Draft...Draft 2 24 Abstract: 25 Distributed fiber optic sensing (DFOS) is gaining increasing...

Draft

Quantifying Progressive Failure of Micro-Anchored Fiber Optic Cable–Sand Interface via High-Resolution Distributed

Strain Sensing

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2018-0651.R1

Manuscript Type: Article

Date Submitted by the Author: 21-Apr-2019

Complete List of Authors: Zhang, Cheng-Cheng; Nanjing University, Department of Geoengineering and Geoinformatics, School of Earth Sciences and Engineering; University of California, Berkeley, Department of Civil and Environmental EngineeringZhu, Hong-Hu; Nanjing University, School of Earth Sciences and EngineeringLiu, Suping; Nanjing University, Department of Geoengineering and Geoinformatics, School of Earth Sciences and EngineeringShi, Bin; Nanjing UniversityCheng, Gang; North China Institute of Science and Technology

Keyword: Micro-anchor, Progressive failure, Interfacial shear stress, Strain distribution, Distributed fiber optic sensing (DFOS)

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

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1

1

2 Quantifying Progressive Failure of Micro-Anchored Fiber Optic Cable–Sand Interface

3 via High-Resolution Distributed Strain Sensing

4

5 Cheng-Cheng Zhang1,2, Hong-Hu Zhu1, Su-Ping Liu1, Bin Shi1, and Gang Cheng3

6

7 1School of Earth Sciences and Engineering, Nanjing University, Nanjing, Jiangsu 210023,

8 China.

9 2Department of Civil and Environmental Engineering, University of California, Berkeley, CA

10 94720-1710, USA.

11 3North China Institute of Science and Technology, Beijing 101601, China.

12

13 Corresponding author: Prof. Hong-Hu Zhu, Ph.D.

14 Address: 362 Zhugongshan Bldg, 163 Xianlin Ave, Qixia District, Nanjing, Jiangsu 210023,

15 China.

16 E-mail: [email protected]

17 Telephone: +86 158-9599-6665

18

19

20 Revised manuscript submitted to Canadian Geotechnical Journal for re-review

21 and possible publication as an Article

22

23 21 April 2019

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24 Abstract:

25 Distributed fiber optic sensing (DFOS) is gaining increasing interest in geotechnical monitoring.

26 By using soil-embedded fiber optic cables, strain profiles as well as deformation patterns of

27 geotechnical infrastructures can be captured. Probing the fiber optic cable–soil interfacial

28 behavior is vital to the advancement of DFOS-based geotechnical monitoring and our

29 understanding of the soil–inclusion interaction mechanism. To this aim, laboratory pullout tests

30 were performed to investigate the progressive failure of the interface between

31 unanchored/micro-anchored cables and the surrounding sand. High-resolution strain profiles

32 recorded using Brillouin optical time-domain analysis (BOTDA) not only elucidated the

33 influence of anchorage on strain measurements, but also allowed the classical soil–inclusion

34 interaction problem to be studied in detail. Interfacial shear stresses calculated from step-like

35 strain profiles provided clear evidence of the contribution of each micro-anchor to the pullout

36 resistance. The cable–soil contact is a combination of overall bonding and point fixation

37 depending on the level of mobilized interfacial shear stress, and therefore the validity of

38 measured strains is correlated to a three-stage process of interface failure. This study also shows

39 that installing heat-shrink tubes on the fiber optic cable is a rapid, low-cost, effective approach

40 to make an anchored DFOS system for deformation monitoring of earth structures.

41

42 Keywords: Micro-anchor; Progressive failure; Interfacial shear stress; Strain distribution;

43 Distributed fiber optic sensing (DFOS)

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44 Introduction

45 Deformation measurements play an important role from evaluating the performance of massive

46 and complex geotechnical structures to validating and refining relevant analytical and

47 numerical models. Traditional instrumentation using strain gauges, linear variable displacement

48 transducers, inclinometers and extensometers only allow deformation to be recorded at discrete

49 locations or directions, and therefore localized features of the monitored geotechnical

50 infrastructures may not be identified in some cases (Pelecanos et al. 2018).

51 The distributed fiber optic sensing (DFOS) technology turns common telecommunication

52 fiber optic (FO) cables into sensing elements, which enables continuous strain measurements

53 at kilometre scales and beyond (Shi et al. 2003; Thévenaz 2010; Habel and Krebber 2011; Bao

54 and Chen 2012; Soga and Luo 2018). Recent advances in FO sensing have rendered this

55 technique better suited to geotechnical applications (Schenato 2017; Nöther and von der Mark

56 2019; Soga et al. 2019). FO cables can be readily integrated into geotechnical structures such

57 as ground anchors, piles, retaining walls, and geosynthetics, because of their geometrical

58 versatility. Recently, field and laboratory attempts have been made to monitor and evaluate the

59 performance of geotechnical structures using quasi-distributed fiber Bragg gratings (FBGs)

60 (e.g., Lee et al. 2004; Zhu et al. 2011; Huang et al. 2012; Zhang et al. 2014b; Borana et al. 2017;

61 Zhu et al. 2017) or Rayleigh and Brillouin scattering-based fully-distributed approaches (e.g.,

62 Shi et al. 2003; Klar et al. 2006, 2016; Mohamad et al. 2012; Lienhart 2015; Schenato et al.

63 2017; Ni et al. 2018; Zhang et al. 2018; Wheeler et al. 2019).

64 Recent trends aimed at monitoring soil deformation using embedded FO cables have

65 encouraged increased use of micro-anchors (Fig. 1; Iten et al. 2011; Hauswirth et al. 2012,

66 2014; ASTM F3079-14 2014; Zhu et al. 2014; Damiano et al. 2017). In ground-improvement

67 engineering, anchorages have already been utilized to enhance the pullout resistance of soil

68 reinforcements such as ground anchors (Pérez et al. 2017). For geogrids, the soil in front of

69 transverse ribs is subject to passive earth pressure; this effect, along with the solid geogrid

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70 surface–soil skin friction, results in the mobilized interaction mechanism (Koerner et al. 1989;

71 Bergado et al. 1993; Liu et al. 2009; Moraci et al. 2014). The passive resistance can be further

72 increased by adding anchorages to the transverse elements. One such geogrid named grid-

73 anchor has been introduced by Mosallanezhad et al. (2008) and Alamshahi and Hataf (2009).

74 This was made by attaching short anchors to one side of the geogrid and so greater bearing

75 resistance can be obtained. More recently, Sadat Taghavi and Mosallanezhad (2017) developed

76 an anchored geogrid by adding a set of steel equal angles to the geogrid; the pullout resistance

77 of the new reinforcing system can be increased by up to 65% compared to traditional ones. For

78 DFOS-based geotechnical monitoring, micro-anchors are expected to enhance the interlocking

79 effects between a FO cable and the surrounding soil and therefore extend the measurement

80 range of a DFOS system. Schenato et al. (2017) used the DFOS technology to measure strains

81 exerted on a corrugated FO cable induced by shallow landslide triggering; the evolution of the

82 landslide coincided with the phases identified during the progressive cable–soil failure.

83 Hauswirth et al. (2010) developed a system with three-dimensional micro-anchors attached to

84 a FO cable, and evaluated its performance through pullout and shearing tests. Lately, this

85 system was successfully applied to detect landslide movements in Switzerland (Hauswirth et

86 al. 2012) and ground deformation induced by tunneling in the UK (Hauswirth et al. 2014).

87 The accuracy of strains measured by a DFOS system with soil-embedded FO cables is

88 subject to the cable–soil interaction mechanism. Probing the cable–soil interfacial properties is

89 thus of great importance for the advancement of both the DFOS technology and our

90 understanding of the interaction mechanism between soil and an inclusion. As such, classical

91 pullout tests have been introduced to study the FO cable–soil interfacial behavior (Iten et al.

92 2009; Zhang et al. 2014a). The test procedure is similar to that of an earth reinforcement such

93 as a soil nail (Wang et al. 2017). The difference lies in that the FO cable is treated as both a soil

94 inclusion and a distributed strain sensor, and therefore no extra strain gauges are needed which

95 might potentially affect the FO cable–soil interfacial properties. In addition, the axial stiffness

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96 of a FO strain cable (equivalent to Young’s modulus multiplied by cross-sectional area) is

97 comparably low, typically in the range between 1–60 kN (Iten et al. 2011; Klar et al. 2016;

98 Schenato et al. 2017). This results in an evident progressive failure behavior of a smooth FO

99 cable in soil under low overburden pressures (Iten et al. 2009; Zhang et al. 2014a). However,

100 until now, the pullout performance of an anchored FO cable embedded in soil has not been

101 investigated in detail. While it is widely accepted that an unanchored soil inclusion has a linear

102 distribution of axial force (accordingly, a uniform distribution of interfacial shear stress) at the

103 critical state (Fig. 2a), these distributions have not been directly measured for an anchored

104 inclusion (Fig. 2b).

105 In this study, a rapid, low-cost, effective approach was first proposed to make an anchoring

106 system for DFOS-based geotechnical monitoring. Then, laboratory pullout tests were

107 conducted to investigate the micro-anchored FO cable–sand interfacial characteristics. High-

108 resolution strain profiles along the FO cable were captured during progressive interface failure

109 by using a Brillouin optical time-domain analysis (BOTDA) interrogator, which elucidated the

110 influence of anchorage on the measured FO strain data and allowed the soil–inclusion

111 interaction to be studied in detail. Finally, the implications of the experimental results for

112 DFOS-based geotechnical monitoring, as well as the limitations of the present study, were

113 discussed.

114

115 Principle of DFOS using BOTDA

116 DFOS is a technology that enables spatially continuous, long-distance, and near-real time

117 measurements along a FO cable. The FO cable itself is not only the transmission medium but

118 also the sensing element. When a light wave generated from a FO interrogator travels through

119 the core of an optical fiber, backscattered lights (Rayleigh, Raman, or Brillouin) are generated

120 at any point along the fiber (Hartog 2017).

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121 For Brillouin scattering (Fig. 3), the frequency shift of the backscattered light is

122 approximately linearly proportional to the axial strain or temperature exerted on the optical

123 fiber (Bao and Chen 2012):

124 (2)B BB B0 T

T

125 where and = Brillouin frequency shifts before and after a measurement, respectively; B0 B

126 = axial strain change; = temperature change; and and = coefficients T B / B / T

127 for strain and temperature changes, respectively. According to eq. (1), if the Brillouin frequency

128 shifts along the entire length of the fiber are detected, a continuous distribution of strain and

129 temperature with respect to distance can be determined. As the spontaneous Brillouin scattering

130 light is very weak, it is recommended to utilize BOTDA to measure strain and temperature

131 along the optical fiber. By deploying the pulse pump and probe at both ends of the fiber, the

132 frequency changes in stimulated Brillouin scattered light can be detected with high spatial

133 resolution and accuracy. Further information about the fundamentals of the BOTDA technology

134 may also be found in Thévenaz (2010), Schenato (2017), and Soga and Luo (2018), which is

135 beyond the scope of this paper.

136

137 Materials and Methods

138 Materials

139 The soil used in this experimental investigation was a clean, angular river sand. A sieve analysis

140 was carried out and the obtained grain size distribution curve is shown in Fig. 4. From this curve,

141 the values of and were 0.23 mm and 0.35 mm, respectively. The coefficient of 10D 50D

142 uniformity, , was 1.61, and the coefficient of curvature, , was 1.06. The sand was uC cC

143 classified as a poorly graded sand (SP) according to the Unified Soil Classification System

144 (ASTM D2487-17 2017). Following ASTM D4253-16 (2016) and ASTM D4254-16 (2016),

145 the maximum and minimum dry density, and , were determined to be 1.69 g/cm3 dmax dmin

146 and 1.21 g/cm3, respectively. By using direct shear tests (ASTM D6528-17 2017), the friction

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147 angle, , of the sand at a relative density, , of 23% was measured to be 32.3°. Detailed rD

148 physical and mechanical properties of the sand are summarized in Table 1.

149 FO strain sensing cables for monitoring soil deformation have to meet two main

150 requirements, including being robust enough to survive in harsh construction conditions and

151 ensuring efficient strain transfer from soil to the fiber core. A 2 mm-diameter tight-buffed

152 polyurethane-coated FO cable (Nanzee Sensing, Suzhou, China) was used as the strain cable

153 (Fig. 5a), whose performance has been tested in several field monitoring projects as well as

154 physical model tests by the authors’ research group. Detailed properties of this cable are

155 summarized in Table 2. The soft polyurethane coating lowers the Young’s modulus of the cable,

156 which however is still capable of withstanding moderate impacts during installation. Due to its

157 relatively low modulus, it can be easily prestrained and directly integrated into loose material

158 such as soil. Note that this cable was chosen for the current experimental study for that it has

159 shown good performance both in the field and laboratory. However, if the construction activity

160 involves heavy equipment, it is recommended to use cables of higher robustness such as steel

161 strand- or fiber reinforced polymer-buffered cables.

162 Two types of heat-shrink tube, made of polyethylene (PE) and polymethyl methacrylate

163 (PMMA), were used to make micro-anchors on the FO cable. These two tubes are commonly

164 used to protect a fused optical fiber; they will shrink radially to wrap tightly around the optical

165 fiber by heating with a hot air gun or a built-in heater of an optical fiber fusion splicer. The

166 tubes were shrunk onto the cable coating at a certain interval using a KL-500 fusion splicer

167 (Jilong, Nanjing, China), as shown in Fig. 5b. Two separate FO cables, each having one type

168 of tube, were prepared and tested independently. The average diameter of the micro-anchored

169 cables was calculated according to the anchor distribution, and the average Young’s modulus,

170 , of the anchored segments was estimated based on the cross-section geometry. Detailed aE

171 micro-anchor properties are listed in Table 3.

172

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173 FO Interrogator

174 The experimental investigation presented in this paper used a NeubreScope NBX-6050A

175 interrogator (Neubrex, Kobe, Japan). This instrument provides a minimum readout resolution

176 of 10 mm with a spatial resolution of 50 mm and a noise level of about 7.5 , allowing for

177 distributed measurements along a FO cable of 1 km. The spatial resolution, which is a key factor

178 affecting strain measurements, achieved using the BOTDA technology is higher than that of

179 the Brillouin optical time-domain reflectometry (BOTDR) technology (normally, 500–1000

180 mm; Shi et al. 2003; Pelecanos et al. 2018). Here, the minimum readout resolution (i.e., 10 mm)

181 and the highest spatial resolution (i.e., 50 mm) of this BOTDA interrogator were adopted to

182 obtain optimal measurements at a laboratory scale.

183

184 Test Setup and Procedure

185 A schematic drawing of the test setup is shown in Fig. 6. The test container was 1500 mm long,

186 200 mm wide, and 200 mm high, made of aluminum alloy walls, 15 mm thick, having a 60

187 mm-diameter hole in the middle of the front wall. The width and depth of the test container

188 were 100 times the cable diameter and therefore the boundary effect during testing was avoided.

189 The test bed was prepared using a sand raining technique. When the prepared sand reached

190 the mid-height of the test container, it was gently levelled out and the FO cable centered

191 carefully in the container. The depth of sand above and below the cable was 100 mm. No

192 additional confining pressures were applied on the surface of the sand bed. The density and

193 water content of the sand measured after testing were 1.32 g/cm3 and 1.92%, respectively. This

194 corresponded to a relative density, , of 23%, indicating that the sand sample was in a loose rD

195 state (Mitchell and Soga 2005). The embedded cable length was 1200 mm, whereas a 200 mm-

196 long free segment was left between the embedded cable and the front wall of the container to

197 minimize boundary effects. A special clamp having two rubber pieces acting as a cushion was

198 utilized to clamp the free cable segment (Fig. 7); the clamp was then connected to a tensile

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199 tester. The free segment at the other end ran from the top of the test container. Finally, the free

200 segments at both ends of the cable were connected to the FO interrogator.

201 Prior to the test, a zero measurement was performed using the FO interrogator to record

202 the initial strain distribution along the FO cable. During testing, the pullout displacement was

203 applied using an electric motor with a velocity of 0.1 mm/s and was later calculated according

204 to the motor speed and time elapsed; the pullout force was recorded using a force gauge with a

205 resolution of 0.1 N. At each displacement step of 1 mm, the displacement was maintained until

206 a strain measurement was performed using the FO interrogator.

207 Preliminary tests were carried out to ensure the suitability of the test setup and procedure.

208 Afterward, micro-anchors with two different diameters, i.e., Da = 3.6 mm and 6.0 mm, were

209 investigated. A smooth cable without micro-anchors was also tested for comparison.

210

211 Results

212 Characteristics of Pullout Force–Displacement Curves

213 Curves of pullout force, , versus pullout displacement, , are shown in Fig. 8. Notice that 0F 0u

214 the elongation of the free cable segment was deduced from the measured displacement. A

215 nonlinearity was observed from the curves before the peak pullout force was reached, due to

216 the partial failure of the cable–soil interface. This was expected because the axial stiffness of

217 the cable was comparatively low and therefore progressive failure was evident during testing

218 (Zhang et al. 2014a).

219 Moreover, there was only a slight difference between the slopes of the initial sections,

220 which was confirmed by the secant interfacial shear stiffness calculated at a displacement step

221 of 2 mm, with the average value being 198.7 kPa/m (Fig. 9). This indicated that the effect of

222 anchorage on the cable–soil interfacial shear stiffness was not obvious. On the contrary, its

223 influence on the peak pullout force and peak interfacial shear stress (ISS) was much more

224 pronounced. For the unanchored cable, the pullout force peaked at a displacement of

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225 approximately 3.82 mm and then reduced with increasing displacements. This illustrated that

226 the unanchored cable–soil interface exhibited a strain-softening behavior during pullout, which

227 agreed well with the results of Zhang et al. (2014a). In contrast, a strain-hardening behavior

228 was observed for the micro-anchored cables, which largely increased the peak ISS (Fig. 9). The

229 peak ISS was increased by 78.48% and 146.6% for the micro-anchored cables with Da = 3.6

230 mm and 6.0 mm, respectively, as compared to the unanchored cable. This demonstrated that

231 the use of micro-anchors can increase the interfacial bond between FO cable and soil and

232 therefore extend the measurement range of a DFOS system (Hauswirth et al. 2010; Iten et al.

233 2011; Damiano et al. 2017).

234

235 Behavior of Unanchored Cable–Sand Interface

236 Prior to data analysis, the monitored strains along the 200 mm-long free cable segment were

237 converted to tensile forces and compared with force gauge measurements (Fig. 10). There was

238 generally good agreement between the two forces, indicating the validity of the measured strain

239 data. Fig. 11 shows the obtained strain data (relative to the zero strain measurement) along the

240 FO cables for each displacement step. Because the strain profiles exhibited no waviness, no

241 signal processing procedure (e.g., filtering) was performed. In addition, temperature

242 compensation for the measured strains was not considered as the variation of temperature was

243 negligible during testing. For ease of comparison, the pullout force–displacement curves are

244 shown in the upper right corner. The displacement steps are denoted as closed circles for the

245 strain distributions presented and discussed.

246 For the unanchored FO cable, the strain propagated from the cable head toward the toe

247 under increasing displacement steps (Fig. 11a). This indicated that initially only a small portion

248 of ISS was mobilized to resist the pullout force; however, with the increase of the pullout force

249 the ISS increased gradually in terms of both magnitude and mobilized length. Once the peak

250 pullout force was reached (displacement step = 5 mm), the maximum strain began to decline,

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251 indicating the decrease of the average ISS. To examine the evolution of ISS in detail, the pullout

252 behavior of the unanchored FO cable in sand was further simulated using a pullout model

253 incorporating strain-softening of the cable–soil interface (Zhang et al. 2014a). The correlation

254 between pullout force and pullout displacement for five pullout phases (Phase I–V) can be

255 expressed as (Zhang et al. 2014a):

256 (3)

1 10

12

2 2 s max max 2 s max20

2 res 2 2 s 1 2 res

2 max2 2 200

2 1 2

2 2r res max max res

0r r 1 2 2

π tanh (Phase I)

π cot π π cot(1 ) (Phase II)sin

π tanπ tan (1 ) (Phase III)

ππ π ( )4 2 4

DG L u

DG L D D LGuL G

D LDG L GuFG

DLD E D EuL L G G G

res

(Phase IV)

π (Phase V)D L

257 where D, L, and E = diameter, length, and Young’s modulus of the unanchored FO cable,

258 respectively; and = lengths of softening and residual zones, respectively; and = sL rL 1G 2G

259 cable–soil interfacial shear stiffnesses corresponding to ascending and descending branches,

260 respectively; and = peak and residual cable–soil ISSs, respectively; and max res

261 . The expression of axial strain and ISS distributions and further details 4 / ( 1, 2)i iG ED i

262 of the model can be found in Zhang et al. (2014a).

263 The values of independent parameters for simulating the behavior of the unanchored FO

264 cable during pullout are as follows: D = 2 mm; L = 1,200 mm; E = 0.34 GPa; = 3.00 MPa/m; 1G

265 = 55.83 kPa/m; = 0.75 kPa; and = 0.40 kPa. The simulated results are shown in 2G max res

266 Figs. 12a–c. Note that here the pullout force was calculated according to strain readings along

267 the free cable segment. There was generally good agreement between the measured force–

268 displacement curve and the simulated curve, except for the final residual phase where the

269 measured force did not rigorously reach a constant value (Fig. 12a). Five pullout phases are

270 also marked in the figure according to the simulation results. Prior to reaching the final residual

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271 phase (Phase V), the percentage of displacement generated during each pullout phase (Phase I–

272 IV) was 3.04%, 37.18%, 39.15%, and 20.63%, respectively. The two transitional phases—

273 Phase II (elastic–softening phase) and Phase IV (softening–residual phase)—was significant,

274 further illustrating the progressive failure nature of the cable–soil interface. The distribution of

275 ISS along the FO cable was highly nonuniform (Fig. 12c). Initially, the ISS increased along the

276 whole length of the cable. Once the peak ISS was reached, the ISS began to decrease for the

277 segment close to the cable head, whereas that along the remaining segment continued to

278 increase. The ISS was fully mobilized when the peak pullout force was reached. Afterward, the

279 ISS along the whole length of the cable decreased toward the residual value ( = 0.40 kPa).res

280

281 Behavior of Anchored Cable–Sand Interface

282 The pattern of strain profile for the micro-anchored cables was different from that of the

283 unanchored one (Figs. 11b and c). The former exhibited a unique step-like pattern due to the

284 addition of micro-anchors. The inclination of the strain curve of unanchored segments was

285 smaller than that of anchored segments, indicating that the ISS along the unanchored segments

286 was comparatively low. Moreover, although the average ISS over the whole length of the FO

287 cable increased sharply with increasing displacement steps, the variation of ISS along

288 individual segments (unanchored or anchored) appeared to be less significant. To the authors’

289 knowledge, no analytical model is available in the literature to reproduce such behavior as well

290 as the strain profiles shown in Figs. 11b and c. Therefore, the ISS along each segment was

291 estimated using:

292 (4)seg seg d4 d

E Dx

293 where = axial strain gradient; and and = average Young’s modulus and d / dx segE segD

294 diameter of a particular segment, respectively. For the unanchored segments, linear fits were

295 used to obtain the slope of a curve; the average coefficients of determination (R2) were 0.96 and

296 0.83 for the anchored cable with Da = 3.6 mm and 6.0 mm, respectively. For each anchored

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297 segment, the slope was regarded as the strain difference between two neighboring unanchored

298 segments divided by anchor length. For clarity, the unanchored segments are marked as A, B,

299 C, D, and E from left to right, whereas the anchored segments are marked as a, b, c, d, and e

300 (Figs. 11b and c). Note that the unanchored segment at the cable toe was neglected considering

301 its short length, and therefore the last anchored segment e was not considered as well. Finally,

302 the overall average ISS was estimated using , where = average diameter of the 0 / πF DL D

303 FO cable.

304 The calculated ISSs are shown in Fig. 13. The overall average ISS over the whole cable

305 length increased gradually toward a constant value (Figs. 13a and d), consistent with the

306 correlation between the pullout force and the pullout displacement (Fig. 8). The unanchored

307 segments of the anchored FO cables exhibited strain-softening (cable with Da = 3.6 mm in

308 particular; Figs. 13b and e), which was similar to the behavior of the unanchored FO cable.

309 However, the average ISS along the unanchored segments decreased toward 0.46 kPa (or 0.53

310 kPa) for the anchored cable with Da = 3.6 mm (respectively, Da = 6.0 mm), which was larger

311 than the residual ISS along the unanchored cable ( = 0.40 kPa).res

312 Upon applying a pullout displacement, the ISS was simultaneously mobilized along the

313 unanchored segments (Figs. 13b and e) and the anchored segments (Figs. 13c and f). However,

314 as expected, the ISS along the unanchored segments was much smaller than that along the

315 anchored segments, demonstrating that the inclusion of micro-anchors led to the difference in

316 peak ISS (Fig. 9). Additionally, the average ISS along the unanchored segments peaked at a

317 displacement step of approximately 7 mm for the anchored cable, which was earlier than the

318 peak of average ISS along the anchored segments. The latter reached a peak value at the

319 displacement step being almost identical to that which resulted in the overall failure of the

320 anchored cables. The difference in average ISS between anchored and unanchored cable

321 segments of the micro-anchored FO cable was further characterized using their ratio, which is

322 defined as

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323 (5)b b a

a a b

E AkE A

324 where and = effective axial stiffnesses of the anchored and unanchored cable a aE A b bE A

325 segments, respectively; and and = average ISSs along the anchored and unanchored a b

326 cable segments, respectively. Fig. 14 shows the difference in average ISS between the anchored

327 and unanchored segments calculated using eq. (4). The ratio increased approximately linearly

328 with increasing displacement steps, further illustrating the contribution of anchored and

329 unanchored segments to the ISS during pullout. For the contribution made by each micro-

330 anchor, a close examination of Figs. 13c and f suggested that anchored segments close to the

331 cable head contributed, in general, more to the ISS than those close to the toe. However, the

332 ISS of anchored segment c became the largest after applying the displacement step of 9 mm

333 (Fig. 13f). This could have occurred if this particular micro-anchor had a larger diameter and a

334 rougher surface, as the property of each micro-anchor could not be strictly controlled during

335 heat shrinking.

336

337 Discussion

338 Implications for Geotechnical Monitoring

339 The proper deployment of FO strain sensing cables is one of the major concerns in DFOS-based

340 geotechnical monitoring (Damiano et al. 2017; Schenato 2017). This becomes extremely

341 difficult to deal with natural geomaterials (e.g., soils) as compared to man-made materials.

342 Accordingly, anchoring systems have been used by geotechnical practitioners to prevent the

343 relative slippage between FO cable and soil (Hauswirth et al. 2010, 2014; Iten et al. 2011; Zhu

344 et al. 2014; Damiano et al. 2017). Such a system has been preliminarily evaluated by using

345 classical pullout tests in this paper. The obtained results indicate that the mechanical coupling

346 between the strain sensing cable and the surrounding soil can be effectively enhanced (Fig. 9)

347 with relatively little effort, that is, by shrinking commercially available heat-shrink tubes onto

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348 the cable coating and therefore the equally spaced tubes can serve as a micro-anchorage system

349 (Fig. 5b).

350 FO strain cables are usually point fixed (Pelecanos et al. 2018) or overall bonded (Shi et

351 al. 2003) to a monitored object. Iten et al. (2011) proposed that a combination of overall bonding

352 and point fixation is possible by using a soil-embedded micro-anchored FO cable, which is

353 further confirmed by the development of ISS along the anchored and unanchored cable

354 segments calculated from the high-resolution strain profiles (Fig. 13). The results reveal that

355 the micro-anchored FO cable–soil contact is a combination of overall bonding and point

356 fixation depending on the level of mobilized ISS, and therefore the validity of FO strain data is

357 correlated to a three-stage process during the cable–soil interface failure (Fig. 15 and Table 4).

358 In Stage I, the cable is bonded along its entire length to the soil considering that neither the

359 unanchored nor the anchored segment reaches the peak ISS. Since deformation compatibility

360 between the cable and the soil is ensured, the strain measurements can truly reflect the soil

361 deformation. In Stage II, the peak ISS of the unanchored segment is reached and therefore the

362 anchors contribute a substantial part of the ISS. In this stage, the micro-anchored FO cable is

363 similar to a gauged strainmeter and so the measured strain is averaged over the gauge length,

364 namely, anchor spacing. Therefore, one has to carefully consider the anchor spacing so as not

365 to compromise the spatial resolution of the DFOS system (Schenato 2017). Stage III follows

366 when the anchors begin to fail provided that the cable itself has not yielded. The measured data

367 are completely unreliable in this stage. In this section, the reliability of strain data measured

368 from a micro-anchored FO cable has been linked to the progressive failure process of the cable–

369 soil interface, but for field monitoring how to distinguish when the interface has transitioned

370 from one stage to another remains to be investigated.

371

372 Limitations

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373 The quality of distributed FO strain data is intrinsically influenced by its distributed nature. The

374 measured strain is averaged over a certain length called spatial resolution, which has remarkably

375 increased during the past few years to several millimeters for the optical frequency-domain

376 reflectometry (OFDR) technology (Ni et al. 2018; Friedli et al. 2019). In this study a spatial

377 resolution of 50 mm and a readout resolution of 10 mm were achieved by using BOTDA.

378 Because this spatial resolution was two times the length of the micro-anchor (i.e., 25 mm, Fig.

379 5b), the quality of the obtained strain data along the anchored segments was therefore inevitably

380 influenced. Moreover, similar to a geogrid the passive earth resistance produced against the

381 micro-anchors should be an important component of the mobilized interaction mechanism

382 between the anchored cable and the surrounding soil. This effect was, however, not fully

383 considered in this preliminary study. Further research is needed to obtain a more accurate strain

384 profile using advanced technologies such as OFDR and, hence, a refined analysis of the passive

385 earth pressure effect can be performed.

386 Furthermore, although anchoring systems such as the one proposed in this study or by

387 other researchers (e.g., Hauswirth et al. 2010) can effectively improve the cable–soil

388 mechanical coupling, they do not allow lateral strains to be measured in a soil. In fact, it is a

389 limitation of the DFOS technology that only strains along the longitudinal axis of a FO cable

390 can be recorded. Therefore, the information a single FO cable can provide on the global strain

391 state in a soil at a specific spatial location is limited.

392

393 Conclusions

394 In this study, the interaction between unanchored/micro-anchored FO strain cables and sand

395 was investigated through laboratory pullout tests. High-resolution strain profiles along the FO

396 cables during cable–soil interface failure were recorded by using the BOTDA technology. The

397 strain profiles showed that both unanchored and micro-anchored FO cables exhibited

398 remarkable progressive failure behavior in dry, loose sand during pullout. The unanchored

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399 cable exhibited a strain-softening behavior, which was described by using an existing pullout

400 model whereby the evolution of ISS was obtained. The simulated pullout force–displacement

401 curves and strain distributions were generally in good agreement with measured curves. The

402 micro-anchored cables had unique step-like strain profiles. The average ISS along the anchored

403 segments were much higher than that along the unanchored segments; their ratio increased

404 approximately linearly with increasing displacement steps. Moreover, the anchored segments

405 close to the cable head contributed, in general, more to the ISS than those close to the toe.

406 Shrinking commercially available heat-shrink tubes onto the cable coating is a rapid, low-

407 cost approach to make an anchored DFOS system for geotechnical monitoring. The inclusion

408 of micro-anchors largely increased the peak ISS and hence the mechanical coupling between

409 FO cable and soil, without significantly affecting the interfacial shear stiffness. The micro-

410 anchored cable–soil contact is a combination of overall bonding and point fixation depending

411 on the level of ISS. The validity of FO strain data is correlated to a three-stage process during

412 the cable–soil interface failure: (1) the measured strain is valid when the cable is bonded along

413 its entire length to the soil; (2) the measured strain is an average value over the gauge length

414 when the unanchored segment fails and the cable is therefore point-fixed to the soil; and (3) the

415 measured strain becomes unreliable once an overall interface failure occurs.

416

417 Acknowledgments

418 This work was supported by the National Natural Science Foundation of China (NSFC) grants

419 41722209, 41672277, 41427801, and 41702347. C.-C. Zhang acknowledges a fellowship from

420 the China Scholarship Council grant 201706190165 for his academic visit to the University of

421 California, Berkeley. The authors thank D.-D. Chen, F. Li, Y.-F. Ni, and S.-H. Zeng (all of

422 Nanjing University) for laboratory assistance and Prof. K. Soga (the University of California,

423 Berkeley) for fruitful discussions.

424

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425 Notation list

426 The following symbols are used in this paper:

427 = cross-sectional area of fiber optic cableA

428 = curvature coefficient of soilcC

429 = uniformity coefficient of soiluC

430 = diameter of cableD

431 = effective grain size of soil10D

432 = average grain size of soil50D

433 = micro-anchor diameteraD

434 = relative density of sandrD

435 = diameter of a particular cable segmentsegD

436 = average cable diameterD

437 = Young’s modulus of cableE

438 = Young’s modulus of anchored cable segmentaE

439 = Young’s modulus of unanchored cable segmentbE

440 = Young’s modulus of a particular cable segmentsegE

441 = pullout force0F

442 = cable–soil interfacial shear stiffness corresponding to an ascending branch1G

443 = cable–soil interfacial shear stiffness corresponding to a descending branch2G

444 = specific gravity of soilsG

445 = embedded cable lengthL

446 = length of softening zonesL

447 = lengths of residual zonerL

448 = temperatureT

449 = pullout displacement0u

450 = pullout model coefficient

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451 = axial cable strain

452 = Brillouin frequency shift after a measurementB

453 = Brillouin frequency shift before a measurementB0

454 = cable–soil interfacial shear stress (ISS)

455 = peak ISSmax

456 = residual ISSres

457 = average ISS along anchored cable segmentsa

458 = average ISS along unanchored cable segmentsb

459 = friction angle of soil

460

461 References

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616 Table 1. Physical and mechanical properties of the sand.

Parameter Unit Value

Specific gravity sG — 2.67

Effective grain size 10D mm 0.23

Average grain size 50D mm 0.35

Coefficient of uniformity uC — 1.61

Coefficient of curvature cC — 1.06

Minimum dry density dmin g/cm3 1.21

Maximum dry density dmax g/cm3 1.69

Friction angle ° 32.3

617

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618 Table 2. Properties of the tight-buffed single-mode fiber optic (FO) strain cable.

Outer diameter

(mm)Coating

materialBuffer Coating

Average

Young’s

modulus

(GPa)

Unit

weight

(kg/km)

Tensile

strength

(MPa)

Effective

axial stiffness

(kN)a

Polyurethane 0.9 2.0 0.34 4.1 23.1 1.1

619 aDetermined under a tensile strain of 1%.

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620 Table 3. Properties of two types of micro-anchor.

MaterialLength

(mm)

Spacing

(mm)

Diameter

(mm)

Average Young’s modulus

of anchored segment

(GPa)a

Average

diameter of cable

(mm)b

PE tubec 25 250 3.6 0.78 2.17

PMMA

tubed25 250 6.0 2.70 2.42

621 aCalculated based on cross-section geometry.

622 bCalculated based on micro-anchor distribution.

623 cPE = polyethylene.

624 dPMMA = polymethyl methacrylate.

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625 Table 4. Validity of FO strain data related to a three-stage process of the cable–soil interface

626 failure.

StagePeak ISS of unanchored

segment reached or nota

Peak ISS of anchored

segment reached or not

Coupling

conditionFO strain data

I No NoOverall

bondingValid

II Yes NoPoint

fixationb

Averaged over

gauge lengthc

III Yes Yesd Decoupling Invalid

627 aISS = interfacial shear stress.

628 bThe micro-anchored FO cable is similar to a gauged strainmeter.

629 cThe gauge length is equivalent to anchor spacing.

630 dProvided that the cable itself has not yielded.

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631 Figure captions

632 Fig. 1. Schematic diagram of ground deformation sensing using a micro-anchored fiber optic

633 (FO) strain cable.

634 Fig. 2. (a) Distributions of axial force and interfacial shear stress (ISS) along an unanchored

635 soil inclusion during pullout at the critical state; and (b) hypothesized axial force and ISS

636 distributions for an anchored soil inclusion.

637 Fig. 3. Schematic of the principle of distributed fiber optic sensing (DFOS) using Brillouin

638 optical time-domain analysis (BOTDA).

639 Fig. 4. Grain size distribution curve of the soil.

640 Fig. 5. (a) Structure of the FO cable; and (b) layout of micro-anchors on the FO cable (unit:

641 mm).

642 Fig. 6. Schematic of the test setup (unit: mm; not to scale).

643 Fig. 7. Schematic of the clamp used to clamp the FO cable (unit: mm; not to scale).

644 Fig. 8. Experimental curves of pullout force versus pullout displacement under different micro-

645 anchor diameters.

646 Fig. 9. Influence of micro-anchor on the secant interfacial shear stiffness and peak ISS. The

647 secant interfacial shear stiffness was determined under a displacement step of 2 mm.

648 Fig. 10. Comparison between pullout forces measured by the force gauge and those calculated

649 using FO strain measurements.

650 Fig. 11. Strain profiles along the FO cables captured using BOTDA during the progressive

651 failure of the cable–soil interface: (a) unanchored FO cable; (b) micro-anchored FO cable (Da

652 = 3.6 mm); and (c) micro-anchored FO cable (Da = 6.0 mm).

653 Fig. 12. Simulated results for the unanchored FO cable: (a) pullout force–displacement curve;

654 (b) strain profiles; and (c) ISS profiles. Five pullout phases are marked in (a) according to the

655 simulation results.

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656 Fig. 13. Overall average ISS and ISS along unanchored and anchored segments for the micro-

657 anchored FO cable with: (a–c) Da = 3.6 mm; and (d–f) Da = 6.0 mm.

658 Fig. 14. Difference of average ISS between anchored and unanchored segments of the micro-

659 anchored FO cables.

660 Fig. 15. Validity of FO strain data as related to a three-stage process of the cable–soil interface

661 failure. The unanchored segment B and two neighboring anchored segments a and b for the

662 micro-anchored FO cable with Da = 6.0 mm are taken as an instance.

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Stable ground Unstable groundShear zone

Movement directionFO cable Micro-anchors

Fig. 1. Schematic diagram of ground deformation sensing using a micro-anchored fiber optic (FO) strain cable.

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(a)

(b)

ISS

Axial force

ISS

Axial force

Pulloutforce

Pulloutforce

Mobilized ISS

Mobilized ISS

Fig. 2. (a) Distributions of axial force and interfacial shear stress (ISS) along an unanchored soil inclusion during pullout at the critical state; and (b) hypothesized axial force and ISS distributions for an anchored soil inclusion.

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DraftBrillouin frequency

FO cable distance

Appliedstrain

Pumping pulse light

Brillouin backscattering

Probelight

Light intensity

Fig. 3. Schematic of the principle of distributed fiber optic sensing (DFOS) using Brillouin optical time-domain analysis (BOTDA).

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0

25

50

75

100

101

Grain size (mm)10010-1 10-2

Perc

enta

ge fi

ner b

y w

eigh

t (%

)

Fig. 4. Grain size distribution curve of the soil.

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Draft

(b)

250

1,200

250 250 250 50150

25

6.0

3.6

Da

(a)

Polyurethane coating

Optical fiber

Buffer

Fig. 5. (a) Structure of the FO cable; and (b) layout of micro-anchors on the FO cable (unit: mm).

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Draft1,500

Soil

200 200

Test container

Clamp

FO cable

1,20010.2

Forcegauge

BOTDAinterrogator

Tensile tester

Computer

Fig. 6. Schematic of the test setup (unit: mm; not to scale).

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FO cable

Rubber pieces(69×20×2.2)

Aluminumpieces

(69×20×5.6)

Connected totensile tester

Bolts

Cross-sectional view

Plan view

Fig. 7. Schematic of the clamp used to clamp the FO cable (unit: mm; not to scale).

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DraftPullout displacement, u0 (mm)

Pullo

ut fo

rce,

F0 (

N)

UnanchoredAnchored (Da = 3.6 mm)Anchored (Da = 6.0 mm)

0

5

10

15

20

25

0 5 10 15 20 25

Fig. 8. Experimental curves of pullout force versus pullout displacement under different micro-anchor diameters.

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Draft

Seca

nt in

terfa

cial

shea

r stif

fnes

s (k

Pa/m

)Peak ISS (kPa)

Anchored(Da = 3.6 mm)

Unanchored Anchored(Da = 6.0 mm)

0

50

100

150

200

250

0

0.5

1

1.5

2

2.5Secant interfacial shear stiffnessPeak ISS

Fig. 9. Influence of micro-anchor on the secant interfacial shear stiffness and peak ISS. The secant interfacial shear stiffness was determined under a displacement step of 2 mm.

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0

5

10

15

20

0 5 10 15 20Calculated pullout force (N)

Mea

sure

d pu

llout

forc

e (N

)

UnanchoredAnchored (Da = 3.6 mm)Anchored (Da = 6.0 mm)

1:1 ratio

Fig. 10. Comparison between pullout forces measured by the force gauge and those calculated using FO strain measurements.

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0

1,000

2,000

3,000

4,000

5,000

2,000

4,000

6,000

8,000

10,000

0

3,000

6,000

9,000

12,000

15,000

Stra

in (μ

ε)St

rain

(με)

Stra

in (μ

ε)

0

7 11 1422

1 2 34 5 6

7 9

1 2 34 5 6

Disp. steps (mm)

7 9 1113 15 1719 21 24

1 2 34 5 6

0 200 400 600 800 1,000 1,200Distance from FO cable head (mm)

(a)

(b)

(c)

u⁰ (mm)

F⁰ (

N)

B

C

D

E

B

C

D

E

a b c d

a b c d

A

A

0

8

0 8 16 24

0

14

0 8 16 24

0

24

0 12 24

u⁰ (mm)

F⁰ (

N)

u⁰ (mm)

F⁰ (

N)

Fig. 11. Strain profiles along the FO cables captured using BOTDA during the progressive failure of the cable–soil interface: (a) unanchored FO cable; (b) micro-anchored FO cable (Da = 3.6 mm); and (c) micro-anchored FO cable (Da = 6.0 mm).

e

e

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Draft

0

1,000

2,000

3,000

4,000

5,000

0

2

4

6

0 5 10 15 20 25Pullout displacement (mm)

Pullo

ut fo

rce

(N)

MeasuredSimulated

Stra

in (μ

ε)

Distance from FO cable head (mm)(a) (b)

7 mm 9 mm

1 mm 2 mm3 mm 4 mm5 mm 6 mm

Applied

0

0.2

0.4

0.6

0.8

Sim

ulat

ed IS

S (k

Pa)

Distance from FO cable head (mm)(c)

0 200 400 600 800 1,000 1,200

0 200 400 600 800 1,000 1,200

Simulated

1 mm 2 mm 3 mm4 mm

5 mm

6 mm7 mm

8 mm

Fig. 12. Simulated results for the unanchored FO cable: (a) pullout force–displacement curve; (b) strain profiles; and (c) ISS profiles. Five pullout phases are marked in (a) according to the simulation results.

III III IV V

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Draft

0

0.5

1

1.5

2

2.5

-0.5

0

0.5

1

1.5

0

250

500

750

0 7 14 21 28 35Displacement steps (mm)

0

0.5

1

1.5

2

0

0.2

0.4

0.6

0.8

0

20

40

60

0 5 10 15 20 25

Aver

age

ISS

over

who

le c

able

leng

th (k

Pa) (a)

Displacement steps (mm)

ISS

alon

gun

anch

ored

seg

men

t (kP

a)IS

S al

ong

anch

ored

seg

men

t (kP

a)

(b)

(c)Av

erag

e IS

S ov

erw

hole

cab

le le

ngth

(kPa

)IS

S al

ong

unan

chor

ed s

egm

ent (

kPa)

ISS

alon

g an

chor

ed s

egm

ent (

kPa)

(d)

(e)

(f)

BA C D E Avg.

dba

c Avg.dba

c Avg.

BA C D E Avg.

Fig. 13. Overall average ISS and ISS along unanchored and anchored segments for the micro-anchored FO cable with: (a–c) Da = 3.6 mm; and (d–f) Da = 6.0 mm.

Residual ISS alongunanchored FO cable

Residual ISS alongunanchored FO cable

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Draft

0

5

10

15

0 5 10 15 20 25

y = 0.39x + 2.64R² = 0.95

y = 0.53x + 4.53R² = 0.97

Displacement steps (mm)

Diff

eren

ce o

f ave

rage

ISS

kAnchored (Da = 3.6 mm)Anchored (Da = 6.0 mm)

Fig. 14. Difference of average ISS between anchored and unanchored segments of the micro-anchored FO cables.

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Draft

-0.5

0

0.5

1

1.5

0

250

500

750

0 7 14 21 28 35Displacement steps (mm)

Stage I Stage II Stage III

ISS

alon

g an

chor

ed s

egm

ent (

kPa)

ISS alongunanchored segm

ent (kPa)

Unanchored seg. B

Anchored seg. bAnchored seg. a

Fig. 15. Validity of FO strain data as related to a three-stage process of the cable–soil interface failure. The unanchored segment B and two neighboring anchored segments a and b for the micro-anchored FO cable with Da = 6.0 mm are taken as an instance.

Page 46 of 46



Draft...Draft 2 24 Abstract: 25 Distributed fiber optic sensing (DFOS) is gaining increasing...

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