste samples, and retrieve the 3D sensors. Characterization of solid waste and in situ unit weight measurements are performed using procedures proposed by Zekkos et al. (2010) and Zekkos et al. (2006), respectively. Waste characterization is mainly performed to evaluate solid waste composition. The percentage by weight of soil-like material (20 mm) is known to be one of the most important factors affecting the dynamic properties of solid waste (Zekkos et al.



2008) and is essential information to interpret field testing results. A portable gas detector is used to ensure that gas levels do not exceed an allowable threshold level. The in situ large-scale unit weight measurement resembles the ASTM D1556-07 standard sand-cone density method (Zekkos et al. 2006). A trench is excavated at the testing location using a small backhoe excavator. The excavated solid waste is collected in a pre-weighed dump truck or wheel loader. To measure the weight of the excavated solid waste, the total weight of the truck with the loaded solid waste is weighed at scales available at the landfill. Bulk solid waste samples are collected from the trench and are stored in 55-gallon, sealed HDPE drums for further characterization and laboratory testing. Uniform clean gravel is used to estimate the trench volume. The unit weight of this gravel is obtained by averaging measurements using two 55-gallon HDPE drums. The uniform gravel is loaded into the dump truck or the wheel loader. The truck with the gravel is weighed. The trench is backfilled with the gravel and the truck with the remaining gravel is re-weighed so that the weight of gravel that is placed in the trench can be calculated. The trench volume can be estimated by dividing the weight of calibrated gravel in the trench by its unit weight. The unit weight of solid waste is calculated by dividing the measured weight of the excavated waste by the calculated trench volume. In situ waste characterization included qualitative description of composition, age, degradation state, and moisture content (Zekkos et al. 2010). Waste composition described the materials that are contained in the excavated solid waste, such as plastic, paper, wood, rugs, tires, clothing, and other organics, etc. Waste age can be estimated using dates on magazines, newspapers, receipts, and other documents found in the waste. Waste degradation is approximated using four different levels of degradation based on illegibility and discoloration of newspaper. Moisture content in the solid waste can be visually described as dry, damp, wet, or standing water.

Data Analysis The analytical techniques used to reduce the raw data are presented below using data from testing location #3 at the Los Reales landfill in Arizona. The testing setup at this location is shown in Fig. 1.

LOAD–SETTLEMENT TESTING

Using calibration factors of the load cell and three linear potentiometers, raw data output from the load cell and linear potentiometers are converted to load and displacement, respectively. The displacement time histories from three linear potentiometers are averaged and plotted versus load. The load–settlement relationship evaluated at the Los Reales landfill is presented in Fig. 5.

FIG. 5 Load–settlement curve at location 3 in the Los Reales landfill, AZ.

CALCULATION OF MEAN CONFINING STRESS AND AXIAL STRAIN DISTRIBUTIONS

The stress state in the solid waste influences its dynamic properties (e.g., Zekkos et al. 2008). In the field tests, the static stress is equal to the stress induced by the static vertical load on the concrete footing plus the geostatic stress. The vertical (rz) and radial (rr) stresses induced by the static vertical load are approximated using the Foster and Ahlvin (1954) method. The geostatic vertical stress (rg) is calculated as the in situ (total) unit weight times the depth. The vertical stress (rv) is calculated as the sum of rg and rz. The horizontal stress (rh) represents the combination of rr and the estimated coefficient of lateral pressure at rest (K0) times rg. K0 is calculated from the estimated in situ Poisson’s ratio values. Poisson’s ratio is evaluated in situ using the measured Vs and Vp and varied, in general, between 0.2 and 0.35. The mean confining stress (r0) is calculated as: rz þ rg þ 2 rr þ K0 rg (1) r0 ¼ 3 The Ahlvin and Foster (1954) method is also used to calculate the axial strain distribution in the solid waste due to the application of vertical static load on the concrete footing. The axial strain profile between 3D geophones at two different depths is used to estimate the change in vertical spacing between geophones.

CROSSHOLE AND DOWNHOLE SEISMIC TESTS

A key part in the analysis of the crosshole and downhole seismic tests is evaluating the travel times of the seismic waves. Two techniques that are widely used in measuring travel times are implemented in this work: (1) true-interval time measurements (e.g., Stokoe and Woods 1972; Woods and Stokoe 1985), and


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FIG. 6 Crosshole seismic test records: (a) Vp-X and (b) Vs-XZ.

(2) the cross correlation method (e.g., Roesler 1977; Woods 1978; Woods and Stokoe 1985; Sully and Campanella 1995). True-interval time measurements are performed by visually picking similar points (i.e., first arrival or first trough/peak) in the waveforms from the same source impact. Even though there is some subjectivity in the selection of the arrival times, this technique provides repeatable velocity measurements if the waveforms are of high quality. In the cross correlation method, all points in the waveforms are used to measure the travel time between sensors. Basically, cross correlation between two waveforms is calculated by shifting the waveform from the first sensor relative to the waveform from the second sensor in a step increment equal to the sampling interval. At each step increment, the cross correlation magnitude is calculated by integrating the product of these waveforms. The cross correlation magnitude reaches a maximum value when these waveforms overlap the most. The time shift corresponding to the maximum cross correlation magnitude can be used as the travel time. The advantage of the cross correlation method is that it can be automated to expedite the analysis process. However, it also has several limitations. First, the cross correlation method provides an “average” velocity, not a phase velocity that is needed to calculate Gmax and constrained modulus (Mmax). Second, the cross correlation requires clean waveforms without strong near-field terms. In crosshole seismic testing, Vp-X measurements are performed using time records from the X-axis component in two geophones located at the same depth. Propagation velocity is calculated by dividing the horizontal spacing by the wave travel time between these geophones. Example of a Vp-X measurement from crosshole seismic testing is presented in Fig. 6(a). The travel time between the geophones is measured by picking the first arrivals, as indicated by triangles in both waveforms. Vs-XZ measurements are performed using the time records from the Z-axis component in 3D geophones located at the

same depth. Figure 6(b) shows an example of a Vs-XZ measurement from crosshole seismic testing. The travel time between geophones is measured by picking the first trough as denoted by triangles in both waveforms. Alternatively, it can be measured by picking the first peak as indicated by circles in both waveforms. The two travel time picks yielded similar results for all crosshole seismic tests performed. In downhole seismic testing, vertically propagating waves are used to measure time delays between the waveforms monitored by two geophones in each backfilled borehole. Vp-Z, Vs-ZX, and Vs-ZY are measured using signal records from geophone components in Z, X, and Y directions, respectively. An example of the Vp-Z measurement is shown in Fig. 7(a). The points indicated by two triangles are used to measure the travel time between the geophones. Examples of Vs-ZX and Vs-ZY measurements are presented in Fig. 7(b) and 7(c). The travel times from these shear waves can be estimated by picking the first arrivals as well as the first troughs/peaks. These two travel time picks yielded similar shear wave velocity values. Figure 8(a) shows an example of the use of the cross correlation method to measure Vp-Z using waveforms from geophones G15 and G13 in the Z direction (Fig. 7(a)). Generally, Vp-Z estimated from the cross correlation method yielded a value that was about 18 % higher than the value of Vp-Z measured from the true-interval time measurement method. The application of cross correlation method for measuring Vs-ZX using waveforms in geophone G15 and G13 in the X direction (Fig. 7(b)) is presented in Fig. 8(b). The Vs values from the cross correlation and the true-interval time measurement method were nearly the same. The Vs-ZX measured from cross correlation was about 3 % higher than the Vs-ZX measured from the direct time resolution method. Figure 8(c) presents the application of cross correlation method for evaluating Vs-ZY using waveforms in geophone G15 and G13 in the Y direction (Fig. 7(c)). The Vs-ZY measured from



FIG. 7 Downhole seismic test records: (a) Vp-Z, (b) Vs-ZX, and (c) Vs-ZY.

cross correlation was about 5 % higher than the Vs-ZY measured from the true-interval time measurement method. Similarly, in crosshole seismic testing, Vp-X measured using the cross correlation method yielded different Vp-X values compared to those measured from the true-interval time measurement method. Vs-XZ measured using the cross correlation method was similar to Vs-XZ measured using the true-interval time measurement method. In this study, both for crosshole and downhole testing, Vp is evaluated using the true-interval time measurement method, and Vs is evaluated by true-interval time measurement method as well as the cross correlation method. STEADY-STATE DYNAMIC TESTING

Steady-state dynamic testing is performed to investigate the nonlinear stress–strain response of solid waste. This stress–strain response is commonly characterized by the relationship between shear modulus and induced shearing strain. Data analysis to calculate shear modulus and shearing strain is presented in detail below.

Shear Modulus Calculation In nonlinear field testing, the loading plate of the mobile field shaker vibrates in the horizontal X direction, which generates vertically propagating shear waves with horizontal particle motion in the X direction. Figure 9(a) shows the raw output time records of the X-component geophones in the west hole array (shown in Fig. 1). The shear wave velocities are calculated by dividing the vertical spacing between geophones by the associated time intervals. The time intervals are determined using time lags between peaks in the steady-state portion as indicated in the records. These peaks are identified by solid circles in the mid-portion of the record in Fig. 9(a). Shear modulus is calculated from the measured shear wave velocity and the mass density of solid waste (q) using the equation: (2)

G ¼ q Vs2

The total unit weight of the solid waste from the large-scale in situ measurement is used to obtain the corresponding mass

FIG. 8 Cross correlation analysis used to evaluate: (a) Vp-Z, (b) Vs-ZX, and (c) Vs-ZY.


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FIG. 9 Example of steady-state testing result: (a) X-component geophone output time records and (b) Z-component geophone output time records.

density. Shear moduli calculated using geophone pairs in the west hole array are then averaged with their counterpart geophone pairs in the east hole array to determine the average shear modulus of the solid waste over each depth interval. Shearing Strain Calculation Calculation of shearing strain is needed to evaluate the shear modulus reduction-log shearing strain (G-log c) and the normalized shear modulus-log shearing strain (G/Gmax-log c) relationships. Shearing strain induced in the waste can be calculated using four different analytical methods, namely the displacement-based (DB) method, the plane shear wave method, the plane Rayleigh wave method, and the apparent wave method (Rathje et al. 2005). The DB method, described below, was used in this study as it best represents the measured motions and does not require knowledge of the wave propagation velocities. Other shearing strain calculation methods and their comparison with DB method are discussed in more detail in Chang (2002), Rathje et al. (2005), and Cox (2006).

A schematic for the 2-node DB method is presented in In this method, a 3D sensor is considered a node with a single-degree of freedom in the X direction. Shearing strain in the 2-node DB method is calculated using: Fig. 10(a).

(3)

FIG. 10

c¼

uX1 uX2 DuX12 ¼ 2b 2b

Displacement Based (DB) methods for calculation of shearing strain: (a) 2-node and (b) 4-node (after Rathje et al. 2005).



where: uXi ¼ the horizontal displacement of node-i, and b ¼ half of the vertical spacing between two nodes. A schematic of the 4-node DB (bilinear quadrilateral) method is presented in Fig. 10(b). In this method, a 3D sensor is considered as a node with 2-df in the X and Z directions. Four 3D sensors form a single quadrilateral element. Shearing strain at any point inside the element can be calculated using (Rathje et al. 2005): 1 uX1 X uZ1 Z cXZ ðX; ZÞ ¼ 1 1 4 a b b a uX2 X uZ2 Z uX3 X 1þ 1 1þ þ þ b a b a b a uZ3 Z uX4 X uZ4 Z 1þ 1 1þ þ þ a b a b a b

shearing strain calculated using the 2-node method becomes smaller than that using the 4-node DB method. At shearing strain of about 103%, shearing strain calculated using the 2-node method is about 90 % of shearing strain calculated using the 4-node method (Fig. 11(b)). At shearing strain of about 101%, shearing strain calculated using the 2-node method is less than 60 % of shearing strain calculated using the 4-node. The reason for this discrepancy is that the rocking motion created by the combined motions of the baseplates of the shakers increases with the amplitude of dynamic horizontal motion (Cox 2006). Thus, the vertical motion induced by rocking of the baseplate contributed more to the induced shearing strain at larger horizontal dynamic loads. On the basis of these results, it is recommended that shearing strains at the center of a quadrilateral element be calculated using the 4-node DB method.

(4)

where: uZi ¼ the vertical displacement of node-i, and a ¼ half of the horizontal spacing between two nodes. To use these DB methods, raw output time history data from the 3D sensors are converted to particle velocity time histories using the calibration factor of each geophone. Displacement time histories are obtained by numerically integrating the recorded velocity-time histories. The 2-node DB method is simple and requires fewer sensors. However, as shown in Fig. 9(b), the shakers do not vibrate in the horizontal direction only, but also induce some rocking, which creates a small vertical component motion. As a result, the vertical dynamic displacement of the geophones should not be neglected. A comparison between shearing strain calculated using the 2-node and 4-node DB methods is presented in Fig. 11(a) for testing at the Los Reales landfill. As expected, shearing strain calculated using the 2-node and 4-node DB methods yield similar results at small shearing strains. As shearing strain increases,

Example Results WAVE PROPAGATION VELOCITIES

Crosshole and downhole seismic testing allows assessment of Vp and Vs with different propagation and polarization directions. As noted earlier, mean confining stress distribution is estimated using the Ahlvin and Foster (1954) method for varying static vertical loads imposed by the shakers. With this information, the relationship between wave propagation velocity and mean confining stress can be investigated in situ. The relationship between Vs-ZX and r0 evaluated from downhole seismic testing in the west hole array at the Los Reales landfill is shown in Fig. 12. The measured Vs-ZX values are generated for each of the three pairs of vertically adjacent 3D sensors. Each Vs value represents the shear wave velocity at midpoint depth between sensors. At each load increment, r0 is calculated and its relationship with Vs-ZX is evaluated. Following Stokoe et al. (2011), a power function is fitted to the data:

FIG. 11 Comparison of shearing strains calculated using the 2-node and 4-node displacement-based methods.


11

12


FIG. 12 Relationship between Vs-ZX and mean confining stress evaluated at the Los Reales landfill.

0.11. In the NC regime, the nZX value is significantly higher (nZX ¼ 0.25–0.30), which is consistent with a value of NC nZX of 0.27 reported by Zekkos et al. (2014). A similar relationship of wave velocities and stresses can also be generated for Vs-ZY, Vs-XZ, Vp-Z, and Vp-X.

NONLINEAR SHEAR MODULUS CURVE

(5)

VsZX ¼ AZX

nZX r0 Pa

where: Pa ¼ atmospheric pressure, AZX ¼ Vs at 1 atm, and nZX ¼ an exponent which represents the effect of confining stress on Vs-ZX. In Fig. 12, a bi-linear relationship of Vs-ZX with r0 is observed at depths of 0.13 and 0.36 m. At a depth of 0.71 m, a linear relationship between Vs-ZX with r0 is observed. A bi-linear relationship indicates that, at low stresses, the waste is in the overconsolidated (OC) state due to waste compaction. As mean confining stress increases beyond the maximum past mean confining stress (of about 30 kPa in this case), the solid waste becomes normally consolidated (NC). In the OC regime, the stress exponent nZX is found to be low, ranging from 0.09 to

The effect of mean confining stress on the G-log c and the G/Gmax-log c relationships is illustrated in Fig. 13(a) and 13(b), respectively. These curves are obtained from a quadrilateral element that is formed by geophones G13, G12, G14, and G15 (Fig. 1). In this example, Gmax increased from 15 to 28 MPa as mean confining stress increased from 15 to 77 kPa. For this range of mean confining stress, the G-log c curves moved to the right with increasing r0 and showed an increasingly linear response (Fig. 13(a) and 13(b)). These trends are similar to trends previously observed in laboratory testing of municipal solid waste (e.g., Lee 2007; Zekkos et al. 2008; Yuan et al. 2011). Waste composition is one the most important factors that affects the nonlinear dynamic properties of solid waste (Zekkos et al. 2008). The data collected can also be used to assess the impact of waste variability on G/Gmax-log c relationship by examining different quadrilateral elements. Figure 14(a) presents examples of G-log c from three different elements at nearly the same estimated mean confining stresses (12–15 kPa). Thus, differences in G-log c relationships can be attributed to variability in waste composition. The small-strain shear modulus ranges from 15 to 22 MPa. Note that the Gmax values estimated from downhole seismic testing are consistently a bit higher (1.06–1.13 times) than the Gmax obtained from the lowamplitude steady state dynamic testing. These differences are largely attributed to frequency effects on the small-strain dynamic properties of MSW material, which are known to be significant (e.g., Lee 2007; Zekkos et al. 2008; Bray et al. 2009). The steady-state dynamic tests were conducted at a

FIG. 13 Effect of mean confining stress on (a) shear modulus and (b) normalized shear modulus curves.



FIG. 14 Effect of waste variability on (a) shear modulus and (b) normalized shear modulus reduction curves.

considerably lower (50 Hz) excitation frequency than the small-strain transient downhole seismic testing (100–300 Hz). Figure 14(b) illustrates the variability in waste composition effect on the G/Gmax-log c relationships. G/Gmax-log c curves for waste recommended by Augello et al. (1998), Matasovic and Kavazanjian (1998), and Zekkos et al. (2008) are also presented in this figure. In general, the curves recommended by Augello et al. (1998) and Zekkos et al. (2008) are in good agreement with the data shown. The recommended curve from Matasovic and Kavazanjian (1998) is more linear than the data shown. For the data shown, the largest shearing strain evaluated in this test is 1 101%. This shearing strain level occurred at the center of the shallowest quadrilateral element. Overall, the G/Gmax-log c relationships were evaluated over the range of shearing strains from 5 104% to 2 101% in this study. Figure 14(b) also shows a modified hyperbolic model (Darendeli 2001) for normalized shear modulus degradation data of solid waste with confining stress at 12–15 kPa. This model is described by a coefficient of curvature, a, and a reference strain, cr. Figure 14 also shows the results from the largest quadrilateral element formed by G23, G22, G8, and G11 (as shown in Fig. 1), which represents the “average” response of the instrumented waste mass.

Summary and Conclusions Reliable seismic response analysis of landfills requires representative dynamic properties of the solid waste. An experimental method to investigate the dynamic properties of solid waste in situ is presented. This testing method includes crosshole and downhole seismic testing in the small-strain range, combined with nonlinear testing. In addition, load–settlement testing and in situ unit weight measurements are performed. The results from this field testing method were: (1) load–settlement curve, (2) wave propagation velocities in varying propagation and polarization directions as well as their variation with confining stress, (3) in situ shear modulus-log shearing strain, and normalized shear modulus-log shearing strain relationships as well

as their variation with confining stress. The steady-state dynamic testing was performed using large mobile field shakers of NEES@UT and 3D geophone based sensors units embedded in the solid waste to capture the waste response. This field method offers an in situ evaluation of the impact of mean confining stress and variability of waste composition on dynamic properties of solid waste. Field testing was performed in a number of landfills (Municipal Solid Waste and Hazardous) and the examples of results from the Los Reales landfill in Arizona were shown to illustrate the field method. The relationship between log Vs and log r0 exhibits bi-linearity and can be regressed using two exponential fitting curves. For the example data shown, a low stress exponent (0.09–0.11) is observed in the OC regime and a higher stress exponent (0.25–0.30) is found in the NC regime. Nonlinear shear modulus curves were developed in situ for shearing strains ranging from 104% to approximately 0.2 %. The trend in the shear modulus reduction curves from this testing is generally consistent, but not identical, to earlier curves recommended for Municipal Solid Waste (e.g., Augello et al. 1998; Matasovic and Kavazanjian 1998; Zekkos et al. 2008). For the example data of normalized shear modulus-log shearing strain shown (at confining stress