Electrical Resistivity Imaging of Laboratory Soilcrete Column Geometry

R. G. Bearce, S.M.ASCE1; M. A. Mooney, M.ASCE2; and P. Kessouri3

Abstract: Ground improvement via jet grouting is commonly used to strengthen weak ground and/or create hydraulic barriers. Delivering soilcrete columns with tightly controlled and known diameters is critical to performance; however, techniques to assess jet grout geometry during construction are lacking. This paper reports the results of a study on electrical resistivity imaging of soilcrete by investigating the effects of electrode configuration and electrical protocol type on laboratory scale soilcrete columns constructed in a tank filled with sand. Experimental results are verified via numerical modeling and the model is used to analyze the changes in soilcrete resistivity that result from geometric variation. The results of this study indicate that resistivity imaging with direct contact electrodes can estimate the diameter of laboratory scale jet grout columns to within 5% of the as-built column diameter. A relationship between electrode spacing and column diameter is identified and quantified to more readily extend the diameter estimation approach developed in this research to field-scale geometries. Additionally, time lapse monitoring of soilcrete resistivity was performed over the course of curing. Results indicate that resistivity imaging should be performed as early as possible to obtain the greatest resistivity contrast between the soilcrete and in situ soil. DOI: 10.1061/(ASCE)GT.1943-5606.0001404. © 2015 American Society of Civil Engineers.

Introduction approaches also have been proposed. Mechanical wave propagation techniques, including downhole or surface seismic Jet grouting is an in situ ground improvement technique used to (Madhyannapu et al. 2010) and crosshole sonic logging (CSL) strengthen weak or unstable ground and/or create hydraulic barriers (Niederleithinger et al. 2010; Bearce et al. 2014; Spruit et al. via columns of soilcrete (i.e., a mixture of grout and in situ soil). 2014), can characterize the changes in concrete/soilcrete strength This process is illustrated in Fig. 1(a). Successful performance of via increased wave speed, but cannot estimate geometry because jet grout columns and column assemblies requires constructing the monitoring tubes are within the grouted structure. Furthermore, precise column geometries. However, the realized diameter of jet these methods require permanent casings and sufficient soilcrete grout columns is influenced by in situ soil properties and stress curing time for ultrasonic and seismic wave propagation (more than state (Essler and Yoshida 2004); therefore, onsite inspection of 2 days). Borehole ground penetrating radar also has been proposed, geometry, preferably in real time, is critically important to jet grout but requires a cased borehole directly outside the column (T&A construction. Jet grout column geometry is often assessed in prac- Survey 2013). tice by radial coring, probing, or column excavation (e.g., Duzceer Direct current (DC) electrical resistivity has been used to and Gokalp 2004; Yoshida 2010; Burke 2012; Bruce 2012; Wang characterize soil improvement techniques such as injection et al. 2012). However, these approaches require waiting several grouting, compaction grouting, and hydraulic barrier walls days for sufficient soilcrete curing and often are unfeasible to (e.g., Daily and Ramirez 2000; Abu-Zeid et al. 2006, 2009; perform below the water table. Further, the destructive nature of Santarato et al. 2011). While these improvement techniques are these approaches limits them to use on test columns; these not identical to jet grouting, the application of the geophysical techniques cannot be used on production columns. technique is quite similar (i.e., DC resistivity exploits the resistivity A number of nondestructive approaches have been proposed contrast between improved and unimproved soil). The electric in the past to measure jet grout column geometry, including cylinder method (ECM) is a commercially-available DC resistivity mechanical downhole devices (Passlick and Doerendahl 2006) technique used to estimate the geometry of a jet grouted column and temperature monitoring (Meinhard 2002; Mullins 2010; (Frappin and Morey 2001; Frappin 2011). The ECM employs a Sellountou and Rausche 2013).Thermal imaging has been used central borehole with a slotted casing in the center of the column successfully to assess diaphragm walls and diaphragm wall (either pushed into the fresh column or drilled in after 1–2 days of joints (Doornenbal et al. 2011; Spruit et al. 2011). Geophysical curing). After casing placement, a chain of electrodes is lowered

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. into the water-filled casing to allow electrical coupling between 1Ph.D. Candidate, Dept. of Civil and Environmental Engineering, the jet grout and the electrodes (i.e., the electrodes are coupled Colorado School of Mines, Golden, CO 80401 (corresponding author). to the water, which is coupled to the jet grout through the slots E-mail: [email protected] in the casing). This approach uses a type of pole-pole test protocol 2Professor, Dept. of Civil and Environmental Engineering, Colorado that requires reference electrodes on the ground surface. Frappin School of Mines, Golden, CO 80401. E-mail: [email protected] and Morey (2001) concluded that the ECM can estimate to within 3 Postdoctoral Researcher, Dept. of Geophysics, Colorado School of 10% of the column diameter. However, in regions where geometry Mines, Golden, CO 80401. E-mail: [email protected] changes are the result of changing soil conditions, there is an Note. This manuscript was submitted on April 23, 2015; approved on July 14, 2015; published online on November 19, 2015. Discussion period additional 0.5 m error. This can result in considerable uncertainty. open until April 19, 2016; separate discussions must be submitted for in- This paper presents the results of a study to advance DC resistivity dividual papers. This paper is part of the Journal of Geotechnical and imaging of jet grout column geometry. The study focused on Geoenvironmental Engineering, © ASCE, ISSN 1090-0241. examining the influence of direct coupling of electrodes to the

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Fig. 1. (a) Illustration of the jet grouting method; (b) the jet grouting method applied to foundation underpinning

jet grout column (versus slotted casing in which coupling is indirect characterized by measuring the potential difference across two through water) as well as using the traditionally surface-based or more measurement electrodes of known separation distance Wenner-α measurement protocol into a central borehole-based (M and N, Fig. 2). Using the injected current and the measured approach. Laboratory-scaled soilcrete column experiments were potential, the material’s resistance R (Ω) is calculated. To obtain conducted to carry out the investigation. Finite element modeling the apparent resistivity ρa (Ωm) from resistance, a geometric was performed to support the experimental results and to assess correction factor must be applied accuracy. ψMN ρa ¼ · k ¼ R · k ð3Þ iAB Background where ψMN = potential difference measured across electrodes M and N (V); iAB = current injected across electrodes A and B Electrical Resistivity Imaging (A); and k = geometric correction factor (m). ρa (obtained from DC resistivity testing is an electrical geophysical technique based the DC resistivity test) is not the same as a material’s true resistivity on Ohm’s law that has been used widely in geophysical exploration ρ. ρa is a weighted average of all ρ in the volume of material for decades and is becoming more prominent in civil engineering influenced by the injected electrical field. For a homogeneous quality assurance and quality control (QA/QC) applications. In medium, ρ ¼ ρa, but in heterogeneous media, ρa is influenced practice, DC resistivity measurements usually are performed using by the different values of ρ. In practice, ρ is often obtained using commutated direct current (i.e., a square-wave alternating current) inversion of ρa data (Revil et al. 2012). or low frequency alternating current (AC) to assess the real com- The geometric factor k is related to the electrode spacing a for a ponent of the material’s resistivity and avoid material polarization Wenner-α array with point electrodes on the surface of an infinite resulting from sustained DC injection. The commutated direct cur- homogeneous halfspace rent approach is utilized by the ABEM Terrameter LS (ABEM In- k ¼ 2 · π · a ð4Þ strument AB, Sweden) used in this research. The DC resistivity ’ technique characterizes a material s electrical resistivity or ability where a = distance between any two adjacent array electrodes to resist current flow. The principle behind the DC resisitivity tech- (a ¼ AM ¼ MN ¼ NB, Fig. 2). For a full space condition (in ’ nique is macroscopically governed by Ohm s law [Eq. (1)] practice electrodes are deep enough in the ground that no surface E boundary effects exist) j ¼ ð1Þ

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. ρ k ¼ 4 · π · a ð5Þ 2 where j = conduction current density (A=m ); E = electrical field in k = ρ ’ Ω Borehole resistivity measurements have a variable factor in the V m; and = material s electrical resistivity ( m). The electrical near surface region that transitions from a half-space to full-space field is defined as the gradient of the electrical potential [Eq. (2)] condition (Revil et al. 2012; Guo et al. 2014). The laboratory setup E ¼ −∇ψ ð2Þ used in this study mimics a field soilcrete column and will be subject to a variable k factor near the surface. Other geometric com- where ψ = electrical potential (V). In practice, current is injected plexities of the laboratory setup are not as easily addressed with across a pair of electrodes (A and B, Fig. 2) to create an electric analytical solutions (e.g., ring electrodes, soil tank boundaries). field in the subsurface. Fig. 2 illustrates a borehole configuration; Therefore, finite element (FE) modeling via COMSOL Multi- however, the more common approach is on the ground physics (COMSOL, Burlington, Massachusetts) is used to obtain surface (i.e., rotate image 90° clockwise). The electric field is a more accurate estimate of k. The application of Eq. (3)

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Fig. 2. 2D axisymmetric cross section of current flow lines for the direct coupled ring electrode array at increasing electrode spacing; estimation of ρa using Eq. (3) is shown for each a based on the potential across electrodes M and N labeled in each plot; these simulations show the current/ equipotential lines in the laboratory tank, and thus boundary effects are noticeable for lines near the tank boundary

for a ring electrode array in a homogeneous medium constrained combined with SP to form soilcrete with an approximate cement to the laboratory soil tank geometry is illustrated in Fig. 2.The content of 8–9% by volume. In practice, field jet grout columns figure depicts a 2D radial cross section of the Wenner-α meas- can have widely variable cement contents, but this value is reason- urementprotocolatincreasingvaluesofa. Current flow lines able for field jet grout columns in sand. near the tank boundary and ground surface are influenced by To prepare soilcrete specimens, a PVC casing (outside diameter the finite volume of the laboratory soil tank. The Wenner-α of 7.6 cm) was placed in the center of the soil tank. Dry sand was measurement protocol injects current (iAB) across electrodes A deposited uniformly to a height of 20–30 cm by air pluviation from and B and measures the potential (ψMN) across electrodes M a consistent drop height (25–30 cm). The sand was not mechani- and N. For the borehole Wenner-α array, each measurement cor- cally compacted, but this was not important for the study. The sand responds to ρa at a depth zMN (i.e., the midpoint of electrodes M was saturated by continuously raising and maintaining the water and N). In practice, a is increased by using every other electrode, table approximately 1–2 cm below the surface of the placed sand every third electrode, etc. For the Wenner-α protocol, increasing throughout sample preparation. A form tube was slipped over the a results in increased volume of measurement influence with PVC casing and 10 cm of sand was filled around the outside of the decreased measurement sensitivity (i.e., the measurement is a form tube to fix its position and prevent soilcrete from leaking out weighted average of the resistivity in a larger region, the boun- the bottom of the tube [Figs. 3(b and d)]. Premixed soilcrete was dary of which is further from the array). poured into the form tube to achieve the desired column section height [Fig. 3(d)]. Sand was deposited around the soilcrete-filled form tube until the height of soilcrete and confining sand were Experimental Setup and Testing Protocol equal [Fig. 3(e)]. Then, the form tube was extracted, allowing To perform the investigation, scaled soilcrete cylinders were the sand to confine the fresh, wet soilcrete and form a soilcrete constructed within a cylindrical soil tank of 1 m diameter and cylinder [Figs. 3(c and f)]. 2 m height [Fig. 3(a)]. A poorly-graded sand (SP) was used as This study employed two types of central casing/electrode array the medium surrounding the soilcrete columns. The SP material combinations. The first array type consists of PVC casing with

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. has a D50 ¼ 0.81 mm, and Cu ¼ 1.5. The resistivity of the sand externally mounted ring electrodes in direct contact with the was verified by conducting a background resistivity profile measured media [Fig. 4(a)]. The second array mimics the slotted (i.e., a Wenner-α profile from a soil tank full of sand prepared with casing approach used by the ECM (Frappin and Morey 2001) the same technique as the soilcrete/sand system). Increased sand and is illustrated in Fig. 4(b). The slotted casing used in the density can result in higher resistivity, but this effect was not ob- laboratory was wrapped in a fluid-permeable geotextile to prevent served in the laboratory data (in which the soil column height was soilcrete/soil infiltration. Both images show the full length array only 1.3 m, providing insufficient overburden pressure to meaning- with an expanded detail window of array photographs and 2D fully alter the density and thus resistivity profile with depth). The axisymmetric cross sections of the cylindrical setup. The inside resistivity of the sand ρs (Ωm) under saturated conditions had an of both array tubes are hollow, water tight, and contain instrumen- average value of 20 3.5 Ωm. Grout was prepared by mixing tap tation wiring. water and portland Type I cement (Quikcrete Companies, Atlanta, Two soilcrete specimens were prepared and tested. Specimen 1 Georgia) with a 2∶1 water∶cement ratio. This grout mixture was [Fig. 5(a)] was tested with a direct coupled ring electrode array, and

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Fig. 3. (a) Laboratory soil tank with two stages (2 m height, 1 m inside diameter); (b) staged construction of 30 cm diameter soilcrete cylinder prior to addition of sand and soilcrete; (c) soilcrete cylinder after extraction of form tube; (d–f) a cross-sectional illustration of the sequential soilcrete/sand placement process

specimen 2 [Fig. 5(b)] was tested with a slotted casing and internal surface (tens of meters from the borehole in field practice). ring array. The slots are not visible on the exhumed specimen 2 Sufficient electrode separation on the tank’s ground surface could casing because of the geotextile. Because the column construction not be obtained in the laboratory, and thus no direct comparison of process resulted in minor geometric variations, the dimensions Wenner-α and pole-pole is available. shown in Fig. 5 are average values obtained from multiple

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. measurement profiles of the exhumed columns. In regions where the as-built diameter D ¼ 30 cm, the average diameter of the Finite Element Modeling exhumed specimen was equal to 29.8 1.7 cm (i.e., 1σ). For the reduced diameter regions (D ¼ 18 cm), average exhumed A 3D scale model of the laboratory soil tank and test arrays were specimen diameter was equal to 17.8 1.2 cm. constructed in COMSOL Multiphysics. This software package is The Wenner-α protocol was performed using an ABEM extensively used as a forward modeling tool for the DC resistivity Terrameter LS system at prescribed times over the first 240 h test (Kelekanjeri and Gerhardt 2008; Chou et al. 2010; Clement (10 days) of soilcrete curing. Pole-pole protocols were attempted et al. 2011), and for DC resistivity applied to geotechnical and geo- (to obtain a comparison to the ECM approach), but these tests were logical problems (e.g., Kim et al. 2009; Huang and Lin 2010; Wang not possible because of the limited geometry of the laboratory et al. 2011; Araji et al. 2012). The laboratory tank with ring electro- tank. The pole-pole array requires one injection electrode and one des contains complex geometries and finite boundaries.The FE potential electrode placed at a theoretical infinity on the ground model was constructed using free tetrahedral elements with

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Fig. 4. Illustration of full length electrical array with expanded cross sectional diagram and photographs for (a) direct coupled ring electrodes; (b) ring electrodes in a water-filled slotted casing; the photographs and FE renderings in (b) do not show the geotextile to better appreciate the geometry of the slotted casing; the geotextile location is shown in the expanded illustration and also visible in Figs. 3(b and c) and Fig. 5(b)

Fig. 5. Diagram of soilcrete specimen/array/soil geometry with exhumed specimen for comparison for (a) specimen 1 and (b) specimen 2; the height of the soil around the column corresponds to the height of the soil in the tank during the test and not the full height of the tank

uniform directional scaling. High resolution regions (e.g., ring elec- M and N and converted to ψMN (V) via the known ring volume. trodes) had a minimum element dimension of 1 mm, and regions of Eq. (3) is used to estimate ρa with FE iAB, ψMN, and k. near zero current (e.g., soil near the tank boundary) had a maximum Geometric factors for the arrays and protocols used in this re-

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. element size of 7 cm. The FE model is governed by the electric search were estimated by simulating the DC resistivity test in a currents physics interface, which solves a current conservation homogeneous 10 Ωm material (confined to the geometry of the equation (based on Ohm’s law) using the scaler electric potential lab tank) for each value of a (e.g., Fig. 2). The geometric correction as the dependent variable (COMSOL 2014). A series of stationary for this data are affected by more aspects of the system geometry electrical models is used to simulate the DC resistivity test. The than a alone. The laboratory scale setup is limited in size, and will modeling mimics the experimental protocol by sequencially inject- have boundary effects compared to the half/full space conditions in ing and measuring each electrode combination in the laboratory the field. In addition, the ring electrode diameter (8 cm) is relatively Wenner-α protocol. To simulate an individual DC resistivity large compared to the minimum a for the array (3 cm). The combi- measurement, a volumetric current source (A=m3) is applied to ring nation of these geometric complexities requires the use of a custom electrode A (of known volume) and sinked to an identical ring k factor determined from FE modeling of the DC resistivity test. electrode B, such that the desired iAB is injected (e.g., Fig. 2). This technique is widely used and accepted in literature (e.g., Rücker Volumetric potentials (V=m3) are obtained from ring electrodes et al. 2006; Kelekanjeri and Gerhardt 2008; Yi et al. 2009;

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Guo et al. 2014). To mimic the laboratory array setup, k was The a ¼ 3 cm data from the slotted casing electrodes (Fig. 7) estimated at 3 cm intervals over the entire height of the array in reveal ρa values of 17 Ωm, which, unlike the direct coupled ap- a homogeneous 10 Ωm material for each value of a. proach, are not indicative of ρsc (1.5–2 Ωm). The water in the cas- To assess the validity of the FE model, a simplified version of ing (ρw ¼ 33 Ωm) results in ρa measurements that are influenced the laboratory setup was modeled with point electrodes (to by ρw, ρsc, and ρs. Further, slotted casing data exhibit a more eliminate ring electrode geometric complexity) in a 10 m diameter gradual change in response when transitioning from sand to soil- by 10 m height homogeneous cylinder (to eliminate boundary ef- crete (z ¼ 40 cm, and z ¼ 95 cm). The water column forms a fects). The FE model results showed excellent agreement with homogeneous buffer zone between the electrodes and the soilcrete Eq. (3). Surface electrode simulations had k values consistent with or sand. Compared to the sharp changes in response of the direct Eq. (4) and measurements at midpoint depth (i.e., full space) had coupled electrodes (Fig. 6), material transitions and changes in D k values consistent with Eq. (5). Near surface measurements had are difficult to detect in the slotted casing data. k values that transition from half to full space conditions. These A comparison of the two data sets suggest that the direct a ¼ 3 validation tests were performed for , 6, 9, and 12 cm. coupled ring electrodes provide a considerable measurement advantage over the slotted casing approach for a Wenner-α array. The direct coupled electrodes provide a high resolution estimate of Results ρsc from the a ¼ 3 cm measurement, and reveal sharper contrasts when transitioning between materials and variations in D. The slot- Apparent resistivity results for the two soilcrete cylinders are ted casing approach cannot directly estimate ρsc because of the shown in Fig. 6 (direct coupled electrodes) and Fig. 7 (slotted cas- influence of borehole water, and exhibits less sensitivity to changes ing) for data acquired after 1.5 h of curing using the Wenner-α in D than the direct coupled approach. protocol (a ¼ 3, 6, 9 and 12 cm). Scaled images of the exhumed FE models of both specimens and array configurations were specimens and corresponding FE models are shown for reference. constructed to further inform the experimental results. Each soil- All data are presented in terms of ρa [Eq. (3)] obtained from crete column was modeled with the geometric specifications shown experimental ψMN and iAB with FE k factor. in Fig. 5. FE model inputs for ρsc, ρs, and ρw were obtained from The a ¼ 3 cm data for the direct coupled electrodes (Fig. 6) benchtop resistivity tests and/or a ¼ 3 cm direct coupled Wenner-α reveal ρa values of approximately 1.6 Ωm in the regions of the soilcrete column in which the as-built, modeled column diameter data (Table 1). FE modeling of the direct coupled array (Fig. 6) showed excellent agreement with the experimental data. There D is equal to 30 cm (z ¼ 40–62,82–110 cm). These ρa values are was minor disagreement in the regions above and below the very similar to the soilcrete’s true resistivity (ρsc) of 1.5–2.0 Ωmas determined from benchtop tests on soilcrete of the same mix and soilcrete column, but results were very close over the soilcrete a age. This result suggests that a ¼ 3 cm ρa measurements are column depth interval for all values of . FE modeling of the slotted sensitive only to ρsc and are not influenced by the surrounding casing array did not exhibit the same quality of fit as the direct a ¼ 3 untreated sand resistivity (ρs). A very slight increase in a ¼ coupled electrodes. The cm result showed reasonable 3 cm ρa is observed in the D ¼ 18 cm region (z ¼ 62–82 cm), agreement, but there was more scatter in the experimental data. a ¼ 6 suggesting that ρa is influenced by both ρsc and ρs in this region FE results for and 12 cm were reasonably well fit over a ¼ 9 (recall that ρs is 20 Ωm). The increase in ρa in the reduced diameter the soilcrete column interval, but cm FE response deviated region (z ¼ 62–82 cm) is manifested more prominently in the data from experimental results at z ¼ 60–100 cm. The reason for this as a increases. This response is expected as an increase in a will lack of fit is not entirely clear given that the other data sets showed increase the depth of measurement. These trends support a relation- reasonable fit in this region; however, it is likely because of the ship between a and D. It will be confirmed in this paper that for increased modeling complexity of the slotted casing setup. No ad- cases in which D ≥ 10a, ρa measurements can be used as an ditional variation of input parameters can be justified to improve indicator of ρsc with depth. these fits (e.g., no reason to assume variable ρw or ρs with depth). Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved.

Fig. 6. Comparison of experimental and FE apparent resistivity responses for specimen 1 after 1.5 h of curing; plots and column images are scaled such that horizontal dashed lines can be used to relate geometry changes in the column to changes in the data response; z position of the data points represents the center of each four electrode array configuration

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Fig. 7. Comparison of experimental and FE resistivity responses for specimen 2 after 1.5 h of curing; plots and column images are scaled such that horizontal dashed lines can be used to relate geometry changes in the column to changes in the data response; data sets are clipped at the bottom due to electrode failure in the bottom two electrodes

Table 1. Experimentally Measured Resistivity Values of the Sand (ρS), (i.e., areas with more closely spaced contour lines have higher cur- Soilcrete (ρSC), and Water (ρW ) Used in the Laboratory Experiments rent density). The images are zoomed to better illustrate the detail Experimental FE of the more closely spaced current lines near the array, and, thus, not all eight regions are visible. For the DC resistivity test, a higher Parameter Benchtop Array Specimen 1 Specimen 2 current density is indicative of higher measurement sensitivity. ρS (Ωm) 18–26 20 3.5 20 20 The coupling between the ring electrodes and soil allows the ρ Ω – 1 6 0 1 SC ( m) 1.5 2.0 . . 1.6 1.6 injected current to propagate directly into the soil (in this ρW (Ωm) 33 N/A N/A 33 simulation, ρs ¼ 10 Ωm). In contrast, the slotted casing approach Note: FE resistivity inputs for each model are also reported. [Fig. 8(b)] loses a significant amount of measurement sensitivity because approximately 40% of the current does not propagate beyond the borehole water column. Flow lines in the water column To further understand the measurement capability of the two are more closely spaced than in the soil, suggesting that the electrical arrays, FE modeling was used to estimate the percent Wenner-α protocol with a slotted casing array has the highest of current iAB propagating into a homogeneous medium (10 Ωm). sensitivity to ρw. The direct coupled approach also has the largest Axisymmetric cross sections for a ¼ 3 cm are shown for the direct current density near the array [Fig. 8(a)], which results in the high- coupled array [Fig. 8(a)] and the slotted casing array [Fig. 8(b)]. est sensitivity to the soil/soilcrete. This observation explains why Current flow lines for each model were separated into eight mag- the experimental a ¼ 3 cm ρa (Fig. 6) is sensitive to the ρsc only. nitude-based regions. The area between any adjacent pair of The protocol used by the ECM would not suffer from this issue contour lines contains 12.5% of the total current in the system as significantly (i.e., electrode B is on the ground surface so current Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved.

Fig. 8. 2D axisymmetric cross section of current flow lines of electrical array and homogeneous soil tank configuration for (a) a direct coupled ring electrode array; (b) a ring electrode array within a water-filled slotted casing at a ¼ 3 cm

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 Fig. 9. Comparison of FE resistivity responses for columns with diameter profiles of 1.1D, D, and 0.9D to experimental resistivity response for (a) a ¼ 3 cm; (b) a ¼ 6 cm; (c) a ¼ 9 cm; (d) a ¼ 12 cm; (e) experimentally predicted column diameter D¯ from each value of a

naturally flows out of the borehole). The geometric contraints of the correlation approach was applied to experimental ρa to provide laboratory prevented the evaluation of pole-pole arrays in this an estimate of column diameter D¯ [Fig. 9(e)]. research; however, it is reasonable that the pole-pole protocol also The estimated D¯ are in good agreement with the as-built D. For could see improved results using direct coupled electrodes instead the D ¼ 30 cm regions, the average D¯ was equal to 30.2 1.5 cm ¯ of a slotted casing. (5% D). In the D ¼ 18 cm region, average D ¼ 17.9 0.6 cm To better characterize the relationship between a and D, (3% D). Because the measurement was taking an axisymmetric additional FE models of specimen 1 were constructed with diam- average of the volume around the ring electrode array, the diameter eter profiles of 1.1D and 0.9D (i.e., 10% of the as-built diameter variation in the exhumed specimens may address the accuracy ¯ D). FE ρa responses for columns with diameter profiles of 0.9D, D, with which D can be estimated. The average as-built D of 1 1D ρ ρ ρ 29 8 1 7 and . are defined as að0.9DÞ, aðDÞ, and að1.1DÞ, respectively exhumed specimen 1 was equal to . . cm for the larger ρ ρ ρ D¯ ¼ 30 2 1 5 (Fig. 9). For each response, að1.1DÞ < aðDÞ < að0.9DÞ because regions, which is very similar to the average . . cm increasing D results in the measurement imaging more of the estimated via resistivity imaging. In the D ¼ 18 cm region, average lower resistivity soilcrete. D of the exhumed specimen was equal to 17.8 1.2 cm ¯ As shown in Fig. 9(a), a 10% variation in the D ¼ 30 cm diam- and D ¼ 17.9 0.6 cm. ¯ eter regions (z ¼ 42–62 cm, z ¼ 82–105 cm) has relatively little or D was also well fit in transitional regions corresponding to ρ ≈ ρ ≈ ρ column diameter reduction (z ¼ 62 and 82 cm). Uniform diameter no influence on the response (i.e., að0.9DÞ aðDÞ að1.1DÞ). D=a varies from 9 to 11 in this region, and ρa is influenced regions and diameter reduction transition regions showed similar ρ ρ by ρsc only. For the a ¼ 6 cm measurements, however, misfit between experimental a and the aðDÞ response, suggesting ρ ρ ρ að1.1DÞ < aðDÞ < að0.9DÞ, indicating that the 10% variation in the D ¼ 30 cm regions does influence ρa [Fig. 9(b)]. In this example, D=a varies from 4.5 to 5.5 and ρa is influenced by both ρ ρ a ρ ρ sc and s.As increases, the deviation between að0.9DÞ, aðDÞ, and ρ 10% D ¼ að1.1DÞ increases [Figs. 9(c and d)]. The variation in the 18 cm diameter region has a more significant influence on ρa, modeled at all values of a. The sensitivity of ρa to D (for D=a < 5) was exploited to estimate column diameter. For example, in Fig. 10(a) (a ¼ 12 cm), the experimental ρa value at z ¼ 51 cm deviates from the expected response ρaðDÞ. Because the value falls between the ρ ρ ρ Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. aðDÞ and að0.9DÞ responses, the experimentally measured a suggests that the column diameter at this depth lies between D and 0.9D. To estimate the diameter that best fits the experimental data, defined as D¯ , a linear correlation was assumed using points ρ 1 1D ρ D ρ 0 9D ( að1.1DÞ, . ), ( aðDÞ, ), and ( að0.9DÞ, . ) [Figs. 10(b and c)]. Over the range of D evaluated (10% D), the correlation 2 between D and ρa is sufficiently linear (R ≥ 0.98 for all combinations of z and a). This correlation and corresponding D¯ are shown at z ¼ 51 cm (in which D ¼ 30 cm) and z ¼ 71 cm (in which D ¼ 18 cm) in Figs. 10(b and c), respectively. No single Fig. 10. (a) FE diameter study compared to experimental data for a ¼ 120 D ρ z ¼ 51 correlation equation was reported because this relationship differs cm; (b) linear correlation between and a for cm; D ρ z ¼ 72 for every value of a and z, and also depends on D=a. This (c) linear correlation between and a for cm

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 that column diameter reduction did not reduce the accuracy of the that resistivity growth followed a logarithmic behavior with curing measurement. For soil to soilcrete transitions (i.e., the top and time. bottom of the column), experimental ρa values occasionally fell outside the 10% D envelopes (e.g., z ¼ 100–105 cm) [Figs. 9 (a–d)]. The sharp transition between soil and soilcrete at the array Conclusions interface resulted in a ρa response that is significantly less sensitive to diameter variation. This observation helps to explain why D¯ near Borehole DC resistivity tests were performed on laboratory scale the top and bottom of the column show the greatest misfit from D. soilcrete columns to assess the usability of the Wenner-α protocol In general, measurements where D=a ≤ 5 provide sufficient change with direct coupling of electrodes to improve column geometry es- in resistivity response for use as estimators of diameter. The lower timation. The protocol was tested on two array configurations: the value of D=a, the more sensitive the measurement will be to (1) electrodes in direct contact with the soilcrete, and (2) electrodes changes in D. This relationship also is affected by the resistivity in a slotted, water-filled casing encased in soilcrete. FE models of contrast between the soilcrete and the soil. the soil tank and specimens/arrays were constructed and compared Electrical resistivity profiling exploits the contrast in with experimental data to assess the capability of the model as a resistivity between the surrounding soil and the soilcrete. In this tool for column geometry prediction. α study, ρs=ρsc≈12, and Frappin and Morey (2001) recommend The study revealed that the Wenner- array with direct coupled ρs=ρsc > 10. The highest ρs=ρsc ratio occurs within the first two electrodes provides several advantages over the slotted casing hours of mixing (depending on cement type and water to cement configuration. With direct coupled electrodes, the current is ratio of the grout). The relatively low resistivity of fresh soilcrete injected directly into the soilcrete, resulting in a higher current den- stems from the conductive ionic electrolyte solution making up the sity in the soilcrete compared to the slotted casing approach. In the pore fluid in the concrete/soilcrete (Rajabipour et al. 2007). The slotted casing configuration, considerable current remains in the resistivity of the pore fluid depends on the cement composition column fluid, e.g., 40% per FE analysis; therefore, the direct and ionic concentration in the pore fluid (Backe et al. 2001; Chung coupled electrodes provide significantly better geometric resolution þ þ þ − 2− 2004). Ions in the pore fluid (e.g., Na ,K ,Ca2 ,OH ,SO4 ) are than the slotted casing array using same Wenner-α protocol. This associated with the formation of cementitious compounds that bond conclusion was evidenced in both experimental and FE results. soil grains together (e.g., calcium-silicate-hydrates) (Taylor 1997). ρa measurements from the direct coupled data were compared to This cementing process reduces ionic concentration and causes the FE ρa predictions to estimate column diameter via a linear corre- concrete/soilcrete to become more resistive with curing time. lation between D and ρa. For D ¼ 30 cm regions, exhumed speci- Additionally, bonds formed between soil grains and cementing men 1 D ¼ 29.8 1.7 cm, and average D¯ ¼ 30.2 1.5 cm. In the compounds reduce porosity, which further increases resistivity D ¼ 18 cm region, exhumed specimen 1 D ¼ 17.8 1.2 cm, and (Rajabipour et al. 2007). D¯ ¼ 17.9 0.6 cm. The uncertainties in D¯ correspond to 5% D To assess the change in ρsc that results from curing, average in the D ¼ 30 cm regions and 3% D in the D ¼ 18 cm region. values of ρsc were determined using direct coupled a ¼ 3 cm There was no appreciable difference in D¯ accuracy when transition- specimen 1 data from column sections in which D=a ≥ 10. Average ing between different column diameters; however, when making ρsc values with 1σ error bars are displayed for curing times ranging the more drastic transition from soil to soilcrete at the array inter- from 1.5 to 240 h in Fig. 11. As expected, ρsc increased with curing face (i.e., the top and bottom of the column), the method lost its time. The growth was significant in the first 10 h of curing, and sensitivity to diameter change. continued to grow at a slower rate thereafter. Growth continued An analysis of experimental results and FE modeling revealed for the duration of monitored curing and would likely continue an important relationship between electrode spacing a and column to grow past 10 days. Least squares regression fitting indicated diameter D using the direct coupling configuration. If D=a ≥ 10, the measured ρa was influenced by the soilcrete only. ρa measurements in which D=a ≤ 5 were influenced by ρsc and ρs. D=a ≤ 5 ρa was sensitive to the soilcrete and the soil, indicating that D=a ≤ 5 measurements are best suited for characterizing column geometry. In general, the lower the value of D=a, the more sensitive the measurement will be to changes in column geometry. This conclusion can be applied to field jet grout construction. Direct couple electrode configurations can be implemented with push- probe technology (effort underway). The normalized observations with D=a observed in this study can be readily extended to field-scale D=a values (e.g., a 3 m diameter column and an array

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. a ¼ 30 with min cm). Time lapse Wenner-α data (using direct coupled electrodes) suggested that ρsc values ranged from 1.6 Ωm(1.5h)to 8.5 Ωm (10 days), resulting in a significant reduction in the resistivity contrast between the soil and soilcrete as curing time increased. Furthermore, measurement uncertainty increased significantly with curing time (σ ¼ 0.1 Ωm after t ¼ 1.5 h; σ ¼ 1.6 Ωm after t ¼ 10 days). While the exact temporal variation in soilcrete resistivity would be mix-dependent, this result indicates ρ 1σ Fig. 11. Experimental sc with error bars from curing times of 1.5 that soilcrete resistivity testing should be performed as early as to 240 h; specific curing times are highlighted and a best fit regression possibly to maximize the resistivity contrast between the soilcrete analysis function is shown and in situ soil and minimize the uncertainty in ρsc. This is well

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088 suited for field conditions in which testing immediately follows jet GeoConvention 2014, Canadian Society of Petroleum Geologists, grouting. Calgary, Canada. Huang, Q., and Lin, Y. (2010). “Selectivity of seismic electric signal (SES) of the 2000 Izu earthquake swarm: A 3D FEM numerical simulation Acknowledgments model.” Proc. Jpn. Acad. Ser. B, 86(3), 257–264. Kelekanjeri, V. S. K. G., and Gerhardt, R. (2008). “A closed-form solution Funding for this study was provided by the National Science for the computation of geometric correction factors for four-point resis- Foundation under the Partnership for International Research and tivity measurements on cylindrical specimens.” Meas. Sci. Technol., 19, Education (PIRE) Program (OISE-1243539). The authors also wish 25701. to thank Dr. Ernst Niederleithinger of the BAM Federal Institute for Kim, J. H., Yi, M. J., Park, S. G., and Kim, J. G. (2009). “4-D inversion of Materials Research and Testing, and Colorado School of Mines DC resistivity monitoring data acquired over a dynamically changing earth model.” J. Appl. Geophys., 68(4), 522–532. (CSM) student, Justin Downs, for their support and assistance in “ this research. Madhyannapu, R., Puppala, A., Nazarian, S., and Yuan, D. (2010). Quality assessment and quality control of deep soil mixing construction for sta- bilizing expansive subsoils.” J. Geotech. Geoenviron. Eng., 10.1061/ – References (ASCE)GT.1943-5606.0000188, 119 128. Meinhard, K. (2002). “Sizing for strength.” European Foundations. Abu-Zeid, N., Balducci, M., Bartocci, F., Regni, R., and Santarato, G. Mullins, G. (2010). “Thermal integrity profiling of drilled shafts.” J. Deep (2009). “Indirect estimation of injected mortar volume in historical Found. Inst., 4(2), 54–64. walls using the electrical resistivity tomography.” J. Cult. Heritage, Niederleithinger, E., Hübner, M., and Amir, J. M. (2010). “Crosshole sonic 11(2), 220–227. logging of secant pile walls—A feasibility study.” Proc., Symp. on the Abu-Zeid, N., Botteon, D., Cocco, G., and Santarato, G. (2006). “Non- Application of Geophysics to Environmental and Engineering Prob- invasive characterization of ancient foundations in Venice using the lems (SAGEEP), Vol. 2, Environmental and Engineering Geophysical electrical resistivity imaging technique.” NDT&E Int., 39(1), 67–75. Society, Denver, 685–693. Araji, A. H., Revil, A., Jardani, A., Minsley, B. J., and Karaoulis, M. Passlick and Doerendahl. (2006). “Quality assurance in jet grouting for a (2012). “Imaging with cross-hole seismoelectric tomography.” Geophys. deep seated slab in Amsterdam.” Piling and Deep Foundations Conf., J. Int., 188(3), 1285–1302. Deep Foundations Institute, Hawthorne, NJ. Backe, K., Lile, O., and Lyomov, S. (2001). “Characterizing curing cement Rajabipour, F., Sant, G., and Weiss, J. (2007). “Development of electrical slurries by electrical conductivity.” Society of Petroleum Engineers conducvitity-based sensors for health monitoring of concrete materials.” Drilling & Completion, Society of Petroleum Engineers, 201–207. Transportation Research Board 2007 Annual Meeting CD-ROM, The Bearce, R., Mooney, M., Niederleithinger, E., and Revil, A. (2014). National Academies of Sciences, Engineering, and Medicine, “Characterization of simulated jet-grout column curing using acoustic Washington, DC. tomography.” GeoCongress 2014, ASCE, Reston, VA. Revil, A., Karoulis, M., Johnson, T., and Kemna, A. (2012). “Review: Bruce, D. A. (2012). Specialty construction techniques for dam and levee Some low-frequency electrical methods for subsurface characterization remediation, CRC Press, Boca Raton, FL, 81–91. and monitoring in hydrogeology.” Hydrogeol. J., 20(4), 617–658. Burke, G. K. (2012). “The state of practice in jet grouting.” Proc., 4th Int. Rücker, C., Günther, T., and Spitzer, K. (2006). “Three-dimensional Conf. on Grouting and Deep Mixing, ASCE, Reston, VA. modelling and inversion of DC resistivity data incorporating Chou, T. K., Chouteau, M., and Yi, M. J. (2010). COMSOL multiphysics topography—I. Modelling.” Geophys. J. Int., 166(2), 495–505. software: Time-lapse electrical resistivity inversion, COMSOL, Santarato, G., Ranieri, G., Occhi, M., Morelli, G., Fischanger, F., and Burlington, MA. Gualerzi, D. (2011). “Three dimensional electrical resistivity tomogra- “ ” Chung, D. L. L. (2004). Electrically conductive cement-based materials. phy to control the injection of expanding resins for the treatment and – Adv. Cem. Res., 16(4), 167 176. stabilization of foundation soils.” Eng. Geol., 119(1–2), 18–30. “ Clement, R., Bergeron, M., and Moreau, S. (2011). COMSOL multiphy- Sellountou, E. A., and Rausche, F. (2013). Quality management by means sics modelling for measurement device of electrical resistivity in of load testing and integrity testing of deep foundations ” , Pile Dynamics, laboratory test cell. Proc., COMSOL Conf., COMSOL, Burlington, MA. Cleveland. COMSOL Multiphysics. (2014). COMSOL multiphysics users guide, Spruit, R., Hopman, V., van Tol, F., and Broere, W. (2011). “Detecting COMSOL, Burlington, MA. defects in diaphragm walls prior to excavation.” Proc., 8th Int. Symp. Daily, W., and Ramirez, A. L. (2000). “Electrical imaging of engineered on Field Measurements in GeoMechanics, ASCE, Reston, VA. hydraulic barriers.” Geophysics, 65(1), 83–94. Spruit, R., van Tol, F., Broere, W., Slob, E., and Niederleithinger, N. (2014). Doornenbal, P., Hopman, V., and Spruit, R. (2011). “High resolution “Detection of anomalies in diaphragm walls with crosshole sonic monitoring of temperature in diaphragm wall concrete.” 8th Int. Symp. logging.” Can. Geotech. J., 51(4), 369–380. on Field Measurements in GeoMechanics, Australian Centre for “ — Geomechanics, Australia. T&A Survey. (2013). 3D borehole radar Determination of jet grout ” Duzceer, R., and Gokalp, A. (2004). “Construction and quality control of column diameter. Amsterdam, Netherlands. jet grouting applications in Turkey.” 3rd Int. Conf. on Grouting and Taylor, H. F. W. (1997). Cement chemistry, 2nd Ed., Academic Press, Ground Treatment, ASCE, Reston, VA. London. “ Essler, R., and Yoshida, H. (2004). “Jet grouting.” Ground improvement, Wang, S., Mu, M., Chen, D., and Ren, G. (2012). Field design of jet grout-

Downloaded from ascelibrary.org by Colorado School of Mines on 07/26/17. Copyright ASCE. For personal use only; all rights reserved. 2nd Ed., CRC Press, Boca Raton, FL, 160–195. ing parameters on soilcrete columns.” Appl. Mech. Mater., 170–173, Frappin, P. (2011). “CYLJET– An innovative method for jet grouting col- 3068–3071. umn diameter measurement.” 1st Int. Conf. of Engineering Geophysics, Wang, X., Yue, H., Liu, G., and Zhao, Z. (2011). “The application of Al Ain, United Arab Emirates, Society of Exploration Geophysicists, COMSOL multiphysics in direct current method forward modeling.” Tulsa, OK. Procedia Earth Planet. Sci., 3, 266–272. Frappin, P., and Morey, J. (2001). Jet grouted column diameter Yi, M. J., Kim, J. H., and Son, J. S. (2009). “Borehole deviation effect in measurement using the electric cylinder method, Soletanche Bachy, electrical resistivity tomography.” Geosci. J., 13(1), 87–102. Internal Publication, France. Yoshida, H. (2010). “The progress in jet grouting in the last 10 years in the Guo, K., Milkreit, B., and Qian, W. (2014). “Geometry factor for near surface Japanese market.” Proc., 35th Annual Conf. on Deep Foundations, borehole resistivity surveys: A key to accurate imaging and monitoring.” Deep Foundations Institute, Hawthorne, NJ.

J. Geotech. Geoenviron. Eng., 2016, 142(3): 04015088