GEO-MATERIALS: NON-DESTRUCTIVE EVALUATION IN GEO-SYSTEMS

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1 GEO-MATERIALS: NON-DESTRUCTIVE EVALUATION IN GEO-SYSTEMS D. Fratta, Civil and Env. Engineering, LSU. Baton Rouge, LA A. L. Fernández, GEOCONSULT. San Juan, PR J. C. Santamarina, Civil and Env. Engineering, Georgia Tech. Atlanta, GA 3033 Abtract. Soil and fractured roc are particulate material, i.e., their trength, tiffne and dilative/contractive behavior are controlled by the tate of effective tre; in addition, fine grained particle are alo affected by contact-level electrical and capillary force. Elatic wave propagate through thee material aeing their tate, without altering their propertie or procee taing place within them. Furthermore, wave-baed boundary meaurement can be inverted to render a tomographic image of the medium. Therefore, the propagation of elatic wave open unique poibilitie for powerful reearch and engineering tool in geo-material. Thi paper review the mot relevant apect of wave propagation in geo-material, and preent two cae tudie in which tomographic image are obtained. The interpretation of tomographic image in term of the tre field i dicued. INTRODUCTION The non-detructive evaluation of geomaterial (oil and fracture roc) preent unique feature that are not common to other material. In particular, the tate of effective tre determine the tiffne, the trength and the dilative-contractive tendencie in particulate media. Hertz theory predict that two phere made of a perfectly linear material exhibit a non-linear elatic load-deformation behavior. Furthermore, Mindlin contact theory how that an enemble of particle i non-elatic [1, ]. Thee two obervation permit concluding that oil and roc mae are inherently non-linear and non-elatic. Furthermore, interparticle local force (electrical and capillary) and cementation between particle affect the tiffne and the trength of geomaterial. In addition, geomaterial are inherently multiphae, whereby the mineral eleton coexit with the fluid phae that fill the pore. While the fluid phae ha very limited effect on the hear tiffne, it may ignificantly affect the compreional tiffne of nearurface geomaterial. Variou poroelatic effect may alo develop (e.g., Biot low P-wave and Mendel-Cryer effect). Thi paper tart with a brief review of fundamental apect of geomaterial behavior in relation to elatic wave propagation and tomographic imaging. Then, two cae tudie are preented to dicu the ue of non-detructive evaluation technique to obtain engineering parameter and to evaluate the behavior of earth tructure in the near-urface. ELASTIC WAVE VELOCITY IN GEO-MATERIALS The relevance of the tate of effective tre on tiffne and velocity i addreed firt, followed by a review of the implication of capillarity and cementation. Micromechanical model are invoed in thi preentation.

2 Effective Stre The longitudinal modulu E of a imple cubic pacing of monoize elatic phere ubjected to iotropic effective tre σ' i [1, ]: E = 3 E σ` ( 8 1 ν ) 1 3 (1) where E and ν are the Young modulu and Poion ratio of the material that mae the phere. The ma denity of the imple cubic pacing i ρ=π ρ /6 where ρ i the denity of the material that mae the phere. Then, the P-wave velocity i: E V 6 P = ( π ρ 8 1 ν ) [ ] 1 1 σ` 6 () For frehly remolded real oil and fractured roc, predictive empirical equation are power relation uch a [3, 4, 5, 6]: or β σ' V P = α 1 Pa (3) β σ' σ' S = α 1 Pa 1 Pa χ V (4) β σ' +σ' V S = α Pa (5) where the α coefficient and the β exponent depend on the type of geomaterial, the nature of interparticle contact and the tability of the granular eleton. The β exponent varie from 0.18 for dene and to 0.45 for highly platic clay [7], σ ` i the effective tre parallel to the direction of wave propagation, and σ ` i the effective tre in the direction of particle motion (S-wave). Equation 4 and 5 highlight the prevalent role of the tate of tre on the polarization plane. In fact, Equation 5 ugget that the mean tate of tre on the polarization plane determine the propagation velocity. A typical dataet i preented in Figure 1. Preure cell accelerometer coil Power amplifier Signal analyzer F (deviatoric force) S-wave velocity [m/] Confining tre [Pa] (b) Figure 1: Reonant column tet permit meauring wave velocity and damping in geo-material under different tate of tre condition. (b) Typical variation of S-wave velocity veru tate of tre Iotropic loading Aniotropic loading

3 Capillary Unaturated condition are alway preent above the free water table in the near urface. At high moiture content, the pore fluid phae i continuou (funicular regime). At low moiture content, the pore fluid form menici at particle contact (pendular regime). In either cae, the negative pore fluid pull particle together. The magnitude of the additional contact force in the pendular regime can be readily computed. From Lapace equation: ( 1 1 ) p = T + (6) r1 r where p i the fluid preure, r 1 and r are the radii (ee Figure -a), and T i the urface tenion (radii have different ign). The capillary force between particle i: r F = p π (7) Capillary force are mot important in fine-grained oil and at low confining tre, where the contact level capillary force may exceed the eletal force that carry the applied boundary tree (Figure -b). A the interparticle force increae, o doe the tiffne and the wave propagation velocity. Figure 3-a how a oil cell with bender element to monitor oil procee with S- wave in order to gather information about the evolution of the oil eleton tiffne. Data in Figure 3-b correpond to a aturated pecimen of granite powder ubjected to drying. When the material i fully aturated, it velocity i at a minimum (ma denity i larget). A the material begin drying, the velocity increae primarily becaue of the decreae in ma denity. A drying progree, capillary force develop and the hear tiffne increae. Thi proce continue until the material approache dry condition. At thi point, the velocity hould decreae becaue capillary force vanih. However, alt precipitation and the migration of fine particle to contact render a cemented medium with high tiffne. r 1 r R Normal equivalent tre Normal tre σ Normal tre σ (b) Figure : Capillary force between two pherical particle can be evaluated with Laplace equation. (b) Thi contact-level force can be interpreted a an equivalent effective tre. It affect hear trength [8]. Shear tre Failure envelope Signal generator Ocillocope Soil pecimen Bender element L Saturation [ ] (b) Figure 3: Setup for S-wave propagation monitoring with bender element. (b) Variation of S-wave velocity veru degree of aturation [8]. S-wave velocity [m/] Granite powder Tet direction

4 ET/Gm CbL Model CbL Tet Uncemented Sand Cement Content = 1 % Cement Content = 0.5 % Uncemented and LbC Model LbC Tet E-06 1E-05 1E-04 V [m/] Loading Before Cementation (Initial confinement 415 Pa) β = 0.15 β = 0.18 Uncemented Sand Unload (firt tage) Reload β = 0.03 β = σ/gm Confining Preure (Pa) (b) Figure 4: The effect of cementation on tiffne and (b) hear wave velocity. For comparion, trend and data for uncemented and are alo preented [9]. Cementation Cementation can have a very important effect on the tiffne of near-urface oil, a hown in Figure 4-a (micromechanical model). A in the cae of capillary force, the effect i mot evident at low confining tree. Figure 4-b how data for a cemented and an uncemented and. The following obervation can be made: (1) the velocity in the cemented and i much higher; () the velocity in the uncemented and i more enitive to tre change; (3) cementation can be lot during unloading a the train energy tored in the oil particle i tranmitted to the cementing bridge breaing them in tenion. Heterogeneity and Aniotropy Soil depoit are vertically heterogeneou becaue the effective tree increae with depth (e.g., σ v = γ z). They are alo aniotropic becaue the tate of tre varie in the vertical plane (e.g., σ v = o σ v ). While aniotropy by itelf doe not caue ray path to curve, it doe increae the ray curvature that develop in vertical heterogeneou media. The cloe-form olution for the ray path in a medium with a velocity field that increae linearly with depth and with elliptical aniotropy in the vertical plate i [10]: V [m/] z = ( ) ( < r> < > < > Vv Vv ) < r> x x c ( ) ( z z) a + < r> < > b x x b < > Vv + + b (8) where the upercript and r indicate ource and receiver, and the contant a, b and c are the model parameter (Figure 5). Travel time can be computed a: t = r l V v = r 1+ z' dx < r> x ( z, z' ) V ( z, z' ) ( a + b z) v < > x TOMOGRAPHIC IMAGING IN GEO-MATERIALS c + z' Δz (9) Tomographic imaging i the inverion of boundary meaurement to determine the velocity field within a body. Thi technique permit eeing inide the body. The travel time t i between a ource and a receiver i the integral of the lowne along the ray path. If

5 Model Equation: Vertical velocity: z = a + b V v () z Elliptical varying velocity (vertical plane): ( ) = V ( z) V z,z' 1 z' v + c + z' 4 depth z [m] ource * 1 a=100 m/ b=0.0 1/ c=1.0 receiver ource * * 1 * 1 4 a=100 m/ b=0.0 1/ c=1. receiver depth z [m] 4 a=100 m/ b=5.0 1/ c= ditance x [m] ditance x [m] Figure 5: Effect of heterogeneity and aniotropy in ray path. 4 a=100 m/ b=5.0 1/ c= Source * * * L 1,1 L 1, L,1 L 3,3 L,4 L 3,4 L 3,6 1 3 Receiver Mathematical model: Figure 6: Pixel repreentation of the medium for tomographic analyi of the data. the medium i dicretized into pixel, the travel time integral can be written a a um (Figure 6): t i = Li, V = L i, S t = L S (in matrix form) Solution: S = L g t velocity field, and then image of the tate of tre. t i = r dl V x,z Li, ( ) = V L i, S (10) where L i, i the ditance traveled by ray i in pixel, V i the wave velocity at pixel and S i the lowne (invere of velocity) in pixel. Similar equation can be written for all ray. Equation 10 i a um of product, therefore the et of equation correponding to all ray can be arranged in matrix form a: t = L S (11) the travel time vector t i nown, and the travel length matrix L i computed from geometric conideration auming the ray path are nown. The goal i to determine the lowne vector S [10]: < peudo invere> S = L t (1)

6 Once the vector S i computed, lowne value are mapped onto a color cale to render the tomographic image. Procedure that can be ued to compute the peudo invere of L are reviewed in the literature [10, 11]. CASE STUDY I: KOREAN DE-MILITARIZED ZONE Thi firt cae hitory i preented to demontrate the robut evaluation of the uburface velocity field, including it vertical heterogeneity and aniotropy. The technique i baed on the parametric repreentation of the medium uing a minimum number of parameter, and it deviate from pixel-baed tomography which typically involve a large number of unnown. The ite i in the Korean Demilitarized Zone. The two borehole are 15. m apart. Intrumentation involve a parer ource and a geophone. The ource i activated in one borehole at 0. m interval. Meaurement are determined at 45, 30, 15, 0, -15, -30, and -45 degree with repect to the horizontal. The complete data et include a total of 1050 ray. The data are plotted veru depth (Figure 7-a) and veru ray angle (Figure 7-b) to highlight vertical heterogeneity and aniotropy. Thee plot permit obtaining an initial gue of the material parameter for the model preented in Figure 5 (Equation 8 and 9). Figure 8 how the error-driven iterative inverion of the travel time. Two cae are conidered: homogenou-iotropic and heterogeneou-aniotropic media (model in Figure 5). The L and L error norm are hown in the figure. Clearly, the heterogeneouanitropic model yield the lowet error norm, i.e., the bet prediction of the velocity field. CASE STUDY II: LAGUNILLAS PROTECTION DYKES The Maracaibo lae bain lie on top of a large and hallow oil reervoir. Oil extraction ha caued ubidence, thu a long dye ha been built along the hore to prevent the lae water from invading land and flooding onhore intallation. The preence of the dye Wave velocity [m/] Wave velocity deg deg deg. 0 deg deg. 30 deg. 15 deg. 0 deg Depth [m] Ray angle [deg.] Figure 7: Tomographic data from the Korean Demilitarized Zone. Effect of vertical heterogeneity on average wave velocity (traight ditance divided by meaured travel time). (b) Effect of tre aniotropy on average wave velocity. Model parameter are hown in Figure 5. Wave velocity [m/] Wave velocity [m/] c = 1.1 c = 1. c = 1.3 data (depth: 14.6 m) (b)

7 Travel time [] Travel time [] Figure 8: Tomographic inverion of cro-hole tomographic data - Korean De-militarized zone. Parametric repreentation of the medium according to the velocity field model hown in Figure 5. increae the tate of tre in the foundation and the contractive tendency of the oil, which may lead to liquefaction in thi eimically active region. Three cro-hole geotomographic tudie are performed at location hown in Figure 9. The line of ource and receiver are 3 m apart. Travel time data are inverted uing a pixel-baed repreentation of the medium and preuming traight ray. The regularized leat-quare olution i implemented: S = T 1 1 T ( L L + λ R R) L t (b) (13) where λ i the regularization coefficient and R the regularization matrix. The regularization matrix permit adding a-priori information to the olution. In thi cae, it i aumed that the medium i horizontally mooth (Regularization baed on equilibrium equation i dicued in [1]). The computed image are preented in Figure 10. Note the low hear wave velocity under the berm (ite # ). In term of the tate of tre, thee reult indicate that the berm may be arching. Thi i an important obervation for the potential long term performance of the main dye and the protection berm. Further teting i needed to confirm thi obervation. CONCLUSIONS ray number [ ] Homogeneou and Iotropic Model a = 4500 m/ b = 0 1/ c = 1.0 E = 3.49 % E =.79 % Geo-material (oil and fractured roc) poe unique challenge for the non-detructive evaluation of geoytem and for monitoring uburface procee. Salient characteritic include inherent non-linear and non-elatic behavior, effective-tre dependent tiffne (and trength), and the importance of contact-level force (capillary and electrical) particularly in near-urface oil. Meaurement with eimic wave permit aeing the mall train tiffne, it heterogeneity and aniotropy. Tomographic image of hear wave velocity can be interpreted in term of the tate of the effective tre ray number [ ] Heterogeneou and Aniotropic Model a = 4560 m/ b = / c = 1.10 E = 1.68 % E = 1.31 %

8 Site # m. Site # +.8 m Berm Non-platic ilt Site # m 4.5 m SEA LEVEL Highly platic clay Figure 9: View of the berm, foundation oil, and ite of the geo-tomography tudie ACKNOWLEDGMENTS Figure 10: Image of the velocity field under the protection dye. Thi tudy wa conducted by the author at the Georgia Intitute of Technology (School of Civil Engineering and GTREP). Support wa provided by INTEVEP (Venezuela). REFERENCES Site # 1 Site # Site # 3 NFT BRT TDT Velocity(m/) [m/] >100 < >00 > 5 1. White, J. E. Underground Sound Application of Seimic Wave. Elervier. Amterdam (1981).. Richart, F. E., Hall, J. R., and Wood, R. D. Vibration of Soil and Foundation. Prentice- Hall. Englewood, NJ (1970). 3. Roeler, S. Journal of the Geotechnical Engineering Diviion 150, GT7, (1979). 4. Stooe, K.H., II, Lee, J.N.-K. and Lee, S.H.-H., Characterization of Soil in Calibration Chamber with Seimic Wave in Proc. Symp. Calibration Chamber Teting, Potdam, N Y (1991). 5. Belloti, R., Jamiolowi, M., Lo Preti, D.C.F. and O Neill, D.A. Geotechnique, 46, 1, (1996). 6. Santamarina, J.C. and Cacante, G., Canadian Geotechnical Journal, 33, 5, (1996). 7. Santamarina, J.C., Klein, K. and Fam, M., Soil and Wave (In print), John Wiley & Son (001). 8. Cho, G.C. and Santamarina, J.C. ASCE Geotechnical Journal (In print) (000). 9. Fernandez, A. and Santamarina, J.C., Canadian Geotechnical Journal (In print) (001). 10. Santamarina, J. C. and Fratta, D., Introduction to Dicrete Signal and Invere Problem in Civil Engineering, ASCE Pre, Reton, VA (1998). 11. Mene, W., Geophyical Data Analyi: Dicrete Invere Theory, Academic Pre (1989). 1. Samani, A. M. W. Travel-Time Tomography for Stre Recontruction. Ph.D. Thei Univerity of Waterloo (1997).