Pore-Water Pressures Associated with Clogging of Soil Pipes: Numerical Analysis of Laboratory Experiments

Soil Physics Pore-Water Pressures Associated with Clogging of Soil Pipes: Numerical Analysis of Laboratory Experiments

Clogging of soil pipes due to excessive internal erosion has been hypothesized G. V. Wilson* to cause extreme erosion events such as landslides, debris flows, and gullies, USDA-ARS but confirmation of this phenomenon has been lacking. Laboratory and National Sedimentation Lab. field measurements have failed to measure pore-water pressures within Watershed Physical Processes Research Unit pipes and models of pipe flow have not addressed internal erosion or pipe Oxford, MS 38655 clogging. The objective of this study was to model laboratory experiments of pipe flow in which clogging was observed in order to understand the G. A. Fox clogging process. Richards’ equation was used to model pipe flow, with the Biosystems and Agricultural Engineering soil pipe represented as a highly conductive, low-retention porous medium. Oklahoma State Univ. The modeling used two contrasting boundary conditions, constant flux (CF) Stillwater, OK 74078 and constant head (CH), to quantify pressure buildups due to pipe clogging and differences in simulated pressures between the two imposed boundary conditions. Unique to these simulations was inclusion of pipe enlargement with time due to internal erosion, representation of partially full flow conditions, and inclusion of pipe clogging. Both CF and CH boundary conditions confirmed the concept of pressure buildup as a result of pipe clogging. Pressure jumps of around 54 m for CF and 18 cm for CH occurred in <0.1 s, while soil water pressures 4 cm radially outward from the pipe had not responded. These findings demonstrate the need to measure pressures within soil pipes due to hydraulic nonequilibrium between the pipe and soil matrix. Pore water pressures within the pipe below the clog rapidly (<0.25 s) drained to unsaturated conditions, indicating the ability of soil pipes to drain hillslopes and rapidly recover when clogs are flushed from the soil pipe.T hese dynamic processes need to be incorporated into stability models to properly model hillslope processes.

Abbreviations: CF, constant flux; CH, constant head.

t has been hypothesized that landslides and debris flows result from sudden pressure buildup within soil pipes when a pipe clogs due to internal erosion (Tsukamoto et al., 1982; Pierson, 1983; Brand et al., 1986; McDonnell, 1990; IUchida et al., 2001; Uchida, 2004; Kosugi et al., 2004), but measurement of this phenomenon is limited. Sidle (1984) observed rapid pore-water pressure buildups on hillslopes during storms in Alaska, which he reasoned to be due to flow into soil pipes containing “small breaks or discontinuities.” These rapid positive pressures produced factors of safety that suggested that these hillslope locations were unstable. The association between pipe flow and slope instability is often derived from observations of soil pipes at the head of active landslide scars (Uchida et al., 2001; Ziemer, 1992). The difficulty in identifying such subsurface features in- ad vance and installing tensiometers or piezometers directly within the soil pipe at the correct location before an event has precluded direct measurements from confirm- ing this hypothesis.

Soil Sci. Soc. Am. J. 77:1168–1181 doi:10.2136/sssaj2012.0416 Received 11 Dec. 2012. *Corresponding author ([email protected]). © Soil Science Society of America, 5585 Guilford Rd., Madison WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Soil Science Society of America Journal Laboratory studies (Sidle et al., 1995; Kosugi et al., 2004) et al., 2006; Akay et al., 2008; Nieber and Sidle, 2010; Sharma using artificial soil pipes in sand beds have provided insights et al., 2010; Lu and Wilson, 2012) is to treat the soil pipe as a Soil Physics into pipe-flow processes and corroborated the possibility of highly conductive porous medium and model the flow domain pore-water pressure buildups by pipe discontinuities or pipe using Richards’ equation: clogging. Sidle et al. (1995) simulated restrictions in pipe flow ∂∂q  ∂ ∂ ∂ ∂  ∂ ∂ =+++h h hKzz by having five sections of an artificial (polyvinyl chloride) pipe KKKxx yy zz  [1] ∂∂tx ∂ x ∂ y ∂ y ∂ z  ∂ z ∂ z with different degrees of internal roughness. The artificial pipe q spanned the length of a sand bed but with the upper end closed. where is the water content; h is the soil water pressure; Kxx(h), They observed <10 cm difference in piezometric head in the soil Kyy(h), and Kzz(h) are the unsaturated hydraulic conductivity outside the artificial pipe between the greatest roughness section functions in the principal directions x, y, and z; and t is time. and the least rough section. Kosugi et al. (2004) used open- and These studies differ in the number and geometry of the soil pipes closed-ended artificial (acrylic) pipes (with the upper end always (from a single continuous pipe to multiple disconnected pipes), closed) positioned at the middle and lower sections of a sand the properties of the soil pipe porous medium (assumed value bed to simulate pipe discontinuities or clogging. They observed or calibrated value for saturated hydraulic conductivity), and the subtle (<4 cm) pressure differences in soil adjacent to the closed- boundary conditions applied to the soil pipe region (constant ended pipes compared with the open-ended pipes. head or constant flux). As pointed out by Wilson et al. (2013) Laboratory studies by Wilson (2009, 2011) used actual soil in their review of numerical approaches for modeling pipe flow, pipes in a soil bed that allowed internal erosion of the pipe. These the geometry of the soil pipe region in these studies was “fixed”, studies showed the propensity for pipe clogging as indicated by whereas in reality and in the experiments of Wilson (2009, surges in pipe flow and spikes in sediment concentrations. In 2011), the soil pipe enlarges with time due to internal erosion. addition to the highly dynamic nature of naturally occurring pipe While these numerical studies enhanced our understanding of clogging, extreme hydraulic nonequilibrium, which McDonnell pipe-flow processes, none included the changing geometry of (1990) called disequilibrium, between the pipe and the adjacent the pipe by internal erosion, the effects of pipe clogging on pore- soil was hypothesized to have resulted in essentially no buildups water pressure buildup within the pipe, or the dynamic nature of the observed in pore-water pressures in the soil matrix adjacent to hydraulic nonequilibrium between the pipe and the soil matrix. the soil pipes. All these studies failed to measure pore-water One of the primary issues in modeling pipe flow, and thus pressures directly inside the soil pipes. pipe clogging, is what boundary condition to use to represent In their review on pipe flow, Wilson et al. (2013) noted flow into and along a soil pipe. Wilson (2009) used a steady the need for “…measuring soil water pressures within soil pipes inflow rate into the soil pipe. Such conditions simulated either during pipe flow as opposed to the adjacent soil.” Midgley et al. a soil pipe fed by macropore(s) open at the surface such that (2013) was the first to measure pore-water pressure increases they direct surface runoff into the pipe at a constant rate during associated with pipe clogging within a soil pipe. They created runoff periods or a soil pipe fed by convergence from a network soil pipes in a streambank face at Cow Creek in Stillwater, of macro- and mesopores during periods of perched water. For OK, that were hydraulically connected to a constant-head these conditions, the flow rate would be expected to remain trench. They artificially clogged the exit end of the soil pipe and stable while the soil pipe enlarges by internal erosion. In contrast, installed tensiometers into the clogged section and into the soil Wilson (2011) used a constant head on the soil pipe such that adjacent to the clog. They established a constant head on the the flow rate increased as the pipe enlarged to simulate the pipe and observed pore-water pressure buildups within the clog conditions of a soil pipe through an earthen embankment into material of the pipe before the clog was flushed out and the pipe a water reservoir. reopened. The pore-water pressure was initially around −85 cm The objectives of this study were to model the pipe-flow and increased to almost 20 cm within 3 min, at which point the experiments conducted by Wilson (2009, 2011) (i) to gain clog was flushed from the pipe. While this study showed a proof insights into the pressure buildup process under conditions of principle, it was limited in scope in that it only measured of internal erosion in which the soil pipe enlarged with time pressures within the clog and not in the open pipe above the clog and periodically clogged, and (ii) to evaluate the impacts of and did not include naturally occurring clogs. the boundary conditions used on the effects of pipe clogging- Uchida (2004) noted that most hillslope stability models pressure buildups. ignore the effects of pipe flow on pore-water pressure and therefore cannot predict landslide occurrence. Uchida (2004) MATERIALS AND METHODS proposed that real-time landslide warning systems must consider Experiments Selected for Modeling the processes driving pore-water pressure buildups. Many The experiments conducted by Wilson (2009, 2011) were studies have reported on modeling of macropore flow (see Jarvis selected because of the different boundary conditions imposed [2007] or Gerke [2006] for reviews), and numerous studies have on soil pipes. Both studies involved a single, continuous, open- modeled pipe flow. The most common approach for modeling ended soil pipe through a soil bed at a 15% slope (Fig. 1). The pipe flow (Nieber and Warner, 1991; Kosugi et al., 2004; Nieber experiments conducted by Wilson (2009) involved a 10-mm-

www.soils.org/publications/sssaj 1169 diameter soil pipe immediately above a 5-cm-deep water- condition); however, the outflow rate was erratic but generally restricting layer (silty clay loam compacted to 1.57 Mg m−3) with increased with time due to decreasing transfer of water into the a steady-state inflow rate applied to the soil pipe. The experiments soil matrix as the soil around the pipe wet up (Fig. 2A). The conducted by Wilson (2011) involved a single-layered, 20-cm- erratic outflow despite a steady inflow was consistent with the deep soil bed with a constant head (15- and 30-cm tests) applied observations by Zhu (1997) of tunnel discharges due to frequent to the upper end of the soil pipe with a variety of soil pipe blocking by tunnel collapse and reopening. Tensiometers sizes tested (a 10-mm-diameter soil pipe test was selected for adjacent to the soil pipe (6 cm to side) at the bed center (75 cm modeling). For both studies, the soil pipe was created by packing upslope) indicated a rapid increase in pore-water pressures from the same silt loam loess soil to a bulk density of 1.3 Mg m−3 an initial value of around −75 cm to values near saturation (more around a rod and then removing the rod. The Wilson (2009) than −2 cm) (Fig. 2B). The tensiometer at this midslope position experiments involved a 15-cm soil bed (5 cm of compacted silty just 4 cm directly above the pipe responded next, with a rapid clay loam and 10 cm of silt loam), whereas the Wilson (2011) test increase to near saturation. The tensiometer 8 cm above the pipe involved a 20-cm-deep, silt loam soil bed. Both studies had banks appeared to malfunction, but the tensiometer at this depth at the of tensiometers located at 25, 75, and 125 cm upslope from the 125-cm upslope position indicated a rapid increase to approximately lower end of the bed, but their positions relative to the soil pipe −10 cm (Fig. 2B). None of the tensiometers indicated a pore- differed as indicated in cutouts in Fig. 1. For the Wilson (2009) water pressure buildup, which was reasoned to be due to the fact study, each bank location had two tensiometers positioned at that they were not positioned inside the soil pipe (Wilson, 2009; the same depth as the soil pipe but 6 cm to each side, along with Wilson et al., 2013). tensiometers 4 and 8 cm directly above the soil pipe. For the Sediment concentrations clearly indicated periods of Wilson (2011) study, two tensiometers were positioned 3 cm to high sediment flushing due to sudden internal mass failures of each side of the pipe but 4 cm higher than the pipe, along with the pipe wall, which is believed to have resulted in temporary tensiometers 8 and 12 cm directly above the pipe. pipe clogging (Fig. 2A). These sediment concentrations are not truly representative of the dynamic spiking in sediment because Constant-Flux Test samples were collected continuously at 3-min intervals. Surges in Wilson (2009) used two flow rates, 190 and 284 L h−1, measured to be equivalent to maintaining a constant head of 15 and 30 cm, respectively, on a 10-mm-diameter soil pipe. One of the two tests at the steady inflow rate of 284 L −1h without simulated rainfall was selected for modeling because of the propensity for surging in sediment concentrations (Fig. 2). The test was run at a steady inflow rate (constant-flux boundary

Fig. 2. Results for the constant flux experiment conducted byW ilson Fig. 1. (A) The experimental setup used by Wilson (2009) involved a (2009): (A) the pipe outflow rate (Ro) and the sediment concentration continuous soil pipe positioned immediately above a restrictive layer, with time for the first 120 min of the test; (B) the pore-water pressures with flow into the soil pipe controlled by a pump; (B) the experimental determined by tensiometer at 8 cm (solid dot) and 4 cm (open square) setup used by Wilson (2011) involved a continuous soil pipe in a single- directly above the pipe at the middle (75-cm) slope position and at 6 cm layered soil bed with a constant head on the upper end. to the side of the pipe (open triangle) at the 125-cm upslope position.

1170 Soil Science Society of America Journal flow were also integrated across this sampling interval, thereby within the pipe. Given these conditions, the flow rate rapidly precluding the real shifts in pipe outflow rates from being increased and exceeded the flow rate specified for the constant- depicted in Fig. 2A. Therefore, the video of the test was reviewed flux experiments (284 L −1h ) (Fig. 3A). and instances of surges in sediment export or flow interruption The sampling routine was changed to sampling for 15 s once were recorded (Table 1), along with comments made by those every minute in an attempt to capture more of the dynamics in conducting the test. The flushing of sediment occurred for flow and sediment concentrations. It does appear in Fig. 3A that periods of seconds but was diluted by the remaining sample the flow rate was more dynamic under a constant head with this period. In addition, surges in flow in response to pipe clogging sampling protocol than the previous method of Wilson (2009). were not readily apparent by the 3-min sampling period. As a It is clear from the video observations (Table 2), however, that the result, the high sediment pulses noted at times 2439, 3176, and true dynamics were not captured. In contrast to the constant-flux 3183 s appear as minor increases in Fig. 2A. experiments in which flow was interrupted by clogging but rarely It is interesting to note that while tunnel collapse was not fully stopped, complete stoppage of flow under the constant head observed, several comments were made by those conducting the was common. These stoppages in flow were generally too short to test that indicated a distinct wetting up of the soil surface between be observed by the 15-s sample interval once every minute. tensiometer banks at 125 and 75 cm upslope as early as 47 min In addition to the higher flow rates, the sediment into the experiment. By 3720 s, the expectation was that collapse concentrations were generally an order of magnitude higher for of this area was imminent. Wilson (2009) noted that the constant- the constant-head (CH) than for the constant-flux (CF) test. flux boundary condition on the pipe prevented the flow rate from This is probably due to both the higher flow rates and greater increasing as the pipe enlarged by internal erosion, as would occur area of contact with the pipe walls due to the ability to maintain for a constant-head boundary condition. As a result, the soil pipe a full-flow condition. As a result, tunnel collapse was observed at was only partially full shortly after flow initiation. Instead, the 414 s and again at 502 s (Table 2), and the experiment had to be pipe tended to erode more readily in the lateral direction along terminated at 750 s because the head could not be maintained. the water-restricting layer, and flow tended to spread out laterally While the CF boundary condition created evidence of wetting without being in continuous contact with the pipe roof. This of the surface, a depression in the surface, and tension cracks probably contributed to tunnel collapse not occurring. forming, tunnel collapse did not occur. For the CH test, however, this same area between the upper and middle tensiometer banks collapsed. Constant-Head Test The rapid wetting of the soil above the pipe can be seen in One of the two 15-cm constant-head tests of Wilson (2011) Fig. 3B, as can the effect of the collapse. The tensiometers 4 cm above was selected for modeling. A constant-head boundary condition and 3 cm to the side of pipe were the first to respond, followed on the soil pipe allowed the flow rate to increase as the soil pipe by the tensiometer 8 cm directly above the pipe. The former enlarged by internal erosion and allowed the pipe to maintain tensiometers approached saturation (−8 cm) just before collapse. a full-flow condition assuming that there were no restrictions Tensiometers at both of the positions closest to the pipe at this Table 1. Flow interruption dynamics as indicated by sediment concentration and pipe-flow surges during a test conducted by Wilson (2009) using constant flux into a 10-mm-diameter soil pipe. Time of occurrence Duration Comments ————— s ————— 2439 1 large sediment pulse but no flow interruption 3176 1 large sediment pulse but no flow interruption flow stopped briefly, then surge in flow and sediment concentration, which continued for 3183 1 additional 7 s until clear steady flow 4330 1 big sediment pulse but no flow interruption 4335 1 slight flow interruption and sediment pulse 4338 1 brief flow stoppage and sediment pulse 4342 1 slight flow interruption and sediment pulse continued for additional 16 s until clear steady flow 4710 1 no flow interruption but small sediment pulse 4820 1 no flow interruption but small sediment pulse 5157 1 no flow interruption but small sediment pulse 5172 1 no flow interruption but small sediment pulse 5186 2 flow stopped, then big surge in flow and sediment concentration 5190 16 series of surges in flow and sediment pulses 6360 2 sediment pulse, then slight flow interruption 6390 2 big sediment pulse with flow interruption 6405 3 flow interruption with sediment pulse 6768 24 series of flow interruptions and sediment pulses 6798 4 huge sediment pulse with flow stoppage 6927 1 small sediment pulse

www.soils.org/publications/sssaj 1171 midslope location exhibited decreases in pore-water pressure following the initial collapse (414–430 s) (Fig. 3B). The initial collapse appeared to occur upslope of the midslope tensiometer bank. It is likely that the tensiometer cups lost contact with the soil and were suspended in the air-filled portion of the pipe and thus tensiometer values decreased. The tensiometer near the surface (12 cm directly above the pipe) did not show this decrease in pore-water pressures after the initial collapse but exhibited increased pressures to near saturation (−8 cm). This supports the assumption of loss of contact for the deeper tensiometers because the pipe had not expanded to this upper depth at that time. The second collapse (502–520 s) resulted in these tensiometers falling into the pipe with the collapse material. Pore water pressures continued to decrease until the time of the final collapse (630–661 s), at which time pressures rapidly increased. Clogging of the pipe downslope of the midslope tensiometers probably facilitated reestablishment of contact between the tensiometer cups and the collapsed material and the rapid pressure buildup.

Modeling Pipe Flow These studies led to questions about the processes associated with pipe clogging such as the following: what pore-water pressures would occur within the pipe, what effect would different boundary conditions have on pipe flow and adjacent Fig. 3. Results for the constant-head experiment conducted by Wilson soil water pressures, and what would be the effect of the pipe (2011): (A) the pipe outflow rate (Ro) and the sediment concentration with time; (B) the pore-water pressures determined by tensiometer at being only partially filled on the soil water distribution pattern? 12 cm (solid dot) and 8 cm (open square) directly above the pipe at To address these questions, HYDRUS 2.01 was used to solve the middle (75-cm) slope position and at 4 cm above and 3 cm to the Richards’ equation to simulate flow through the soil pipe and side of the pipe (open triangle) at the 125-cm upslope position. through the porous medium. Consistent with previous work on modeling pipe flow with Richards’ equation, a two-dimensional air-filled barrier for partially filled flow conditions, and (iii) the flow domain was used to simulate the plane along the pipe’s inclusion of pipe clogging. centerline. Unique to these simulations from past studies was (i) For the CF simulations, a 150-cm-long by 15-cm-high soil pipe enlargement with time, (ii) representing the pipe roof as an profile at a 15% slope (Fig. 4A) flow domain was discretized with 0.5-cm vertical and 1.0-cm horizontal node spacing. The lower

Table 2. Flow interruption dynamics as indicated by sediment concentration and pipe-flow surges during a test conducted by Wilson (2011) using a constant head on the upper bed face with a 10-mm-diameter soil pipe. Time of occurrence Duration Comments min s 277 1 flow interrupted briefly 297 1 flow stopped completely for 1 s, with big aggregate flushed out afterward 320 2 flow stopped completely for 1 s followed by sediment pulse 333 3 flow stopped completely for 1 s followed by sediment pulse 350 1 flow stopped completely for 1 s followed by sediment pulse 372 3 flow stopped completely for 1 s followed by sediment pulse 387 1 flow stopped completely for 1 s followed by sediment pulse 395 5 flow stopped completely for 5 s followed by sediment pulse flow stopped completely for 1 s followed by series of surges in flow until small tunnel collapse at 6.97, when 414 16 flow stopped completely for 12 s 483 3 flow stopped completely for 3 s 502 8 big tunnel collapse, with flow stopped completely for 8 s 517 1 flow stopped completely for 1 s followed by sediment pulse 568 1 flow stopped completely for 1 s followed by sediment pulse 614 2 flow stopped completely for 1 s followed by sediment pulse 630 31 complete stoppage of flow for 31 s 675 4 series of 1-s stoppages in flow

1172 Soil Science Society of America Journal 50-mm-deep silt loam bottom layer. The 20-mm initial pipe region, as opposed to a 10-mm pipe, was used to adjust for the rapid growth of the soil pipe. The van Genuchten–Mualem (van Genuchten, 1980) expression was used to represent the hydraulic properties (Table 3), which is the most common approach for modeling pipe flow using Richards’ equation. Some researchers have modeled pipe flow by simply assuming a very high value for the saturated hydraulic conductivity, Ks (Nieber et al., 2006; Nieber and Sidle, 2010; Sharma et al., 2010). Others (Kosugi et al., 2004; Lu and Wilson, 2012; Akay et al., 2008) Fig. 4. Discretization scheme, material properties, boundary conditions, and observation points (red calibrated the Ks to the pipe-flow dots) for (A) constant-flux simulations and (B) constant-head simulations.T he silt loam material is yellow, observations. Nieber and Warner pipe area in blue, and compacted silty clay loam in brown. (1991) assumed a Ks value for the bed face boundary was prescribed as a potential “seepage face” soil matrix and related the Ks for condition and the opening of the soil pipe at the upper bed the soil pipe to the grid cell dimensions and the radius of the face as a “constant-flux” boundary condition. All other external soil pipe. In this study, the water retention (residual soil water boundaries had a zero-flux condition. The material distribution content qr, saturated soil water content qs, and water retention initially involved three layers: (i) 90-mm-deep silt loam topsoil; parameters a and n) and Ks properties of the silt loam and silty (ii) a 10-mm-diameter pipe; and (iii) 50-mm-deep compacted clay loam materials were determined on soil cores obtained silty clay loam bottom layer. As explained below, the roof of the from the soil beds. Water retention properties for the pipe were pipe region was changed to represent an air-filled (restrictive) assumed values to simulate a low-water-retention soil, that is, layer, i.e., a fourth material, as the soil pipe enlarged with time low air-entry value (high a) and sharp slope (high n). TheK s by internal erosion. for the soil pipe material was obtained by calibrating the value The two-dimensional flow domain for the CH inflow to the observed time of arrival of flow at the outlet on starting simulations was a 150-cm-long by 20-cm-high soil profile at a the experiment. Properties for the air layer were default water 15% slope (Fig. 4B). The domain was discretized with 1.0-cm retention properties for sand but with Ks decreased several vertical and 1.0-cm horizontal node spacing. The boundary orders of magnitude to act as an air-filled barrier (i.e., not a full- conditions included a seepage face on the lower bed face and a pipe condition). constant head along the bottom 15 cm of the upslope bed face. Simulations were performed in sequential and integrated All other external boundaries had a zero-flux condition. The intervals to capture changes in the pipe dimensions and pipe material distribution initially involved three layers: (i) 130-mm- properties (Table 4). The video logs of pipe dynamics were used deep silt loam layer; (2) a 20-mm-diameter pipe; and (iii) to create a series of simulation runs in which the pipe enlarged

Table 3. Properties of the layers used in the flow simulations, where θr is the residual water content, θs is the saturated water content, α and n are the van Genuchten (1980) water retention parameters, and Ks is the saturated hydraulic conductivity.

Material Name qr qs a n Ks cm−1 cm s−1 Constant flux simulations 1 silt loam 0.0 0.508 0.0378 1.1935 8.49 ´ 10−4 2 pipe 0.0 0.5 0.5 4.0 5.0´ 102 3 silty clay loam 0.089 0.43 0.1 1.23 1.0 ´ 10−7 4 air 0.045 0.43 0.145 2.68 1.0 ´ 10−7 Constant head simulations 1 silt loam 0.0 0.508 0.0378 1.1935 8.49 ´ 10−4 2 pipe 0.0 0.5 0.5 4.0 5.0´ 102 3 silt loam 0.0 0.508 0.0378 1.1935 8.49 ´ 10−4 www.soils.org/publications/sssaj 1173 with time and/or changed from open to clogged Table 4. Simulation characteristics: pipe sizes correspond to the soil pipe dimensions used in the simulations based on estimates from the experiments conditions. For each subsequent interval, the for the corresponding time interval. previous run’s final pore-water pressure distribution Simulation number Time duration Pipe condition Pipe size was imported as the next run’s initial condition, s mm thereby integrating the simulations. Note that not Constant flux simulations all flow interruptions or stoppages listed in Tables Run 1 324 open 10 1 and 2 were included in the simulations (Table 4) Run 2 2115 open 15 but only enough to represent the dynamics of the Run 3 1 clogged 20 processes. For pipe clogging, it was assumed that the Run 4 736 open 25 pipe would be clogged with silt loam material from Run 5 1 clogged 25 above using the same silt loam material properties Run 6 6 open 25 (i.e., collapse of large aggregates). In each simulation Run 7 1 clogged 25 with clogging, a single 30-mm section of the pipe Run 8 522 open 30 area, centered at the bed middle (75 cm upslope), Constant head simulations Run 1 200 open 20 had the material properties changed from “pipe” to Run 2 77 open 40 “silt loam” to simulate a clogged pipe. In addition, to Run 3 1 clogged 50 simulate the effect of pipe enlargement with time due Run 4 19 open 50 to internal erosion, the area represented as “silt loam” Run 5 1 clogged 50 material was changed according to experimental Run 6 22 open 50 measurements of soil loss to represent new pipe Run 7 2 clogged 50 dimensions. Changes in the pipe radii (R) with time Run 8 11 open 60 in the simulations (Table 4) were obtained from the Run 9 3 clogged 60 experiments knowing the sediment transport rate, Run 10 4 open 60 Run 11 1 clogged 60 qs, and the bulk density, ρd: Run 12 7 open 60 dR q = s [2] Run 13 1 clogged 60 dt rd Run 14 1 open 60 Run 15 1 clogged 60 which assumed uniform soil loss along the entire Run 16 21 open 70 pipe length. For the CF flow simulation, the silt Run 17 3 clogged 70 loam material along the pipe roof was changed to Run 18 12 open 70 the “air” material properties to simulate partially full Run 19 1 clogged 70 pipe flow, whereas, it was changed to “pipe” material Run 20 7 open 70 properties for the CH simulations to simulate Run 21 5 clogged 70 potentially full-flow conditions. Run 22 15 open 70 Run 23 16 clogged 70 RESULTS AND DISCUSSION Run 24 71 open 90 Constant-Flux Flow Simulations Run 25 8 clogged 90 For the CF experiments, flow was rarely stopped (Table 1) but instead showed brief (<1 s) interruptions. To simulate its entire length and a pressure bulb rapidly expanded above the these conditions, a constant-flux boundary condition was imposed clog (Fig. 5). This pressure bulb due to pipe clogging corroborates on a static pipe inlet position (i.e., the inlet did not enlarge as the the concept of “upthrust pressures or buoyancy effects” noted by soil pipe enlarged). Mass transfer of water occurred from the soil McDonnell (1990). pipe into the soil bed along the soil pipe such that at the time of the The pore-water pressures almost instantaneously reached a first clog (2439 s), pore-water pressures had increased (from −71 maximum value (Fig. 6A) and the pressure bulb reached to within to −50 cm) at the soil surface (Fig. 5). The depth of penetration 1 cm of the surface at the end of the first 1-s-duration clog (Fig. below the soil pipe was limited to approximately 2 cm by the 6D). The near-instantaneous jump in pore-water pressure within water-restricting layer. At this time, the soil pipe had enlarged the soil pipe extended the entire upslope length of the pipe, as from an initial diameter of 10 mm to 20 mm, and according to evident in Fig. 6B and 6C. Pressures within the pipe downslope videos of the experiment, the pipe was flowing only partially full. of the clog (Fig. 6C) indicated unsaturated conditions, however, This effect was simulated by expanding the pipe upward with a as would be expected due to the soil pipe acting as a drain. In the less conductive layer along the pipe roof to simulate a partially laboratory experiment, tensiometers above the soil pipe indicated filled void. When a clog was imposed along a 3-cm section of the that the wetting front had reached their depths at this time, but soil pipe at the bed center (nodes at 74–76 cm) for 1-s duration, the values were not near the pressures predicted. Comments by pore-water pressures within the pipe suddenly increased along the researchers during the laboratory test at 2830 s indicated that

1174 Soil Science Society of America Journal the soil surface between tensiometer banks 125 cm upslope and 75 cm upslope was “wet”, with the wetness ending just downslope of the 75-cm bank, and the surface in this wetted area had a “tension crack.” Thus, while the predicted pressures may be off, the pattern is consistent with visual observations. While pore-water pressures in the experiment were recorded for a 1-min period, and thus would miss these short- duration spikes in pressures (Wilson, 2009), the simulated pore-water pressures reached almost 54 m. Such pressures far exceed the 4-m increase in head observed by Brand et al. (1986) during a 6-h period for blocked soil pipes in Hong Kong. While the predicted values appear excessive, the pattern agrees closely with the experimental observations. Furthermore, the simulated pressures mimic those predicted for instantaneous closure in a water hammer analysis (Finnemore and Franzini, 2002). The pressure buildup (Dp) due to a water hammer effect is a function of the fluid density (ρ), the change in velocity (DV), and the celerity of the pressure wave (c, which ranges between 600 and 1200 m s−1 for an elastic fluid inside an elastic pipe):

Dp= rD cV [3] Fig. 5. Pore water pressures for constant-flux simulations before (time 2439.00 s) and during the first pipe clogging event (1 s).

Fig. 6. Results for constant-flux simulations: pore-water pressures at observation nodes (A) within the soil pipe and (B) in the soil above the soil pipe in response to the first clog, (C) pore-water pressures along the soil pipe before 2439 s and during (2439.25 s and 2440 s) pipe clogging, and (D) the depth distribution of pore-water pressures at the soil bed’s center (75 cm) before (2439 s) and 1 s into pipe clogging. www.soils.org/publications/sssaj 1175 For DV = 0.5 m s−1 and ρ = 1000 kg m−3, Dp ranges between 300 and 600 kPa, equivalent to 30.6 to 61.2 m of pressure head. We hypothesized that the discrepancy between the observed and predicted pressures was due to the boundary condition and assumptions about the pipe material and the clog duration. The flow rate imposed on the soil pipe was obtained for an open channel while the simulation represents the soil pipe as a porous medium, thus the back-pressure on the pipe clog far exceeds the 30-cm head equivalent to the imposed flow rate on an open channel. In addition, the simulation imposed a clog for 1 s, while observations did not note a complete stoppage in flow but an interruption with a surge in sediment during a 1-s interval. The clog would certainly be flushed from the pore before such high pressures were observed. Thus, a clog would remain for considerably less time than the 1 s imposed in the simulation. Inspection of the predicted pore-water pressures indicated that the jump in pressures occurred at only 0.06 s after the clogging began. Thus, shortly after this time, the clog would be flushed from the soil pipe. When simulations were repeated using a 0.1-s clog duration, however, maximum pore-water pressures of 5300 Fig. 7. Pore water pressures for constant-flux simulations before (time cm were predicted, which again seem unreasonable. In 3176.00 s) and during the second pipe clogging event (1 s). addition, when using a 0.1-s-duration clog, the wetted bulb The pressure bulb created by the clog at 2439 s had almost failed to reach the surface, only extending above the pipe clog completely dissipated by the time of the second clog at 3176 s to within 4.5 cm of the surface, and therefore not matching (Fig. 7); however, the residual effect appeared to be sufficient the observed wetted-surface pattern. Thus, the discrepancy is to allow this second 1-s-duration clog to create a pressure bulb probably the boundary condition on the soil pipe as a constant that reached the soil surface. The pressure bulb created by the flow rate while representing the pipe as a porous medium as second clog only had 6 s to dissipate before the third clog at opposed to an open channel. 3183 s, as seen in Fig. 8. Thus, the third clog created a pressure Simulations were also repeated with the pipe region above bulb that instantly reached the surface and expanded across the clog being represented as “pipe” material (Table 3), instead of having the roof represented by “air” material, to allow full-pipe flow conditions above the clog during clog periods. The result was enhanced water transfer from the pipe into the upper soil along the pipe above the clog. The maximum pressures predicted within the pipe were lower (29 m) and did not exhibit the water-hammer effect of an almost instantaneous jump to the maximum but instead exhibited a sharp increase after around 0.4 , 0.2 , and 0.15 s for the first three clogs, respectively, and a continued increase until the end of the 1-s clog period. The simulations with full-pipe flow above the clog predicted that the surface would be saturated along the entire upper portion of the soil bed during the second and third clogs, which does not match experimental observations of a saturated bulb only in the bed’s middle area. These discrepancies again suggest that the clog would be flushed out so quickly following pressure buildup that such full-pipe flow conditions would not be observed and the simulations with an “air” layer along the pipe roof better match the observations. This research corroborates the theory of pressure buildups leading to mass failure and demonstrates the need to consider appropriate boundary conditions in field and laboratory experiments and numerical modeling. Fig. 8. Pore water pressures for constant-flux simulations before (time 3183.00 s) and during the third pipe clogging event (1 s).

1176 Soil Science Society of America Journal the soil bed surface in an elliptical pattern (linear in the two- how rapid the pressure buildups dissipated. The pressure buildup dimensional simulation). within the soil and the pressure bulb formed by “upthrust The pore-water pressure buildups within the pipe for the pressures” disappeared almost instantaneously after clog removal second and third clogs (Fig. 9A and 9D) were identical to the and the pipe returned to only partially filled pipe flow. response for the first clog. The response at observation nodes in the soil above the clog (Fig. 9B) were more rapid, however, Constant-Head Flow Simulations particularly for the third clog due to the wetter antecedent Unlike the CF experiment, which exhibited very short (<1-s) conditions. The antecedent moisture effect is clear in the water duration interruptions in flow, the CH experiment exhibited pressure profiles (Fig. 9D) at 0.25 s into the second (3176.25 s) many periods of complete stoppage of flow, with several lasting and third (3183.25 s) clog events. The pressure bulb almost longer than 1 s (Table 2). Flow simulations were performed for instantly reached the surface for the third clog event. After each all interruptions and stoppages listed in Table 2 during the first clog was flushed out, i.e., removed, however, the pore-water 510 s of the experiment for a total of 25 sequentially integrated pressures within the soil pipe (Fig. 9C) and in the soil above the runs (Table 4). These simulations included stoppage durations of clog (Fig. 9D) returned just as quickly to pre-event pressures 1, 2, 3, 5, 8, and 16 s. The simulations were repeated using only (near 0 cm). At 3546 s of the experiment, it was recorded that the the three longest (5-, 8-, and 16-s) periods of flow stoppages (eight surface appeared to be “about to collapse,” with “tension cracks integrated runs) to test if these could capture the main effects. on both sides” of an area that matched the predicted wetted bulb The first clog event occurred after the soil pipe had expanded area. Collapse was not observed, however, and the experiment to 40-mm diameter. Despite this enlargement by internal continued. Tunnel collapse was probably not observed because of erosion, flow was maintained in a full-pipe flow condition due

Fig. 9. Results for constant-flux simulations: pore-water pressures at observation nodes (A) within the soil pipe and (B) above the soil pipe in response to the second and third clog, (C) pore-water pressures along the soil pipe before (3176 and 3183 s) and during (3176.25 and 3183.25 s) pipe clogging, and (D) the depth distribution of pore-water pressures at the soil bed’s center (75 cm) before (3176 and 3183 s) and 0.25 s into each pipe clogging period. www.soils.org/publications/sssaj 1177 to a constant head on the soil pipe. In addition, the soil bed the increases observed within a pipe clog by Midgley et al. (2013) lacked a water-restrictive layer below the pipe; thus, there was no for a CH field test. restriction on the mass transfer of water between the pipe and Within 1 s following removal of the clog, the pore-water the soil matrix along the entire length of the pipe. Before the first pressures returned to essentially the pre-clog conditions. The clogging (277 s), there was a monotonic decrease in pore-water dynamic nature of the pressure buildup and drainage are clearly pressure along the soil pipe length from the constant-head inlet seen in Fig. 11. Buildup and drainage appeared to reach stable to the seepage face outlet (Fig. 10A). The wetting front rising pore-water pressures within around 0.1 and 0.25 s of clog above the clog location was within 8 cm of the surface, while formation and removal, respectively. It is worth noting that at below the clog the soil was under positive pressures to the bottom the time of the predicted pressure buildup within the pipe to of the soil bed (Fig. 10B). The presence of a pipe clog in the bed positive values (25-cm pressure upslope of the clog), soil water center caused a dramatic hydraulic gradient at the clog interface pressures just 4 cm vertically above the clog had not responded (Fig. 10A). There was a clear pore-water pressure buildup above and indicated unsaturated conditions (−1 cm). Thus, the the clog, and drainage of the pipe resulted in negative pore- hydraulic nonequilibrium suggested by McDonnell (1990) water pressures below the clog during this 1-s clog event. The and Wilson (2009, 2011) between measurements made within pressure buildup was not as radical as under the CF boundary a soil pipe vs. in the soil adjacent to a pipe was confirmed. The condition, with an increase above the clog of 18 cm (7–25 cm) in negative soil water pressures just 4 cm above the pipe remained <1 s. The predicted pore-water pressures increased by 8 cm to 15 until 0.17 s, and values at tensiometers 8 cm away from the pipe cm of pressure within the clog center. The predicted pore-water never responded to this pipe clog event. Past studies of hillslope pressure buildup for the CH boundary condition corroborates hydrology using even extensive networks of tensiometers (e.g., Anderson and Kneale, 1980) may miss the critical soil water

Fig. 10. Results for constant-head simulations: (A) pore-water pressures along the soil pipe at 277, 278 , and 279 s of the first clog, (B) depth distribution of pore-water pressures at the soil bed’s center (75 cm) before and at the end of the first pipe clogging, (C) pore-water pressures along the soil pipe before (415 s), during (416 and 431 s), and following (432 s) the longest duration (16 s) pipe clogging, and (D) the depth distribution of pore-water pressures at the soil bed’s center (75 cm) before and during the 16-s pipe clogging.

1178 Soil Science Society of America Journal From a slope stability standpoint, both CH approaches (all events vs. only major events) showed identical wetting up of the soil profile due to the rapid drainage of the pipe back to pre-clog conditions. Pipe clogging probably did affect the wetting up of the soil profile and thus would probably affect the profile stability but not to the extent of the CF boundary condition simulations. These CH simulations generally matched the patterns observed by the tensiometers in the experiment (Fig. 3 and 12A); however, the simulations showed the wetting front reaching the tensiometers 4 cm above and 3 cm to the side of the pipe sooner than observed, due to the lateral distance not being accounted for in the two-dimensional simulation, but reaching the tensiometers 8 and 12 cm directly above the soil pipe later than observed. The differences could be in the hydraulic properties of the soil, but because the hydraulic properties were measured and not calibrated values, these differences are probably due to the effects of clogging pressure buildups on the hydraulic exchange with the adjacent soil not being fully accounted for in the simulations.

Fig. 11. Pipe-flow simulations for constant-head conditions before (277 s), CONCLUSIONS during (277.1, 277.25, and 278 s) and following (278.1 and 278.25 s) the It has been conceptualized for decades that extreme erosion first pipe clogging event (1-s duration). events, such as landslides and debris flows, are caused by pressure buildups due to soil pipe clogging, but quantification of such dynamics as these findings demonstrate the importance of buildups has been lacking. The only study to date that has measured measurements within the pipe in addition to the adjacent soil pressure responses to pipe clogging did so within the clog and not as proposed by Wilson et al. (2013). This is particularly true within the open soil pipe upslope (Midgley et al., 2013). This study given that tensiometers typically require measurement intervals overcame this deficiency by simulating laboratory experiments of of several seconds (Midgley et al., 2013) to minutes (Anderson soil pipe flow for two contrasting boundary conditions: constant and Kneale, 1980; Wilson, 2009), and pipe clogs may remain for flux and constant head. The simulations were conducted using much less than 1 s before being flushed from the pipe. a Richards’ equation approach, with the pipe represented as a The rapid pressure responses within the pipe were due to the highly conductive, low-retention porous medium. Internal erosion high hydraulic conductivity and low water retention properties; results in enlargement of the soil pipe, but with a constant inflow however, in reality with an open channel, the response would rate condition the pipe would flow under partially full conditions. probably be even more rapid than these simulations of a soil pipe Unique to these simulations was the expansion of the soil pipe with represented as a porous medium. As a result of this rapidity, the time due to internal erosion, inclusion of partially full flow conditions pipe quickly returned to the condition before pipe clogging and by representing the expanded pipe roof as a low conductivity–low thus each clog event provided an identical within-pipe response retention medium, and inclusion of pipe clogging. (Fig. 12A). For the CH boundary condition, the expansion of The constant-flux boundary condition resulted in almost the soil pipe with time due to internal erosion did not change instantaneous (<0.06 s) jumps in pore-water pressures within the clog response or the subsequent drainage response. Despite the soil pipe to extremely high values (54 m). While the values the expansion of the soil pipe and the wetting up of the soil predicted seemed unreasonable, the distribution pattern agreed profile with time, the response to every clog event was identical qualitatively with experimental observations. Inclusion of a to the 1-s pipe clog events (six events) regardless of their duration low-conductivity layer along the pipe roof captured the spatial (Fig. 12B–12F). Therefore, from a pore-water pressure buildup pattern observed in the experiment in which a wetted area standpoint, the eight sequentially integrated simulations using resembling the predicted pressure bulb developed at the pipe only the three major events (5, 16, and 8 s) were essentially clog. With each clog event, the wetted bulb area expanded to the identical to the 25 simulations with every event. These soil surface. simulations could have been simplified further by only including In contrast, the constant-head boundary condition allowed the 1-s-duration events. This is evident in the pore-water pressure the pipe to maintain full-flow conditions as the pipe enlarged. response to the 16-s clog, both along the soil pipe (Fig. 10C) and The pressure buildup dynamics were the same regardless of in the soil profile (Fig. 10D), compared with the first 1-s clog clogging duration. Thus, even an extremely short-duration (0.1 event (Fig. 10A and 10B). s) pipe clog will create a sudden jump in pore-water pressure

www.soils.org/publications/sssaj 1179 Fig. 12. Results for constant-head simulations: pore-water pressures at observation nodes (A) above the clog center and within the soil pipe for the entire simulation period, and along the pipe centerline in response to (B) a 1-s clog, (C) a 3-s clog, (D) a 5-s clog, (E) an 8-s clog, and (F) a 16-s clog.

within the pipe. The predicted pressures were nowhere near as These simulations of pipe flow demonstrate the potential high as the excessive pressures predicted with a constant-flux for rapid drainage of a hillslope by pipe flow and almost boundary condition, reaching only as high as the constant head instantaneous pressure buildup within and above a soil pipe (18 cm) and agreeing with observations by Midgley et al. (2013). when clogged. Such processes have been speculated to either The differences in predicted pressures between the CF and CH increase slope stability or cause sudden mass failures of hillslopes, predictions could partially explain why the CH experiments respectively. For both boundary conditions tested (CF and CH), exhibited numerous periods of complete stoppage in flow, some pore-water pressures within the pipe above the clog jumped lasting many seconds, while the CF experiments exhibited only almost instantaneously, while pressures below the pipe decreased brief interruptions without complete stoppage in pipe flow. rapidly as the pipe drained. These findings not only confirm the The high pressures under CF would remove the clog almost hypothesis of pressure buildups within soil pipes due to clogging instantaneously. but demonstrate the hydraulic nonequilibrium between the soil pipe and soil matrix. These simulations demonstrate the need

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