SMALL-DIAMETER TDR CABLES FOR MEASURING DISPLACEMENT IN PHYSICAL SOIL MODELS

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1 SMALL-DIAMETER TDR CABLES FOR MEASURING DISPLACEMENT IN PHYSICAL SOIL MODELS C.M. McAlister 1 and C.E. Pierce 2 1 Graduate Research Assistant, Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 2928; mcaliste@engr.sc.edu 2 Assistant Professor, Department of Civil and Environmental Engineering, University of South Carolina, Columbia, SC 2928; piercec@engr.sc.edu ABSTRACT This paper describes the selection and testing of small-diameter cables for detecting and measuring, in real-time, the development of internal shear zones within laboratory and centrifuge soil models. Visual methods are normally used for measuring soil displacements in centrifuge models. Placement of Plexiglas side walls allows observation of displacements at the end(s) by means of spherical markers placed in the soil, grids marked on the Plexiglas, layers of colored sand or similar means. Dry spaghetti is often used as a displacement marker to record internal behavior after the test is completed; the spaghetti softens from moisture in the soil and deforms with the displacement pattern of the soil. The usefulness of these methods is limited. The advantages of using TDR in physical soil models are that the data is provided in real-time and continuous readings are possible because data acquisition is rapid. In this laboratory study, three braided coaxial cables were tested in a modified direct shear device. Unjacketed cable diameters range from 2.6 to 7.2 mm, which are significantly smaller than cables normally employed for field measurements. Specialized blocks have been manufactured to fully confine each cable in the shear box, while creating a very thin, fixed shear zone. During direct shearing, voltage reflection and shear load is measured as a function of shear box displacement. The smallest diameter cable was the weakest in shear and demonstrated high sensitivity to very small displacements. INTRODUCTION AND BACKGROUND Centrifuge researchers often construct plane strain physical soil models and assume that observations/measurements at the ends of the model accurately represent internal behavior. Modeling slope stability is an obvious example of this plane strain assumption. Plexiglas sides are typically installed to observe displacements at the end(s) by means of marking grids on the Plexiglas, placing spherical markers in the soil, and/or constructing layers of colored sand (Zornberg et al., 1997). These observations can be combined with measurements of the movement of distinct points on the surface of the model by means of LVDTs. The disadvantages of these methods are that friction cannot be entirely eliminated at the boundaries and not all geotechnical problems are plane strain. Internal displacements are more difficult to identify. Huat et al. (1991) used dry spaghetti noodles as displacement markers in their centrifuge models. Moisture from the soil softens the spaghetti and, after the test is completed, the model is cut to expose the deformed shape of the pliable spaghetti, which clearly outlines the final displacement pattern in the soil. The placement of spaghetti noodles is the most frequently used method for measuring internal displacements (Phillips, 21). In a centrifuge study on face stability of shallow tunnels (Chambon et al., 1991), internal shear displacements could only be determined after the conclusion of the test by investigating displaced patterns of horizontal layers of colored sand. The

model soil was moistened and cuts were carefully made to expose various vertical planes.

The primary objective of this paper is to describe the on-going development of TDR as a usable tool for measuring in real time the location and magnitude of shear displacements occurring within 1g

Data on internal displacements would be valuable for any number of geotechnical investigations including slope stability, retaining structures, excavations, tunneling, dam cracking, bearing capacity,

Data are provided in real time and because data acquisition is rapid, nearly continuous readings are possible.

2 model soil was moistened and cuts were carefully made to expose various vertical planes. This method, of course, does not allow real time evaluation of shear displacement; hence, the onset of shear displacement cannot be identified. The primary objective of this paper is to describe the on-going development of TDR as a usable tool for measuring in real time the location and magnitude of shear displacements occurring within 1g and centrifuge (>1g) soil models. Data on internal displacements would be valuable for any number of geotechnical investigations including slope stability, retaining structures, excavations, tunneling, dam cracking, bearing capacity, and pressure grouting. The advantages of TDR in physical soil models are the same advantages the method provides when employed in the field. Data are provided in real time and because data acquisition is rapid, nearly continuous readings are possible. Shear zone thickness can be more accurately assessed with TDR than with inclinometers (Dowding and Pierce, 1994). At present, there appears to be no available method to measure shear displacement internally during centrifuge testing (Kutter, 1999). Therefore, the successful development of a TDR method to identify the onset of shear displacement in the interior of models, and to measure shear displacement during testing, offers a significant advancement in physical soil model testing. Selected Cables EXPERIMENTAL METHODS Prior research by Pierce (1998) revealed that shear load and voltage reflection response is unique to every coaxial cable and depends upon its construction. Three coaxial cables were selected for this study: Alpha 9847, Belden 1855A and CommScope 212k. The first cable, Alpha 9847, was determined to be the most compliant coaxial cable of its size on the market (Dowding and Pierce, 21). This 75Σ cable has a jacketed diameter of more than 1 mm and is larger, in all dimensions, than the two miniature cables listed in Table 1. All three cables have solid, bare copper (BC) inner conductors, different foam polymer dielectrics, and braided copper shields. Figure 1 illustrates the difference in size between the Alpha 9847 cable and the two miniature cables. CommScope 212k and Belden 1855A cables were selected because they are similar in construction except for the size of the inner conductor. The cable with a larger inner conductor has nominal impedance of 5Σ. Conversely, the cable with a smaller inner conductor has nominal impedance of 75Σ. It is theorized that the 75Σ cable will be more compliant and weaker in shear than the 5Σ cable. One drawback to higher impedance cables, however, is that they tend to be lossy (Pierce, 1998). Signal loss is a problem at long distances but is not expected to impact the results of this laboratory investigation of short cables. Make Model Table 1. Manufacturer Specifications of Coaxial Cable Construction Nominal Impedance (W) Inner Conductor Dielectric Shield Jacket Diam Diam Coverage Diam Material Material Material Material (%) Alpha Solid BC 7.24 FPE 81 BC Braid 1.28 PE CoSc 212K Solid BC 2.71 Foam FEP 95 TC Braid 4.1 Cr PVDF Belden 1855A Solid BC 2.59 Gas Inj. 95 TC Braid 4.3 PVC Alpha 9847 Belden 1855A CommScope 212k Figure 1. Photograph of Three Selected Cables

Modified Direct Shear Box The experimental program was devised to shear cables in a modified direct shear device while recording load-displacement and voltage reflection-displacement response.

The upper block rests directly on the lower block, creating a shear zone of negligible thickness at their interface.

3 Modified Direct Shear Box The experimental program was devised to shear cables in a modified direct shear device while recording load-displacement and voltage reflection-displacement response. A pair of aluminum blocks, shown in Figure 2, was manufactured to rest inside the 6.3 cm by 6.3 cm square shear box. The upper block rests directly on the lower block, creating a shear zone of negligible thickness at their interface. Holes were drilled to diameters slightly larger than the cables, making it possible to manually thread the cables through the blocks. One limitation with this design is that cables must be slightly smaller than the holes, thus allowing some initial seating movement during the test before the cables physically shear. Holes for each Cable Shear Zone Anchor Plates Figure 2. Photograph of Manufactured Blocks Used in Modified Direct Shear Prior to insertion, the jacket is removed from the portion of cable placed in the blocks. Anchor plates are equipped with setscrews that tighten on opposing sides of the cable to prevent it from pulling out during shearing. A 2-kg normal load is applied to hold the blocks in place during shearing. The top half of the shear box is raised approximately 2 mm, allowing the blocks to slide. The frictional resistance between sliding blocks was found to be very small; the resistance is subtracted from the measured shear load during each test. Figure 3 shows the final setup prior to testing. A secure cable connection is established and a baseline signal is recorded before shearing starts. Displacement is set at a constant rate of.5 mm per minute for all tests. Shear load is measured from a fixed proving ring and recorded manually. Shear load measurements are recorded until post-peak load is constant for several displacement increments or until the cable severs. Voltage reflection is measured and recorded electronically using a Tektronix 152C tester interfaced with a desktop computer. Voltage reflection responses are captured at discrete displacement intervals from the start of shearing until the cable short-circuits. Shear load and voltage reflection measurements are recorded every.5 mm for Alpha 9847 cables and every.25 mm for Belden 1855A and CommScope 212k cables. Cable Modified Shear Blocks Figure 3. Experimental Setup in Modified Direct Shear Apparatus

4 RESULTS AND ANALYSIS Multiple shear tests are conducted on each of the three cables to assess repeatability of shear load-displacement and voltage reflection-displacement responses. The results from a series of shear tests are presented herein and show that measured responses are unique to each cable. Shear load-displacement and voltage reflection-displacement responses illustrate the stiffness and sensitivity of these cables when sheared along a thin zone. A real time plot, such as the one shown in Figure 4, is the compilation of voltage reflections recorded at discrete displacement intervals for each test. Each signal shown in Figure 4 represents the voltage difference between the baseline signal and a signal measured at a given displacement. Locations of the downward spikes indicate the shearing zone occurs at about 15 cm from the cable connection. The magnitude of each downward spike represents the amount of voltage reflection, which increases with displacement until the cable short-circuits or severs entirely. In this test, voltage reflection peaks at nearly 75 m. After this peak reflection, the cable short-circuits resulting in a full 1 m reflection. In Figure 4, the short-circuited signal flat lines at nearly 13 m, instead of 1 m, only because that location represents the bottom of the viewing window set to capture signals. -2 Length (cm) Voltage Reflection (mρ) Short Circuit Figure 4. Real Time Recording of Voltage Reflection Responses from Shearing Alpha 9847 For each test on each cable, measured shear loads and voltage reflections are plotted at each displacement interval to evaluate trends in the data. Shear load-displacement and voltage reflection-displacement curves compiled from three direct shear tests of CommScope 212k cables are shown in Figures 5 and 6. The results from each of the three trial tests on the same cable are consistent and demonstrate repeatability of the method. Consistency in the results was also observed for Alpha 9847 and Belden 1855A cables. Repeatability is important so that voltage reflections can be accurately correlated to shear displacements when cables are embedded in deforming soil. The trend in Figure 5 appears to be approximately bilinear with a change in stiffness occurring at 2 mm of shear box displacement. It is theorized that this change in stiffness occurs after the cable has fully seated itself inside the drilled hole. The cable physically begins to shear at this point. As illustrated in Figure 6, voltage reflection increases exponentially with shear box displacement. However, voltage reflections are less than 5 m up to 2 mm of shear box displacement, and do not begin to increase significantly until 2 mm is reached. This observation supports the theory that cables do not begin to shear until the shear box displaces 2 mm.

5 Trial 1 Trial 2 Trial 3 3 Shear Load (kn) Shear Box Displacement Figure 5. Shear Load-Displacement Responses from Shearing CommScope 212k Cables Trial 1 Trial 2 Trial 3 35 Voltage Reflection (mρ) Shear Box Displacement Figure 6. Voltage Reflection-Displacement Responses from Shearing CommScope 212k Cables

6 The shear strength of the two miniature cables is lower than the larger-diameter Alpha 9847 cable, but the shear stiffness appears to be slightly higher, as shown in Figure 7. The average maximum shear load sustained by Alpha 9847 was 629 kn. Peak loads for this 7.24 mm diameter cable occurred at shear box displacements averaging 1.5 mm. In all three tests on this cable, however, the cable short-circuits prior to peak. After the peak load was reached, the load decreased to approximately 491 kn and remained constant for several increments of displacement, as shown in Figure 7. This post-peak response is the result of the dielectric failing and the load being transferred solely to the inner conductor. Upon dismantling the test setup, the cable was observed to have stretched across the shear zone such that its total shear deformation exceeded its diameter. Table 2 shows that the two smaller-diameter cables sustained significantly lower peak loads at much smaller displacements than Alpha For example, Belden 1855A sustained an average peak load of 265 kn, which is less than half of the shear load sustained by Alpha Both miniature cables displayed brittle failure; when the peak load was reached, the cable severed completely and the load decreased immediately to zero. Finally, it is observed from Table 2 that the maximum shear box displacements for both miniature cables are approximately 2 mm larger than the cable diameter. This observation further suggests that shearing begins at approximately 2 mm of shear box displacement. Make Table 2. Results from Modified Direct Shear Tests Model Dielectric Diameter Range of Maximum Shear Box Displacement Range of Maximum Shear Load (kn) Alpha CoSc 212K Belden 1855A Alpha 9847 produced larger voltage reflections than both miniature cables, as illustrated by three example tests in Figure 8. A peak voltage reflection of 95 mρ was recorded at 9.6 mm, which was before the peak shear load was achieved. The cable short-circuited within.5 mm following the peak voltage reflection. Belden 1855A and CommScope 212k cables display similar exponentially increasing voltage reflection trends, as shown in Figure 8. For the two miniature cables, a short circuit occurs immediately after the peak voltage reflection was measured. The miniature cables produced higher voltage reflections at smaller displacements than Alpha For example, voltage reflections for both miniature cables are more than 2 m at 4 mm of displacement, compared to less than 1 m for Alpha 9847, as shown in Figure 8. These findings show that smaller-diameter cables are more sensitive to very small shear displacements, and more importantly, to very small changes in shear displacement. For all three cables, there is a rapid increase in voltage reflection as the peak load approaches. There is an upper limit of shear displacement and voltage reflection for all of the cables, where, within the final displacement increment, the voltage reflections increase quickly until the cable short-circuits. SUMMARY This paper presents the concept of using small-diameter TDR cables in physical soil models to measure small, localized internal displacements. To investigate this concept, three coaxial cables were sheared in a modified direct shear device to acquire shear load and voltage reflection data as a function of shear box displacement. The results displayed the unique shear load and voltage reflection responses of each cable. The results produced by the two miniature cables were similar, but were much different from the larger-diameter Alpha 9847 cable. Shear stiffness of the two miniature cables was slightly higher than the Alpha 9847 cable; however, the peak shear resistance was lower. Higher voltage reflections were produced at smaller displacements for both miniature cables. The 75 Ω miniature cable, Belden 1855A, was slightly more compliant and weaker in shear than the 5 Ω miniature cable, CommScope 212k. Future investigations of this concept will include evaluating smaller-diameter, specialty compliant cables in direct shear for potential instrumentation of physical soil models.

7 7 Alpha 9847 Belden 1855A CS 212k 6 5 Short Circuit Shear Load (kn) x x Shear Box Displacement Figure 7. Representative Shear Load-Displacement Responses from Shearing Three Cables 1 Alpha 9847 Belden 1855A CS 212k 9 8 Voltage Reflection (m ρ) For Example Shear Box Displacement Figure 8. Representative Voltage Reflection-Displacement Responses from Shearing Three Cables

8 REFERENCES Chambon, P., Corte, J.-F., Garnier, J. and Konig, D. (1991) "Face Stability of Shallow Tunnels in Granular Soils," Centrifuge 91, Proceedings of the International Conference on Geotechnical Centrifuge Modeling, Boulder, Colorado, pp Dowding, C.H. and Pierce, C.E. (21) Measurement of Localized Soil Deformation with Time Domain Reflectometry, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, under review. Dowding, C.H. and Pierce, C.E. (1994) Measurement of Localized Failure Planes in Soil with Time Domain Reflectometry, Proceedings of Symposium and Workshop on Time Domain Reflectometry in Environmental, Infrastructure, and Mining Applications, U.S. Bureau of Mines, Special Publication SP19-94, pp Huat, B.B.K., Craig, W.H. and Merrifield (1991) "Simulation of a Trial Embankment Structure in Malaysia," Centrifuge 91, Proceedings of the International Conference on Geotechnical Centrifuge Modeling, Boulder, Colorado, pp Kutter, B. (1999) personal communication. Phillips, R. (21) personal communication. Pierce, C.E. (1998) Time Domain Reflectometry Measurements of Localized Soil Deformation, PhD Thesis, Northwestern University, Evanston, Illinois, 237 pp. Zornberg, J.G., Mitchell, J.K. and Sitar, N. (1997) "Testing of Reinforced Slopes in a Geotechnical Centrifuge," Geotechnical Testing Journal, ASTM, Vol. 2, No. 4, pp

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