Experimental Study on the Piping Erosion Mechanism of Gap-Graded Soils Under a Supercritical Hydraulic Gradient


 Seepage-induced piping erosion is observed in many geotechnical structures. This paper studies the piping mechanism of gap-graded soils during the whole piping erosion failure process under a supercritical hydraulic gradient. We define the supercritical ratio Ri and study the change in the parameters such as the flow velocity, hydraulic conductivity, and fine particle loss with Ri. Under steady flow, a formula for determining the flow velocity state of the sample with Ri according to the fine particle content and relative density of the sample was proposed; during the piping failure process, the influence of Rimax on the rate at which the flow velocity and hydraulic conductivity of the sample increase as Ri decreases was greater than that of the initial relative density and the initial fine particle content of the sample. Under unsteady flow, a larger initial relative density corresponds to a smaller amplitude of increase in the average value of the peak flow velocity with increasing Ri. Compared with the test under steady flow, the flow velocity under unsteady flow would experience abrupt changes. The relative position of the trend line L of the flow velocity varying with Ri under unsteady flow and the fixed peak water head height point A under steady flow were related to the relative density of the sample.

during the whole piping erosion failure process under a supercritical 22 hydraulic gradient. We define the supercritical ratio R i and study the 23 change in the parameters such as the flow velocity, hydraulic 24 conductivity, and fine particle loss with R i . Under steady flow, a 25 formula for determining the flow velocity state of the sample with R i 26 according to the fine particle content and relative density of the 27 sample was proposed; during the piping failure process, the influence 28 of R imax on the rate at which the flow velocity and hydraulic conductivity 29 of the sample increase as R i decreases was greater than that of the 30 initial relative density and the initial fine particle content of the 31 sample. Under unsteady flow, a larger initial relative density 32 corresponds to a smaller amplitude of increase in the average value of embankments (Foster et al., 2000;Richards and Reddy, 2007). Piping 45 seepage is a typical form of instability in soil. S. Van. Baars (2009) 46 pointed out in his report that many dam failures were caused by piping. 47 In recent years, an increasing number of piping erosion accidents have 48 occurred worldwide (Brazil,2019;Laos,2018 andChina,2015). Therefore, 49 it can be concluded that piping is a problem worthy of sufficient 50 attention and intensive study, and many scholars have conducted 51 relevant research on this topic (Wang et al., 2015;Hu et al., 2020;52 Zou et al., 2020;Razavi et al., 2020). 53 Research on the condition of piping occurrence is a popular topic 54 of piping research. There are various factors that affect the 55 occurrence of soil piping, mainly involving four aspects: seepage 56 conditions (such as the water head type, seepage direction, etc.), 57 geometric conditions (such as the soil particle gradation, particle 58 size ratio, etc.), physical conditions (such as the soil compactness, 59 cohesion, etc.), and stress conditions (such as the confining pressure, 60 a switching power supply, a signal converter, and an intelligent 142 paperless recorder. The working relationship of each part is shown in 143 Fig. 2(b). 144

Test scheme 145
The development of piping is a process in which fine particles are 146 transported and taken out in the pores of coarse particles, so the 147 content of the fine particles (FC) has a great influence on the 148 development of piping. According to the geometric conditions, Ke and 149 Takahashi (2012) estimated that FC=37% was the ideal state where FC 150 was close to filling the pores between the coarse particles under the 151 condition that the coarse particle part was loose and the fine particle 152 part was dense. Therefore, in this study, we selected specimens with 153 FC=10%, FC=15%, FC=18%, and FC=25%, which represent the different 154 degrees of filling, to conduct experiments. 155 In addition, the initial relative density Dr, which is defined as: 156 157 is a condition that can influence the volumetric strain during piping 158 erosion and has a great effect on the piping mechanism (Zeng, 2016). 159 Therefore, we selected three groups of samples with FC values of 160 10, 18, and 25 and three groups of samples with Dr values of 0.3, 0.6, and 0.8 to conduct the piping test which is shown in Table 1. In this  162 paper, we defined that the smaller hydraulic gradient when fine 163 particles are slightly washed out and the hydraulic gradient at the 164 inflection point of the v-i (v represents velocity; i represents 165 hydraulic gradient) relationship curve is selected as the CHG (Lu, 166 2005  shows the phenomenon of the top surface of the sample when the test 218 was carried out for 193 minutes. It can be seen that there were many 219 fine particles that accumulated on the top surface of the sample, the 220 seepage quantity was continuously rising, and the pore pressure of No The variation in the velocity with time of group FC and Dr during 237 the whole piping development is shown in Fig. 6. Table 2 shows the 238 SCHG i scr when the water head was fixed after the last head lift, 239 hydraulic gradient i f when complete piping failure occurred and CHG of 240 the sample. We define the supercritical ratio as R i =i s /i cr (i s represents 241 the SCHG) and R imax = i scr /i cr because i scr is the maximum SCHG of the whole 242 process of piping erosion. The whole process of the piping erosion 243 test consisted of the upstream water head lifting stage and the piping 244 failure stage after the upstream water head was fixed. In the piping 245 failure stage, according to Chen et al. (2020) Table 3, we selected R imax = 1.0, 1.3, 262 1.6, 1.8, 2.1, 2.5, and 2.8 for each group of samples to conduct the 263 piping test and maintain 90 min at each R imax (it can be seen from Fig is in a decreasing state, and "Area B" is the distribution area where 281 the flow velocity is in a stable state and increasing state. On the 282 whole, the distribution of the three states of the flow velocity with the increase in the hydraulic gradient is the decreasing state, stable 284 state and increasing state successively, regardless of how the initial 285 fine particle content or initial relative density of the samples 286 changed. The stable state is a transitional phase between the 287 decreasing state and the increasing state, and its distribution area 288 is small. 289 In Fig. 8(a), the area where the flow velocity decreased was more 290 to the upper left, that is, the larger the fine particle content of 291 the sample was, the larger the SCHG corresponding to the stable state 292 of the flow velocity. In addition, "Area A and Area B" shifted to the 293 direction of the increase in the hydraulic gradient; in Fig. 8 (b), 294 the flow velocity decreasing state was also more distributed in the 295 upper left, that is, with the increase in the relative density of the 296 sample, the SCHG corresponding to the stable state also increased. 297 The flow velocity gradually decreased over time because of the fine 298 particles inside the sample blocking the pores when they moved, which 299 resulted in a decrease in the permeability of the sample. Since there 300 was no loss of fine particles in the process of blocking the pores 301 with fine particles, the content of the fine particles and relative 302 density of the sample did not change, but the water head loss in the 303 length direction of the sample's seepage diameter increased due to pore 304 blockage, so the hydraulic gradient increased. Therefore, with the 305 gradual increase in the amount of fine particles inside the sample to 306 block the pores, the flow velocity gradually decreased. The movement 307 path of the flow velocity state in the test moved from "Area A" to the 308 right, similar to "Point P" and "Point M" shown in Fig. 8. 309 The flow velocity gradually increased over time because the fine 310 particles inside the sample were washed away from the pores, resulting 311 in greater permeability of the sample. Due to the loss of fine particles, 312 the fine particle content and relative density of the sample gradually 313 decreased, and the water head loss in the length direction of the 314 sample's seepage diameter also decreased, so the hydraulic gradient 315 decreased. Therefore, with the gradual increase in the loss of fine 316 particles inside the sample, the flow velocity increased accordingly. 317 The direction of movement of the flow velocity state in the test was 318 similar to "Point Q" and "Point N" shown in Fig. 8. 319 To further study the relationship between the state of the flow 320 velocity and R i , the abscissa in Fig. 8 is replaced with R i and the 321 distribution diagram of the flow velocity state is drawn, as shown in 322 The dividing line of "Area A and Area B" in Fig. 9 was basically 334 a straight line. Under the condition that the ratio of the sample is 335 the same or close to that in this paper, the flow velocity state of 336 the sample under the action of a certain SCHG can be roughly obtained 337 in terms of the fine particle content and density of the sample, 338 respectively, as follows: 339 In terms of the fine particle content of the sample: 340 Based on Fig. 9, we further plot the change path of the flow 349 velocity state of the whole process of piping erosion, as shown in Fig.  350 10. Take group Dr0.3 as an example (Fig. 10(a) when R imax ＞3 (other 5 groups), the flow velocity then went through three 359 stages: the increasing stage, then the stabilize stage and finally the 360 decreasing stage. Fig. 6(a) shows that the FC25 group did not 361 experience a significant change in the flow velocity until 80 minutes 362 because the fine particle content was too high, which caused the fine 363 particles to block the pores during the early process of raising the 364 water head. When the water head was raised to a height of 3.1, the 365 larger water flow force suddenly flushed away the fine particles, causing the flow velocity to rapidly increase. Fig. 6 Since the hydraulic gradient in the whole process of piping failure 375 after fixing the water head is SCHG, to further study the effect of 376 the SCHG on the flow velocity in the whole process of piping failure, 377 we plot the variation of the flow velocity with R i, which is shown in 378 Fig. 11. 379 When fixing the upstream water head, the value of R i at this time 380 was the maximum, and it can be applicable to both the Dr and FC groups 381 that the greater the value of R imax , the greater the corresponding flow 382 velocity would be when complete piping failure occurred. 383 The dashed line Ln in the increasing stage of the flow velocity is 384 an approximate slope fitting straight line. It can be seen from Fig.  385 11(a) that the smaller the initial relative density is, the larger the 386 value of K Ln , which represents the rate of increase of the flow velocity 387 as R i decreases. In Fig. 11(b), although the fine particle content of 388 FC10 is smaller than that of FC25, because R imax of FC25 is much larger 389 than that of FC10, which represents the much larger seepage force 390 acting on the sample, the corresponding rate of the increase in the 391 flow velocity is K L4 < K L5 . Combined with Table 3, it can be concluded 392 that when R imax of the different sample are close, the rate of increase 393 of the flow velocity as Ri decreases is related to the relative density 394 of the sample. The smaller the relative density, the greater the rate 395 of increase of the flow velocity. When R imax of the different sample 396 vary greatly, the rate of increase of the flow velocity with the 397 decrease in the value of R i is related to R imax . The greater R imax is, the 398 greater the rate of increase in the flow velocity. 399

Hydraulic conductivity 400
The variation in the hydraulic conductivity with time during the 401 whole piping development is shown in Fig. 12. The hydraulic 402 conductivity went through three stages: the upstream water head lifting 403 stage, increasing stage, and stabilizing stage. During the stage of 404 upstream water head lifting, the change in the hydraulic conductivity 405 is more complicated. During the increasing stages, the increasing rate 406 of the hydraulic conductivity of the three groups of the Dr group (Fig.  407 12 (a)) were almost equal, and Point K in Fig. 12(a) demonstrates the 408 rapid increase in the hydraulic conductivity of Dr0.8 because the fine 409 particles that clogged the pores were instantly washed away. In Fig.  410 12(b), FC10 and FC25 had approximately the same rate of increase in 411 hydraulic conductivity and were both larger than that of FC18. 412 To further study the effect of the SCHG on the hydraulic 413 conductivity during the process of piping development after fixing the 414 upstream water head, the variation in the hydraulic conductivity with 415 R i is plotted, which is shown in Fig. 13. 416 On~An (n=1~6) is the upstream water head lifting stage, and the 417 hydraulic conductivity was basically stable with increasing R i . 418 An~Bn is the increasing stage. Fig. 13 (a) shows that K L3 ＞K L1 ＞K L2 . 419 In Fig. 14 (b), K L6 ＞K L4 ＞K L5 . Combined with Table 3, it can be concluded 420 that the rate of increase of the hydraulic conductivity with the 421 decrease in the value of R i is related to R imax, which had a greater 422 impact on the hydraulic conductivity than the initial relative density 423 and initial fine particle content. The greater the value of R imax is, 424 the greater the rate of increase of the hydraulic conductivity. 425

Loss of fine particles 426
The loss of fine particles is the direct cause of the development 427 and destruction of piping. Due to the continuous loss of fine particles 428 during the failure of piping, the pores inside the sample will increase, 429 which can cause the permeability and flow velocity of the sample to 430 increase. To intuitively reveal the change rule of the fine particle 431 loss amount, three sets of samples of the Dr group with the same initial 432 fine particle content were selected to plot the variation in the fine 433 particle loss amount corresponding to each stage of the whole piping 434 development (Fig. 14). 435 In the whole process of piping failure (Fig. 14), the fine particle 436 loss during the upstream water head lifting was very small, almost 437 zero; the increase stage of the flow velocity was the main stage of 438 fine particle loss, accounting for almost 50% of the total fine 439 particle loss; the amount of fine particle loss during the 440 stabilization stage of the flow velocity was greatly reduced; the 441 amount of fine particles lost during the period of decreasing flow 442 velocity increased again (because the duration of the velocity 443 stabilization stage was much less than that of the velocity increasing 444 stage and decreasing stage); after the sample was completely destroyed, 445 the amount of fine particles that were lost was very small. 446 It is known from the development process of the Dr group (  Table 3, we chose to set 6 groups of SCHGs with 488 different multiples from low to high (R i =1.5,2.0,2.5,3.0,3.5,4.0).
After the start of the test, the upstream water head was raised from 490 the height when the sample was saturated. We reciprocated lifting and 491 lowering the water head according to the simplified unsteady 492 circulating water head model determined in section 3.3.1 and repeated 493 it three times for the height of each R i in order from low to high. 494

Establishment of the unsteady water head model 495
To simulate the unsteady water head situation in an actual water 496 conservancy project, the flood peak process line calculated based on 497 the 1994 maximum flood year of the Beijiang River levee (Mao et al. 498 2005;2005;2004) is selected as the prototype of the unsteady water head 499 model in this paper. The experimental unsteady head model is simplified 500 and established according to the following process. 501 The value of 12.33 m (Liang XQ, 1994) was taken as the indoor 502 test peak water level 9 m (Liang XQ, 1994) was taken as the warning 503 water level, and the approximate sine curve of the unsteady head above 504 the warning level was converted into an equivalent stable average 505 water head. As shown in Fig. 15(a), SA+SB+SC+SD=SB+SE+SF. The flood 506 peak water level after equivalent transformation lasted for 6 days, 507 and the entire flood peak fluctuation cycle period was T=11 days, 508 which is shown in the simplified flood peak process line in Figure 15(b). 510 According to the similarity principle (Zhang WJ,2013), it is 511 necessary to make the indoor model test and the real working condition 512 meet the mechanical similarity and use the results of the indoor model 513 test to predict the prototype working condition. We found that 514 Coriolis' law (Mao CX,2013), which is suitable for both the seepage Taking a typical place where piping occurs for the Beijiang River 526 levee as an example, the test model is calculated as follows: the 527 distance between the piping place and Beijiang is 100 m, which can be 528 seen as the length of the seepage diameter of the piping, and the 529 length of the seepage diameter designed by the test model is 250 mm. 530 The simplified entire flood peak fluctuation cycle is Ty = 11 days. 531 According to (1), (2), and (3), the entire flood peak fluctuation cycle 532 of the test model can be calculated as shown in Table 3. 533 3.3.2 Analysis of the flow velocity 534 The curves according to the relationship between the velocity and 535 time are plotted as shown in Figure 16. 536 First, in terms of 6 different SCHGs (R i ), regardless of which 537 group of samples was selected (except group FC25), the flow velocity 538 would go through three stages of decreasing, stabilizing, and 539 increasing in the whole test process from R i =1.5 to 4 successively. The 540 water head of the FC25 group only increased to the height of R i =3.5 541 because of the excessive large amount of fine particles, so when it 542 was raised to the first five heights of R i , the fine particles were 543 blocked in the pores. There was no obvious phenomenon, and then when 544 raised to the height of R i =4, the excessive high peak water head height 545 caused the flow velocity to be too large and washed away the fine 546 particles, resulting in extremely poor overall experimental results. 547 Similar to steady flows (section 3.2), it can also be determined that 548 the sample experienced piping erosion failure when the flow velocity 549 was in the increasing state. Compared with the piping erosion test under steady flows, we found that the value of R i of the occurrence of 551 piping erosion failure of each group of samples under the action of 552 flood peak unsteady flow was smaller than that under the action of 553 steady flow, which was the same as Chen Liang's article (Chen et al. 554 2013). 555 Second, in terms of the three cycles under each water head height 556 corresponding to R i , when the flow velocity went through a decreasing 557 state, the initial peak flow velocity of the second head cycle was 558 larger than the final peak flow velocity of the first head cycle, and 559 the initial peak flow velocity of the third head cycle was larger than 560 From the analysis of Figure 16, we can find that the change rate 585 of the peak initial flow rate and the peak end flow rate at the same 586 cycle of the same level of SCHG is not very large, so we averaged the 587 flow velocity and the hydraulic gradient under each cycle of each R i 588 to further analyze the relationship between the flow velocity and R i . 589 It can be seen from Fig. 17(a) that K L1 ＞K L2 ＞K L3 (L represents the 590 trend line that flow velocity varies with Ri) and that the greater the 591 initial content of fine particles is, the smaller the amplitude of 592 increase in flow velocity with increasing R i . From Fig. 17(b), we can 593 see that K L4 ＞K L5 ＞K L6 and it can be determined that the larger the initial 594 relative density is, the smaller the amplitude of increase in the flow 595 velocity with the increase in R i . were nearly equal. This experimental phenomenon was due to the upstream