CENTRIFUGE TESTS ON ROCK-SOCKETED PILES: EFFECT OF SOCKET 1 ROUGHNESS ON SHAFT RESISTANCE 2

6 Preliminary estimations of shaft resistance of rock-socketed piles are usually 7 conducted using empirical formulations which relate to the uniaxial compressive 8 strength ( 𝜎 𝑐 ) of the weaker material involved (intact rock or pile). However, there 9 are other factors, such as the degree of socket roughness, that could affect the 10 shaft resistance of rock-socketed piles. In this paper, results from geotechnical 11 centrifuge tests are presented to demonstrate the effect of socket roughness on 12 the pile shaft resistance. Aluminum model piles with different degrees of shaft 13 roughness were fabricated and embedded within an artificial rock mixture 14 composed of sand, cement, bentonite and water. Pile loading tests were 15 conducted within the centrifuge and axial forces along the model piles were 16 measured using fiber Bragg grating (FBG) sensing technology. Results are used 17 to demonstrate that centrifuge testing provides a suitable experimental method 18 to study and quantify the effect of socket roughness on the shaft shearing 19 mechanism of rock-socketed piles. Finally, the centrifuge test measurements are 20 compared with several formulations published in the literature, suggesting that 21


Introduction 27
Rock-socketed piles are usually employed to support loads from a superstructure 28 and to transfer the loads to stronger and deeper rock layers, with loads being 29 carried by the pile base, shaft, or a combination of both. It is well known (Pells et 30 al. 1978;Seidel and Collingwood 2001) that shaft resistance can be fully 31 mobilized at much lower pile displacements than base resistance, hence 32 understanding the development of shaft resistance is a key aspect in assessing 33 the behavior of rock socketed piles under working loads. Tests conducted within a geotechnical centrifuge (Leung and Ko 1993) provide 48 some benefits compared with full-scale tests or with tests conducted in the 49 laboratory at 1 g, including (i) the difficulties and costs associated with full-scale 50 7 To assess the influence of socket roughness on the response of a pile to axial 120 loading, the model piles were manufactured with different roughness profiles. 121 Previous works have analyzed the influence of roughness using pile-rock 122 interfaces with triangular asperities (Johnston et al. 1987; Kodikara and Johnston 123 1994; Gu et al. 2003;Xu et al. 2020) or with sinusoidal asperities (Dai et al. 2017). 124 In this research, sinusoidal pile-rock interfaces were used because they provide 125 a reasonable replica of sockets drilled in soft rock with an auger tool (O'Neill et 126 al.,1996;Hassan et al. 1997). However, this is only an approximation, and 127 roughness patterns developed in real rock sockets drilled in the field may be 128 different to those considered herein. The adopted sinusoidal profiles, though not 129 matching exactly with reality, provide the consistency between tests that is 130 required to obtain the desired new insights on the effect of socket roughness on 131 the response of axially loaded rock-socketed piles. with standard tools tend to produce asperities with amplitudes less than or equal 147 to 10 mm (prototype scale), which could be classified as "smooth" piles; however, 148 if the rock is highly fractured or special drilling tools are used, the amplitudes of 149 asperities at the socket could be larger (i.e., more than 10 mm) which would be 150 classified as "rough" piles. piles. An illustration of an FBG strain sensor is presented in Fig. 3a. The FBG 167 sensors were made from a single-mode optical fiber, which was etched using an 168 excimer laser. The reflectivity of the FBG sensors is greater than 90%. Fig. 3b  169 illustrates the method used to install the optical fibers in the piles: (1) the fiber  170   was inserted into the pile through a hole drilled at an inclined angle near the top  171 of the pile (the pile head assembly shown in Fig. 1 . 4a), hence the pile resistance was derived solely from its shaft.  (Fig. 4b). The container was then vibrated again to ensure adhesion 205 between the pseudo-rock mixture and the model pile, according to the procedure 206 described by Dykeman and Valsangkar (1996) and Dai et al. (2017). (4) The 207 containers were stored and cured under high humidity conditions for 44 days. A 208 typical model pile-pseudo-rock assembly is presented in Fig. 4c. In practice, the normal stress applied on the pile-rock interface is zero before the 211 concrete is placed into the socket, and the normal stress acting on the socket 212 sidewalls could increase during placement of concrete (Seidel and Collingwood 213 2001; Haberfield and Lochaden 2018). This aspect is not considered during the 214 centrifuge model preparation conducted herein; however, a parametric study 215 conducted by Seidel and Collingwood (2001), and the analysis of load test data 216 conducted by Asem (2020), strongly suggest that the initial normal stress at the 217 pile-rock interface does not substantially affect the peak shaft resistance of rock-218 socketed piles, unless an expansive concrete is used. Therefore, and since 219 expansive concrete was not employed in this work, it is expected that the effect 220 of the initial normal stress acting on the socket sidewalls could be neglected. 221

Centrifuge tests 222
After 44-days of curing, each pseudo-rock container was placed on the centrifuge 223 and steel plates (30 mm thick) were added to the surface to impose a vertical 224 stress of 120 kPa at 50 g (replicating 6 m depth of overburden with an average 225 unit weight of 20 kN/m 3 ) (Fig. 5b). The pile loading/measurement system was 226 then installed, comprising of a loading frame, two L03 MecVel ball screw 227 actuators (each with a maximum 5 kN load capacity and 100 mm stroke), a load 228 cell, and a connector (Fig. 5). The ball and socket actuator-pile connection, 229 illustrated in Fig. 5c, allowed the pile to move separately from the load actuator 230 during centrifuge spin-up, with the pile moving downwards as a result of the self-231 weight of the pile and associated spacer, load cell, and connector. The model pile 232 settlement was measured using a single linear variable differential transducer 233 (LVDT) positioned on an aluminum plate located above the pile cap (Fig. 5b). 234 The load along the model pile was obtained using the FBG sensors and an FBG 235 interrogator located within the centrifuge data acquisition cabinet (see Fig. 5a). 236 For each test, the acceleration of the centrifuge was gradually increased to 50 g, Pile settlement results are presented in dimensionless form (normalized by the 259 pile diameter) to facilitate discussion of results. This adopted normalization 260 convention will not necessarily allow the interface response from these tests to 261 13 be directly compared to other studies, hence readers should apply appropriate 262 judgement. However, as all tests presented here relate to a consistent pile size 263 and interface type, the adopted convention is satisfactory. 264 Similarly, some corrections were made to the initial segment of the load-265 settlement curve of the model pile with = 0.050, since this pile rotated and 266 moved upwards at the beginning of the tests. The correction involved linearizing 267 the initial curved section of the "raw" load-settlement data, since other curves (for 268 = 0.025 and = 0.106) demonstrated such a linear trend upon initial loading 269 (these aspects are discussed further below, and a Supplemental Data file is 270 presented to provide the "raw" data along with an additional discussion of the 271 correction and its implications on subsequent data interpretation.) 272

Load-settlement response 273
The load-displacement curves for the rock-socketed piles with different degrees 274 of socket roughness are shown in Fig. 6a. The model pile with = 0.000 is not 275 presented in Fig. 6 because it failed during centrifuge spin-up, therefore, its 276 results are not considered in the data analysis since the pile was in a post-peak 277 (failure) state when loading started at 50 g. All piles were loaded until the pile 278 head settlement ( ) exceeded 20% of the pile diameter ( ⁄ >20%). respectively. Similarly, an influence of socket roughness was also observed in 287 the results of field tests (see Table 3) conducted by Horvath et al. (1983) and 288 Seol and Jeong (2007) on full-scale piles socketed in shale and gneiss, 289 respectively, considering shaft resistance only. From Table 3 it can be noted that, 290 for = 1% , rougher piles supported a higher working load that is about 1.3 291 (gneiss) to 1.5 (shale) times higher than for smooth piles. 292

[Table 3 approx. here] 293
As can be observed in Fig. 6a, the load-settlement curve of the model pile with 294 = 0.025 increases linearly to an initial peak value (for = 0.5% ). With further 295 increases in pile settlement, the pile head load decreases, probably representing 296 a loss of the bonding at the pseudo-rock-pile interface. Then, with further 297 displacement (for > 1% ), the pile transfers its axial load to the front of the 298 asperities within the rock, so that its load capacity increases again until a second 299 peak is reached (for = 19.8% ). For rougher piles ( = 0.050 and = 300 0.106), a bonding failure at the pseudo-rock-pile interface is not observed. The 301 load capacity increases until the maximum load capacity is reached; after this 302 load threshold, the load capacity decreases. Also, results in Fig. 6a show that the 303 post-peak shaft resistanceor the shaft's resistance beyond the settlement 304 ( − ) associated with the peak loadtends to be more ductile for rougher 305 piles. This behavior can be explained by the fact that rougher interfaces tend to 306 dilate more and, as a consequence, lead to higher normal stresses at the pile-307 15 rock interface that produce higher interface resistances (Pells et al 1978;308 Gutiérrez-Ch et al. 2021). 309 Finally, the load-settlement results suggest that there might be an upper 310 roughness limit beyond which, for large settlement levels (say, for > 10% ), 311 the load capacity and the global stiffness no longer increase (i.e. increasing 312 roughness above = 0.050 did not have a significant effect; see

Axial load 323
The distribution of mobilized axial load (change in axial load along the pile) with 324 depth during pile loading was obtained using the measured wavelength shifts of 325 the FBG sensors (see Fig. 1). As mentioned earlier, the rock-socketed piles had 326 a polystyrene base; hence the base resistance can be neglected. The results of 327 the mobilized axial load are presented at prototype scale. 328  Fig. 6) for all centrifuge tests conducted. It can be 331 observed (i) that mobilized axial loads along the pile, for a given settlement, 332 decrease with depth; (ii) that mobilized axial loads along the pile increase as the 333 load applied at the pile head increases, until the peak value is reached; and (iii) 334 that mobilized axial loads along the pile decrease after this threshold (i.e., for > 335 − ), but with smaller, or more ductile, reductions in rougher piles. To our 336 knowledge, this is the first time that the influence of roughness on the axial load 337 distribution of rock-sockets has been measured experimentally (in the field or in 338 the laboratory). 339 It is important to highlight that, after processing the measurement data for the 340 model pile with = 0.025, an anomalous distribution of the mobilized axial load 341 with depth was obtained; in particular, the mobilized axial load at 20 mm depth 342 was greater than at 0 mm depth (a "Supplementary Data" file has been provided 343 to discuss details of the measured data and of the uncertainties associated with 344 their interpretation). This trend is unexpected, and may be explained by the fact 345 that, during casting (44 days), the pile could have reacted with the pseudo-rock, 346 causing a change to the relationship between pile/FBG strain and applied load. 347 This is because the pseudo-rock contains cement (alkalis), which can react with 348 aluminum, resulting is some corrosion of the external surface of the piles. After 349 the tests, some corrosion along the pile surface was identified. In such a case, 350 the thickness of the aluminum pile would be less than the pile prior to casting, 351 which would imply an error within the adopted FBG sensor calibration factors 352 (calibrations were conducted for all piles prior to casting; for the pile with (2) where , and +1, are the mobilized axial loads (i.e., change in axial loads upon 377 loading under constant g-level) at two consecutive reference points (e.g., at the 378 pile FBG sensors located at = ⁄ 2.5 and = ⁄ 5, see Fig. 1 for FBG reference 379 ), is the pile diameter, and → +1 is the nominal length between the two 380 consecutive reference points (i.e., from location to + 1). Hence the , 381 computed using Eq. 2 is considered constant from location to + 1. In addition, 382 since and → +1 are nominal values which are equal for all piles, the shaft area 383 in Eq. (2) is assumed to be the same for all the piles. 384 The distribution of , (with depth) for a given pile head settlement is shown in 385 Also, Fig. 9 shows that, as the applied load increases and the maximum 395  Table 3). 453 Similarly, it has also been noted (by Seol and Jong (2007) for piles socketed in 454 gneiss and by Dykeman and Valsangkar (1996) in pseudo-rock) that rough piles 455 mobilized 1.3 to 1.6 times more than smooth piles, for = 1% (see Table  456 3). This behavior might be due to effects of the higher dilation associated with 457 rough piles, which increases the normal stress at rough pile-rock interfaces (i.e. 458 with higher ). 459 Experimental results also showed a quasi-linear (elastic) behavior for values of 460 less than about 1% , which was defined by Asam and Gardoni (2019) as initial 461 shear stiffness ( ) (see Fig. 12 piles. There were, as is often the case with complex experimental studies, some 550 uncertainties in the obtained measurements; these were detailed in the 551 supplementary data along with a discussion on potential implications on obtained 552 outcomes. The experimental uncertainities are considered to be no more 553 significant than typical levels of uncertainty for piling projects. 554 The centrifuge tests conducted with FBG sensors have also provided 555 experimental evidence and confirmation of important aspects of the load-transfer 556 mechanism of rock-socketed piles; in particular, (i) that rougher piles are more 557 resistant, stiffer, and more ductile than smooth piles; (ii) that, particularly for 558 rougher piles, the upper part of the pile tends to attract more load initially, and 559 that such loads tend to "move downwards" as the pile head load continues 560 increasing; (iii) that the load distribution along the pile is more homogenous in 561 smoother piles than in rougher ones, (iv) that little damage seems to occur at the 562 rock-pile interface for pile head settlements of less than about 1% , given the 563 observation that the load increases linearly with settlement within that settlement 564 range, and (v) that there might be an upper roughness limit above which the load 565 capacity and the global stiffness of the rock-socketed pile stops increasing (for 566 26 large pile head settlements of, say, more than 10% ). Finally, average shaft 567 resistances measured in the centrifuge tests were compared with those predicted 568 with several common formulations from the literature. Centrifuge results tend to 569 agree with the overall trend, although there are of course differences between 570 formulations; additional measurements would be required to assess the 571 predictive capabilities of these methods with more confidence. 572

Data Availability Statement 573
Some or all data, models, or code that support the findings of this study are 574 available from the corresponding author upon reasonable request (centrifuge test 575 results).