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Keywords:

  • shallow slope stability;
  • clayey soil;
  • pore pressure;
  • monitoring;
  • hydrologic modeling

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

[1] The hydrologic behavior of shallow weathered soils commonly determines the propensity for slope failure. Here we use laboratory data and field data collected by an automated monitoring system to assess the character of pore water pressure responses in a natural clay slope subject to intermittent rainfall. Although we did not measure pore pressure distributions that triggered slope failure, we obtained three years of field data that provided reliable and largely reproducible documentation of transient pore pressure responses. At depths of tens of centimeters to a few meters below the ground surface, moisture and pressure sensors recorded relatively fast, transient responses to precipitation. The speeds of pore pressure pulses advancing downward in the saturated zone were much larger than those of advective fronts driven by gravity, and the amplitudes of the pulses attenuated with depth. Statistical assessment of 129 pressure head responses demonstrates that this behavior is consistent with predictions of a linear, one-dimensional pore pressure diffusion model. However, the model best simulates measurements if diffusivity is treated as a calibration parameter and if initial moisture conditions match model assumptions. For regional assessment of slope stability, the predictive accuracy of the linear-diffusion model is limited by inherent uncertainties in defining the initial conditions and in assigning the values of hydraulic parameters.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

[2] Pore water pressure monitoring in landslide-prone areas is essential to develop reliable models of hydrological processes responsible for slope failure. The schematic description of such processes has been the subject of research for more than two decades, leading to the development of deterministic methods for landslide hazard assessment which share the common goal of capturing the essential features of the phenomenon using simple, explicit equations with few input parameters [Dhakal and Sidle, 2004; Iverson, 2000; Rosso et al., 2006; Montgomery and Dietrich, 1994]. In the case of slopes composed of fine-grained low-conductivity soils, however, field investigations documenting the hydrologic response to rainfalls are relatively rare. Older studies, relying on traditional piezometers and manual readings documented seasonal piezometric changes originating at the surface and progressively attenuating with depth [Kenney and Lau, 1984]. [Iverson and Major 1987] first proposed that a simple model for vertical diffusive propagation can be used to interpret the wet-season groundwater response in a large earth flow body. In this case, the response to individual rainstorms at shallow depths is not captured by the instruments, and the authors suggested that diffusion would rapidly attenuate short-term fluctuations at depth. Where a shallow impervious substrate is present, [Haneberg 1991] demonstrated that the linear-diffusion equation predicts relatively higher pressures due to the amplification of high-frequency fluctuations propagating from the surface.

[3] Later works have been based on high-frequency piezometric measurements carried out by means of short-time-response devices, the only ones capable of fully capturing the dynamics of pore pressure behavior. Baum and Reid [1995] described the results of extensive monitoring on a slow-moving landslide involving clay-rich debris deposits lying over a deep basalt bedrock. They discovered that surface infiltration can saturate the landslide body in just a few days, and that the saturated soil responds rapidly to heavy rainfall. Shallow pressures increase within a few hours and lag behind with depth as they attenuate, while gradients are invariably dominated by the vertical downward component. The same field evidence was used by Reid [1994] to test the pore pressure diffusion model with a flux boundary condition at the surface, which he considered to better represent the physical process of rainfall infiltrating a hill slope. These boundary conditions were also adopted by Iverson [2000] in his simplified model of vertical diffusion.

[4] In the case of shallow soils, Matsushi and Matsukura [2007] found evidence indicating rapid buildup of a water table on a mudstone bedrock. Rahardjo et al. [2005] monitored natural and simulated rainfall responses in a densely instrumented plot composed of fine-grained residual soils. In this case, the saturated wet front propagating from the surface was identified as responsible for maximum positive pressures measured at a shallow depth well above a deep groundwater table.

[5] The above mentioned experiences demonstrate the importance of the physical context: the depth to bedrock, the antecedent moisture conditions, and the presence and nature of heterogeneities are the most important factors affecting the response of shallow soils to rainfall. Different behavior can be expected in different geologic conditions. The hydrologic behavior of fine soils overlying a clay-shale bedrock has not been given detailed study with these factors in view, despite the widespread occurrence of this geologic setting and its well-known susceptibility to slope instability.

[6] Results are presented from a monitoring program based on the automated measurement of pore pressures at different depths and locations across the head scarp of a typical earth flow in the Italian Apennines. The dynamic hydrologic behavior of shallow soils (2–4 m thick) and parental bedrock is captured by pressure sensors buried directly in the ground in order to minimize time response.

[7] In this paper, we aim to do the following.

[8] 1. Our first aim is to describe field evidence (high-frequency pore pressure measurements over a span of 3 years) to illustrate the hydrologic behavior of weathered clayey soils overlying a clay-shale bedrock.

[9] 2. Our second aim is to evaluate the capability of the one-dimensional (1-D) linear-diffusion model to reproduce field data.

[10] 3. Our third aim is to evaluate the predictive power of the model by comparing the calibrated hydraulic parameters with those measured by field and laboratory tests.

[11] 4. Our fourth aim is to discuss the effects of alternative basal and upper boundary conditions, such as the presence of an impervious or partially leaking bedrock, and the need (when ponding occurs) of a constant-head ground surface boundary.

[12] 5. Our fifth aim is to compare the performance of linear-diffusion and kinematic-wave models to highlight the relative importance of vertical and slope-parallel flow in the short term.

2. Rocca Pitigliana Test Site

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

2.1. General Features

[13] The Rocca Pitigliana landslide is located in the northern Apennines, roughly 50 km south of Bologna, Italy. A topographic map of the area is shown in Figure 1. According to the Cruden and Varnes [1996] classification, the landslide is an active, very slow to moderate, composite earth flow. The length is approximately 900 m, the maximum width is 200 m (in the toe area), and the average slope of the deposit is 11°. The material involved is predominantly brownish-gray silty clay with scattered boulders of limestone and sandstone.

image

Figure 1. Map of the Rocca Pitigliana landslide.

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[14] The source area consists of a bowl-shaped scarp, up to 10 m in height, characterized by failure scars, disturbed slumps, and rotational slips. In the upper part of the earth flow deposition zone, the slope is fairly uniform (20°) and is characterized by sparse vegetation of grass and bushes. Here the landslide material has a thickness of only 2–4 m and overlies the clay-shale bedrock. The monitoring system is located across the head scarp (Figure 1), with the aim of evaluating hydrologic response to rainfall of both the clay cover and the underlying bedrock.

[15] The Rocca Pitigliana landslide reactivated twice in the last century (in 1934 and 1999). The last reactivation in November 1999 (after 110 mm of rain in 4 days) affected most of the landslide body, and the earth flow stopped a few tens of meters from a house (Figure 1).

2.2. Slope Stratigraphy

[16] The unstable slope is composed almost entirely of clay shales belonging to the Cretaceous Argille a Palombini Formation [Pini, 1999]. The unweathered material shows a structure consisting of stiff elongated clay aggregates with polished surfaces (scales) ranging in size from millimeters to a few centimeters. Limestone blocks and disrupted strata floating in the clay matrix are quite common. Surface weathering, softening, and slope movements erase the original scaly structure and create a soil mantle of variable thickness up to a few meters. The upper part of the clay cover is typically brown or light yellow. Given that failures mainly develop within the shallow weathered horizon, the landslide deposits are essentially made up of weathered clay shales.

[17] Core drilling yielded information about local stratigraphy (Figure 2). We distinguish three lithological units: unweathered clay shales (bedrock), weathered clay shales and landslide deposits (clay cover), and weathered fine sand (sandy cover). The sandy cover crops out above the main scarp and is the result of colluvial transport from the arenaceous flysch formation, shown in Figure 1, which extends laterally uphill of the landslide. The area of the sandy cover is quite small, so its influence on overall slope hydrology is probably negligible.

image

Figure 2. Schematic map and cross section of the Rocca Pitigliana monitoring system.

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[18] Table 1 and Figure 3 summarize the main physical characteristics of the two clay units. The weathered clay can be described as a silty clay soil (Figure 3a) of low to moderate plasticity. Smaller plasticity indices are measured on unweathered clay shale, but the differences are probably related to difficult disaggregation rather than actual mineralogical differences. In the clay cover, there is no evidence of an increase in density with depth (Figure 3b). Despite the variation, the mean volumetric water content at saturation can be defined with reasonable approximation; equation image = 0.38 ± 0.03. Data regarding the bedrock unit show a rapid increase of density with depth, with porosity dropping to 0.3 or below at 3 m from the topographic surface (Figure 3b).

image

Figure 3. Physical properties of the clayey units: (a) grain-size distribution, (b) soil porosity with depth (samples collected during drilling operation at the field site and manually collected in the close vicinity of the topographic surface), and (c) frequency distribution of saturated hydraulic conductivity resulting from Guelph-permeameter tests.

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Table 1. Physical Properties of the Two Clay Unitsa
Unitγd (kN/m3)θsatLL (%)IP (%)
  • a

    γd, dry unit weight; θsat, volumetric water content at saturation; LL, liquid limit; IP, plasticity index.

Weathered clay shales (Cover)16.20.38 ± 0.034924
Clay Shales (Bedrock)17.80.25 ÷ 0.354118

2.3. Hydraulic Parameters of the Soil

[19] A series of field and lab experiments was conducted to obtain an experimental estimate of hydraulic diffusivity D [L2/T]:

  • equation image

where K(ψ) is hydraulic conductivity and C(ψ) = dθ /dψ is specific moisture capacity, describing the change in volumetric water content for unit change in the pressure head (ψ). When the soil is saturated, hydraulic diffusivity D reaches its maximum value D0 = Ksat / C0, where Ksat is the saturated hydraulic conductivity and C0 is the specific soil moisture capacity at saturation, which is a function of the compressibility of the solid skeleton and of the water filling the voids.

[20] At saturation, an increase of pressure head causes the water to contract and causes the solid skeleton to expand simultaneously following the decrease in effective stresses. For fine-grained soils, the compressibility of water (∼4.4 × 10−6 kPa−1) is expected to be much smaller than soil compressibility [Freeze and Cherry, 1979] and can, therefore, be ignored for practical purposes.

[21] In order to measure the compressibility of the solid skeleton of weathered clay and obtain an estimate of C(ψ) in conditions of complete saturation (C0), specific odometer tests were conducted on undisturbed cubic samples.

[22] Odometer tests were used to mimic the effective stress variations (Δσv′) experienced by shallow soils while measuring the corresponding volume deformation (Δɛv). In terms of effective stresses, increase and decrease of pore water pressure can be reproduced in the odometer by an unloading-reloading cycle. The loading sequence of the odometer tests was then designed to measure the odometer modulus (M = Δσv′/Δɛv) in small swelling recompression cycles at various confining pressures.

[23] The results of seven odometer tests indicate that weathered clay shale behaves like a normally consolidated soil. Stiffness in swelling and recompression increase linearly with vertical effective stress (σv0'), resulting in a roughly constant M/σv0′ ratio. In more detail, we observed the dependence of stiffness on the magnitude of the imposed stress change (Δσv') with relatively higher values for swelling. In order to illustrate this concept, Figure 4 reports the values of swelling (Ms) and the recompression modulus (Mr)), normalized with respect to the average effective stress (σavg′ = σv0' + Δσv0'/2) and plotted against the magnitude of the imposed stress change (Δσv′). Despite the scatter, we can easily observe that stiffness increases for small stress variations. Since cyclic pore pressure changes in the soil cause very small stress variations, we use the higher-measured values of Ms/σv0′ and Mr/σv0′ to describe the compressibility of weathered clay. Numerical values range from 150 to 350, as shown in Figure 4.

image

Figure 4. Normalized swelling (Ms) and recompression (Mr) moduli as a function of the magnitude of unloading-reloading steps. Power regression lines are plotted to indicate the likely range of soil compressibility.

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[24] The odometer modulus can be converted in C0 values by considering the relationship between vertical deformation and volumetric water content at saturation. The computed values range from 10−2 to 10−3 m−1 between the topographic surface and a depth of 2 m.

[25] Saturated hydraulic conductivity of weathered clay (Ksat) was measured by means of 32 Guelph-permeameter infiltration tests [Reynolds and Elrick, 1985] performed at a maximum depth of 60 cm. Infiltration test results indicate wide variability (Figure 3c). The modal value of Ksat is between 10−6 and 10−7 m s−1, but values up to 5 × 10−4 m s−1 were measured because of the presence of macropores, fissures, and desiccation cracks during the dry season. The relevance of the scale effect, usually attributed to fractures or heterogeneities [Neuzil, 1994], is testified by the measures of conductivity carried out on odometer samples, which indicate values in between 10−10 and 10−11 m s−1. The hydraulic conductivity of the bedrock was measured by three slug tests [Bouwer and Rice, 1976; Bouwer, 1989] performed on existing piezometers. Measurements indicate lower conductivity (Ksat ≈10−8 m s−1) than in shallow soils. On the basis of grain size and porosity, we expected even lower values; thus, it is probable that discontinuities and heterogeneities also play a role within the bedrock.

[26] By combining the measurements of C0 and Ksat, we obtain the modal range of hydraulic diffusivity at saturation D0, shown in Figure 5. The modal ranges of both C0 (the shaded area between the two regression lines in Figure 4) and Ksat (the frequency peak in Figure 3b) are very large, and this creates uncertainty in the estimate of hydraulic diffusivity. The expected (modal) value of D0 varies from 10−5 to 5 × 10−4 m2 s−1.This range will be referred to in the forthcoming analysis. It is clear, however, that experimental measurement of diffusivity is a very difficult task. For example, by considering a variation of one standard deviation around the mean of both C0 and Ksat, the values of D0 range over 3 orders of magnitude.

image

Figure 5. Trends with depth of hydraulic conductivity (peak of the frequency distribution of Figure 3c), specific soil moisture capacity (likely range of compressibility of Figure 4), and corresponding hydraulic diffusivity (range of modal values).

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3. Monitoring System

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

[27] In October 2002, a monitoring system was installed in the source area of the Rocca Pitigliana landslide. The purpose of monitoring was to investigate the hydrologic response to rainfall in the upper part of the slope, where the clay cover is susceptible to shallow failures which may reactivate the whole landslide. The monitoring system was designed to measure positive pore water pressure within the clay bedrock, the sandy cover (3 m thick), and the clay cover (2–4 m thick). Sensors to investigate the dynamics of the unsaturated zone were also installed, although monitoring of the vadose zone was not our goal.

[28] Figure 2 shows a map and a cross-sectional profile of the instrumented area. The monitoring system consists of 18 pressure sensors placed at different depths (from 0.5 to 10 m), three soil moisture sensors (0.1–1.3 m), three tensiometers (0.3–0.8 m), one rain gauge, and one surface wire extensometer. The pressure sensors are temperature-compensated and differential piezoresistive, with a built-in signal amplifier to reduce electrical noise. The measurement range is 0–100 kPa (10 m of water) with a resolution of about 0.8 cm of water. Pressure sensors were first placed in a small cotton bag filled with clean fine sand, and then the bag was placed on top of a 20 cm thick layer of sand at the desired depth. More sand was added around and above the sensor (about 40 cm overall thickness), and the measurement section was sealed with packed bentonite. Compared with the usual installation inside a piezometer, direct burial has the advantage of providing a much faster response in fine soils [Simoni et al., 2004]. Moreover, the sand pocket around the sensor acts as a porous filter with a very large interface area, providing good measurement stability (the readings are averaged over a volume of several dm3) and avoiding the time delay associated with possible imperfect saturation of the sensor. In fact, air bubbles must contract or expand before they can transmit any pressure change, and the large interface allows water to flow in and out of the measuring device to make that happen. Our data show that direct burial can be successfully used to measure the dynamics of pore pressure in low-conductivity soils (section 4).

[29] Soil suction was measured by conventional tensiometers made of porous ceramic cups connected through rigid plastic tubes to vacuum gauges. These instruments required heavy maintenance and frequent repairs to keep them working. Because of problems, such as water freezing during winter, soil drying during summer, soil crack openings, and grazing animals, the tensiometer data were short and discontinuous. The vadose zone was also monitored, using probe sensors that utilized electrical capacitance to measure soil water [Schwank et al., 2006]. These sensors were easy to install, needed no maintenance, and provided fast responses to changes in soil moisture, together with stable long-term use. All data were collected every 20 min, stored in a data logger on site, and downloaded every 2–4 months. An embedded mobile telephone module allowed us to check data and detect anomalies.

[30] The system operated from June 2003 to August 2006. In the analysis, we will focus on the hydrologic behavior of only the clay cover. There are two reasons for this choice: first, the local presence of sandy soil is a peculiar feature of the Rocca Pitigliana and is rather uncommon in the area, and second, the hydrologic behavior of the clay cover is probably regionally representative. This view is supported by the data collected at three other monitoring sites (Ca' di Malta, Silla, and Serra di Carviano; 10 to 30 km from Rocca Pitigliana), where a total of 25 pressure sensors were installed in the clay cover at different locations. Only part of these data have been published [Simoni et al., 2004], but they all confirm the general picture described here.

4. Observed Pore Pressure Response

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

4.1. Available Data

[31] The data recorded by the four sensors buried in the clay cover are shown in Figures 6 and 7. Sensors P11 and P14 (Figure 6) were installed in June 2003, while sensors P17 and P18 (Figure 7) were installed later in February 2005 to collect data at different depths. Power failures caused by lightning strikes are responsible for data loss occurring during summer 2004 and summer 2005.

image

Figure 6. Overall data collected by sensors P11 (0.7 m) and P14 (1.5 m).

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image

Figure 7. Overall data collected by sensors P17 (0.5 m) and P18 (1.0 m).

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[32] During the monitoring period, we recorded 110 rainfall events and related pore pressure responses. Seventy-five were simple, roughly uniform rainfall episodes, and 35 were complex rainfall sequences. Within these complex precipitation events, we isolated 94 rainfall bursts, thus obtaining a total of 169 rainfall pulses (92 of which were in the period from February 2005 to August 2006) useful to investigating the hydrologic behavior of the clay cover.

[33] Each sensor response was classified as follows.

[34] 1. Type 1 was the sharp pressure peak, clearly evidenced by a fast increase followed by slow decrease.

[35] 2. Type 2 was the smooth, sometimes flat, pressure peak (pressure plateau).

[36] 3. Type 3 was the ambiguous response (not clear whether the sensor was responding or not).

[37] 4. Type 4 was no response to rainfall.

[38] Most of the rainfall events produced a well-defined pressure increase in P11, P14, and P17, and only in 30–35% of the cases did the sensors exhibit no response (Table 2). The lack of response was mainly observed during summer thunderstorms, when the top soil is dry and immediately absorbs the water, or at the end of the wet season, when the water table is close to the ground surface and most of the rainfall water ends up as surface runoff. The percentage of no response is higher for the deep sensor P14 (50% of the cases), because pressure waves rapidly attenuate with depth (see section 4.2.).

Table 2. Classification of Sensor Responses Recorded in the Clay Cover From June 2003 to August 2006
SensorDepth (m)Recorded Rainfall PulsesNumber of Sensor Responses
Type 1 (Fast Increase, Sharp Peak)Type 2 (Fast Increase, Smooth Peak)Type 3 (Unclear)Type 4 (No Response)
P110.716993 (55%)19 (11%)12 (7%)45 (27%)
P141.516956 (33%)24 (14%)6 (4%)83 (49%)
P170.59241 (45%)9 (10%)7 (8%)35 (37%)
P181.0922 (2%)1 (1%)3 (3%)86 (94%)

[39] Sensor P18 exhibited apparently anomalous behavior. Although it follows the general seasonal trend (high pore pressures during the wet season and low pore pressures during the dry season), the sensor did not respond in 97% of the cases. The pressure fluctuations shown in Figure 7, in fact, are not correlated with rainfall events but with the variations of atmospheric pressure acting on one side of the piezoresistive diaphragm (differential sensor). This behavior is due to the presence of a stiff, unfractured block of marl (approximately 50 cm in size), which hinders the propagation of pressure waves from the ground surface due to either rainwater infiltration or to atmospheric pressure variations acting on the water table. Major precipitation events can still be recognized, while most short-term oscillations are related to atmospheric pressure changes similar to those long recognized for piezometers in confined aquifers [Jacob, 1940]. Although these data highlight the complexity of hydrological pathways in the clay cover, the data collected by P11, P14, and P17 are consistent and meaningful, and they appear to accurately describe the hydrologic behavior of the clay matrix.

[40] The sensors buried in the underlying clay-shale bedrock (Figure 2) are located below the water table. They measure positive pore water pressures throughout the year and do not show any appreciable response to precipitation, other than moderate (<1 m) seasonal variations.

4.2. Short-Term Response

[41] The pressure sensors buried in the clay cover generally exhibit a distinct pressure head increase in response to rainfall events. Figure 8 shows two examples of the observed behavior in terms of the total head (h) time series. In response to uniform rainfall of 45 mm in 20 h (Figure 8a), the pressure head in P11 and P14 increases almost simultaneously about 6 h after the rainfall begins, rises rapidly to a sharp peak, and then declines asymptotically in the next few days. The total head is greater for the shallow sensor (P11) throughout the recorded period, indicating vertical downward flow, and the pressure head is always positive (h > - Z, where Z is the sensor depth measured vertically downward), indicating fully saturated soil at the sensor depth. At the same time, sensors P12 and P13, located within the bedrock (Figure 2) and measuring positive pressure heads before rain, do not show any appreciable increase of pressure.

image

Figure 8. Representative time series of total head recorded in the clay cover in response to (a) uniform rainfall (18 September 2005) and (b) to a complex storm (25–30 April 2006).

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[42] In case of complex rainfall sequences, overlapping pressure waves propagating downward within the clay cover are typically observed. In most cases, a single-rainfall burst can be correlated to pressure waves at a shallow depth (Figure 8b, sensor P11) which are smoothed and delayed in the deeper sensor P14. Also, in this case, pressure sensors in the bedrock do not respond to the rainfall event.

[43] Such a direct connection between rainfall and pore pressure growth in the clay cover has been documented for 169 rainfall pulses during both the wet season and the dry season. Most wet-season storms consist of a sequence of long-duration (7–20 h) low-intensity bursts (≈1–2 mm/h), while dry-season storms are typically shorter (≈3–6 h) and more intense (2–7 mm/h). In both cases, rainfall intensity often exceeds the saturated hydraulic conductivity of the soil (Ksat ≈ 1.10−7 m/s = 0.36 mm/h). Since more than one sensor usually responds to a certain rainfall pulse, a total number of 190 well-defined pressure waves were recorded during the monitoring period (sum of type 1 responses of P11, P14, and P17; Table 2). These data constitute the bulk of the experimental evidence used to quantitatively describe the hydrologic behavior of the clay cover by means of the parameters defined in Figure 9a. T is the duration of the rainfall pulse, I is the mean rainfall intensity, Δt0 is the lag time between rainfall onset and sensor response, Δtpk is the lag time between sensor response and pressure peak, and Δψpk is the increase of pressure head at peak (Δψpk = ψpk - ψ0).

image

Figure 9. Summary histograms of time to sensor response (Δt0), time to peak (Δtpk), and pressure peak (Δψpk) recorded in the clay cover (all available data).

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[44] Despite the variability in rainfall and initial soil moisture conditions (see section 4.3), the sensors in the clay cover show remarkably similar behavior. In more than 90% of the cases, the pore pressure starts to increase within 4 h from rainfall onset (Figure 9c) and peaks within the following 8 h (Figure 9d). Sensor depth divided by Δt0 indicates that the pressure head signal advances through the soil with an average velocity of Vs = 2 × 10−4−2 × 10−5 m s−1. This value is about 200 times greater than the advective front velocity (Va) estimated by considering 1-D gravity-dominated flow, VaKsat /θsat = 1.10−7 /0.35 = 3.10−7 m s−1 [Stephens, 1995]. Despite the simplified calculation, this means that the initial pressure head response is driven by the passage of a diffusive pressure wave rather than kinematic gravity flux.

[45] Similar behavior has been described by Gillham [1984] for a sandy soil close to saturation, in which the application of a small amount of water may relieve suction in the capillary fringe and produces a rapid, large rise of the water table. In our case, however, the soil is typically fully saturated at sensor depth (Figures 6 and 7); hence, the pore pressure transmission (whether a near-surface capillary zone is present or not) is a diffusive process largely controlled by the compressibility of the soil skeleton [Reid, 1994; Baum and Reid, 1995]. The induced increase of pressure head ranges from a few centimeters to 80 cm, with an average of 20 cm (Figure 9b) and, in the case of prolonged rainfall, the soil reaches an approximately constant value (pressure plateau) close to the hydrostatic.

[46] The average response time (Δt0) of sensors P17 and P14, which are approximately on the same vertical, increases slightly with depth, indicating that the pressure wave travels downward from the ground surface (Table 3). For the same sensors, the increase in depth of the time to peak (Δtpk) and the concomitant decrease of the pressure peak (Δψpk) indicate how the pressure wave becomes slower and smoother, rapidly attenuating with depth. The pressure waves stop (or greatly attenuate) at the bottom of the cover, as suggested by the lack of sensor response within the bedrock.

Table 3. Average Values of Lag Time, Time to Peak, and Pressure Peak Recorded in the Clay Cover (±1 Standard Deviation)
SensorDepth (m)Average Time to Sensor Response equation image (hr)Average Time to Sensor peak equation image (hr)Average Increase of Pressure Head at Peak, equation image (cm)
P170.51.4 ± 1.24.0 ± 2.515.4 ± 10.8
P110.71.6 ± 1.74.3 ± 3.315.5 ± 10.5
P141.52.3 ± 2.29.0 ± 6.95.3 ± 8.0

4.3. Seasonal Trend

[47] Pressure head time series exhibit a consistent event-driven response superimposed on a seasonal trend that modulates a “base” head level (Figures 6 and 7). The base head level is almost always positive at 1.5 m (P14, Figure 6); it is positive only during the wet season at 0.7 m (P11, Figure 6), and it is close to zero (or negative) during most of the year at 0.5 m (P17, Figure 7).

[48] The volumetric water content measured at 0.1 and 0.5 m from the surface (Figure 10) by soil moisture sensors (MS in Figure 2) matches pore pressure records fairly well and indicates that, during fall and winter, the saturated zone remains in close proximity to the surface, while desaturation readily takes place in spring and deepens progressively, reaching 0.5 m in early June.

image

Figure 10. Long-term variation of volumetric water content in two moisture sensors buried in the clay cover.

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[49] Following rainfall events, rapid drainage at depth occurs during the summer months until about late October to November, when deeper sensors attain a higher mean pressure head and fluctuations are much less abrupt (Figure 6). Faster drainage in the dry season can be attributed to higher evapotranspiration flux and to the opening of soil cracks and fissures (which increase the hydraulic conductivity of the soil). The potential evapotranspiration rate during summer, estimated by the Food and Agriculture Organization (FAO) Penman-Monteith method [Allen et al., 1998] using the meteorological data of the Bombiana station (10 km to the south, same elevation), is as high as 3.5 mm/day. During the wet season, the groundwater flow shows a persistent downward gradient, as inferred by comparing the total head at different depths (compare P17 with P14, on the same vertical, and P11 with P14, about 10 m apart; Figures 6 and 7).

5. Hydrologic Modeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

5.1. Linear-Diffusion Model

[50] Field data suggest that the short-term increase of pore water pressure within the clay cover is due to the propagation of diffusive pressure waves that travel vertically downward from the ground surface. Lateral flow could be also important for the seasonal trend, but long-term slope dynamics are ignored because of the small size of the monitored plot.

[51] The mechanism of short-term vertical diffusion has been identified by Hurley and Pantelis [1985], Iverson and Major [1987], Haneberg [1991], Reid [1994], and Iverson [2000] as the one governing the pore pressure response when rainfall duration T corresponds to the time required to transmit slope-normal pore pressures Tnormal = Z2/D0 (where Z is the depth and D0 is the saturated hydraulic diffusivity). For such conditions, Iverson [2000] derived a simplified form of the Richards [1931] equation to describe the response of a semi-infinite homogeneous slope to rainfall of varying intensity and duration:

  • equation image

where ψ is the pressure head, t is the time, α is the slope angle, and Z is the depth measured vertically downward from the ground surface (Figure 11).

image

Figure 11. Definition of the parameters used in hydrologic modeling.

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[52] Equation (2) has the form of the standard linear-diffusion equation and allows analytical solutions in many cases [Crank, 1956]. Linearization of the original nonlinear second-order Richards [1931] equation implies that 1) the depth Z is small compared to the catchment area A (thin-layer assumption, Z/equation image ≪ 1; Figure 11), 2) the rainfall duration is short (T ≈ Tnormal ), and 3) the soil is close to saturation (hydraulic diffusivity is constant). In our case, Tnormal ≈ 2 − 20 h (assuming reference diffusivity D0 = 10−4 − 10−5 m2 s−1) and the typical rainfall duration is T ≈ 1–20 h.

[53] Iverson [2000] obtained an analytical solution of equation (2) by considering the following initial condition:

  • equation image

lower boundary condition

  • equation image

and upper boundary condition

  • equation image

in which Iz is the surface boundary flux (assumed to be equal to rainfall intensity), Kz is the saturated hydraulic conductivity in the Z (vertical) direction, and dz and β are the depth and the pressure head distributions of the steady state water table, respectively (Figure 11).

[54] The initial condition (equation 3a) describes the pressure head distribution at the beginning of the rainfall event as a steady background condition. The lower boundary condition (equation 3b), combined with the assumption of constant hydraulic diffusivity, states that the solution domain is a homogeneous semispace, while the upper boundary condition (equation 3c) assumes that the vertical infiltration rate at the ground surface is equal to rainfall intensity (the rainfall will totally infiltrate). The consistency of these boundary conditions and their effect on the hydrologic response will be treated in section 6.

5.2. Application to Monitoring Data

[55] The validity of the linear-diffusion model was tested by comparing model predictions with monitoring data. The data set used for the analysis contains all the responses characterized by a well-defined increase of pore water pressure (response type 1) for all of the 110 rainfall events. Available responses are 57 for P11, 45 for P14, and 27 for P17, leading to a total of 129 pressure head time series.

[56] The analysis of each data series consisted of the following steps.

[57] 1. The first step was to choose a trial value for the hydraulic diffusivity D0 of the clay cover.

[58] 2. The second step is the computation of the pressure head at sensor depth using the recorded rainfall as the upper boundary and adopting a constant hydraulic conductivity of the soil Ksat = 10−7 m s−1.

[59] 3. The third step is the evaluation of the goodness of fit between simulated (ψsim) and observed (ψobs) pressure heads by means of the Nash-Sutcliffe efficiency coefficient [Nash and Sutcliffe, 1970]:

  • equation image

where ψn is the nth value of the pressure head time series. Ef can range from −equation image to 1, where 1 indicates a perfect match of modeled to observed data.

[60] 4. The fourth step is the evaluation of the calibrated value of hydraulic diffusivity (D0cal) using a convergence algorithm to maximize Ef (D0 resolution = 0.1 on a log scale).

[61] From a theoretical point of view, there is no reason to expect a significant variation of D0cal between different sensors or storms; in fact, the diffusivity of a fully saturated homogeneous soil is constant in time and space, and a single D0 value should fit all the data. Field data tell a different story, they clearly show that the actual sensor response is influenced by soil moisture conditions and by fissures and cracks, which vary in time and space. Therefore, the calibrated value of hydraulic diffusivity inherently accounts for these complexities.

[62] In general, the model performs well, and the analysis of the 129 pressure head time series gives a coherent picture. Figure 12 shows some representative example results of the simulations. The linear-diffusion model is able to reproduce the observed data for both single-rainfall events (Figures 12a, 12b, 12c, and 12d) and prolonged rainfall made of complex burst sequences (Figures 12e and 12f). The time to sensor response, time to peak, pressure peak, and the decay limb are well predicted, regardless of the complexity of rainfall forcing. The high values of the efficiency coefficient confirm the goodness of fit.

image

Figure 12. Example outputs of the one-dimensional linear-diffusion model. Comparison of observed (obs) and simulated (sim) pore pressure response to rainfall for several selected cases.

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[63] Comparison of the calibrated (D0cal) and measured diffusivity ranges (Figure 5) show that calibrated diffusivities are well in the range of the measured values (Figure 13a), indicating that the linear-diffusion model is able to simulate monitoring data using realistic parameters. The mean value of D0cal (log averaged over one July) is about 10−5 m2 s−1 during the wet season and increases up to 1 order of magnitude during the summer months (Figure 13a), probably due to the opening of soil cracks and fissures which increase overall hydraulic conductivity. This secondary porosity does not invalidate the diffusion model, provided that diffusivity is accordingly modified. It should not be forgotten, however, that an a priori application of the linear-diffusion model would prove very difficult because of the uncertainties associated with parameter measurement and because of the sensitivity of the model to such parameters.

image

Figure 13. Application of the one-dimensional linear-diffusion model to the 129 recorded pressure head time series: (a) calibrated values of hydraulic diffusivity aggregated on a monthly basis compared with the range of modal values measured by field and laboratory tests, (b) frequency distribution of the Nash-Sutcliff efficiency coefficient, (c) comparison between observed and computed increase of pressure head at peak, and (d) comparison between observed and computed lag time to peak.

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[64] The goodness of fit is higher than 0.3 in 45% of the cases, while for the remaining Ef, it is low or negative (Figure 13b). This is partly due to the sensitivity of Ef to model bias [McCuen et al., 2006] which produces very low values of Ef when a small offset between the observed and computed time series, or a bias in the magnitude of peak, are present. Other reasons for bad performance are related to violations of model assumptions, as discussed in the section 6. Nonetheless, the predicted increase of pressure head (Figure 13c) and lag time at peak (Figure 13d) agree well with observed data. F statistics indicate that the null hypothesis of the 1:1 relationship between observed and computed values cannot be rejected at the 5% significance level.

6. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

6.1. Upper Boundary in Ponding Conditions

[65] The linear-diffusion model loses its predictive ability when applied outside its validity domain. During the wet season, when the soil is at saturation, rainfall causes the pressure head to quickly reach the hydrostatic level (ψ = Z) which is then maintained during precipitation because no water can infiltrate. In the case shown in Figure 14a, the sensor (P11, Z = 70 cm) has an initial pressure head of 50 cm, and the soil is fully saturated up to the ground surface (moisture sensors measure). Field evidence illustrates that pressure heads soon attain a roughly constant value (smooth peak), corresponding to the hydrostatic level, until the end of precipitation. The linear-diffusion model fails to reproduce the data (Figure 14a), because the constant-flux upper boundary condition (3c) used to linearize equation (2) is violated. When ponding occurs, the infiltration rate becomes lower than the rainfall intensity, and a constant-head upper boundary condition is more appropriate [Tsai and Yang, 2006]. The so-called β-line correction proposed by Iverson [2000] (maximum pressure heads sustainable with a water table at ground surface and the steady, background vertical flow component defined in equation 3a) is unable to work around the problem. By considering the hydraulic diffusivity of D0 = 10−5 m2 s−1 (simulation 1 in Figure 14a) and using the β-line correction to amend the pressure heads, the model predicts constant pressure heads throughout the simulation period, well above observed values. Lower hydraulic diffusivity (D0cal = 3 × 10−6 m2 s−1) improves the efficiency coefficient (simulation 2 in Figure 14a), but the overall fit remains poor (Ef is negative).

image

Figure 14. Comparison of observed (obs) and simulated (sim) pressure head in two cases in which the assumptions of the one-dimensional linear-diffusion model are violated: (a) generation of surface ponding during the rainfall event, and (b) infiltration through an unsaturated soil.

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[66] The pressure head boundary condition proposed by Tsai and Yang [2006] (ψ = 0 at Z = 0) makes the model more realistic, but the problem becomes nonlinear and requires numerical solution. This approach is then hardly suitable for large-scale hazard analysis for which an analytical solution would be required.

6.2. Effect of a Near-Surface Unsaturated Zone

[67] Another model assumption can be violated during the summer season when shallow soil is unsaturated. In this case (Figure 14b), sensor P11 is in the tensiosaturated capillary fringe (no positive pressure head and saturation measured by moisture sensors at 30 cm from ground level) and does not respond to the initial rainfall burst, because all the water is adsorbed by the near-surface unsaturated soil. Once the shallow soil is wet, the following rainfall burst causes a rapid growth of pressure head. The linear-diffusion model cannot replicate this behavior because of the assumption of fully-saturated soil, and two distinct pressure waves are then predicted (Figure 14b). The overall fit is rather good (Ef = 0.31), just because the second wave is well reproduced, but in many cases, the delayed sensor response introduces a time-shift bias in the data which remarkably lowers the efficiency coefficient Ef.

6.3. Comparison With Kinematic Slope-Parallel Flow

[68] Our data strongly support what Iverson [2000] and other authors found on the basis of both theory and measurements: the short-term pore pressure response to rainfall of clay slopes is typically transient, and it includes a large component normal to the slope. However, given the pointwise nature of measurements, one could disregard the evidence described above (the delay and the attenuation of pressure waves with depth) and assume that the observed pressure waves are generated by fast, slope-parallel subsurface stormflow within a network of fissures and macropores. Subsurface stormflow is a dominant runoff-producing mechanism in many upland environments, since the presence of macropores allows very fast flow rates, even through heavy clay soils [Harr, 1977; Beven and German, 1982; Haneberg, 1991].

[69] To investigate this hypothesis, monitoring data have been reanalyzed using a finite-difference solution of the kinematic subsurface stormflow equation [Beven, 1981]. The equation describes the transient response to rainfall of a sloping soil mantle overlying an impervious bed at a shallow depth:

  • equation image

where x is the downslope distance, α is the slope angle, Sy is the specific yield, Klat is the saturated lateral hydraulic conductivity, H is the flow depth normal to the impermeable bed, and I is the rainfall input per unit area parallel to the bed. The equation ignores the effect of the unsaturated zone, assumes that the hydraulic gradient is parallel to the bed, and is simple enough to be implemented into a slope stability model on a small scale. The model was fitted to our 129 pressure head time series using Sy and Klat as calibration parameters to maximize the efficiency coefficient Ef. Results are shown in Figures 15 and 16 and lead to the following observations.

image

Figure 15. Example outputs of the kinematic subsurface stormflow model. Comparison of observed (obs) and simulated (sim) pore pressure response to rainfall for several selected cases.

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image

Figure 16. Application of the kinematic subsurface stormflow model to the 129 recorded pressure head time series: (a) calibrated values of lateral hydraulic conductivity aggregated on a monthly basis compared with the range of modal values measured by field tests, (b) frequency distribution of the Nash-Sutcliff efficiency coefficient, (c) comparison between observed and computed increase of pressure head at peak, and (d) comparison between observed and computed lag time to peak.

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[70] 1. The first observation is that the kinematic-wave model is not able to reproduce the asymmetric profile of the pressure waves (compare Figures 15 and 12).

[71] 2. The second observation is that the best fit is obtained for Sy = 0.05 and Klat≈ 10−4 m s−1 (Figure 16a); that is, conductivity values 2–3 orders of magnitude higher than those measured in the field.

[72] 3. The third observation is that the prediction of pressure peak (Figure 16c) and time to peak (Figure 16d) is not satisfactory; F statistics lead to rejection of the null hypothesis of no difference between measured and computed values with a significance level of less than 1%.

[73] These results confirm that the short-term response of the clay cover is governed by transient vertical infiltration. Therefore, even if part of the infiltrated water would flow downhill as lateral subsurface stormflow (within a shallow soil horizon or an interconnected crack network), the use of slope stability models steady state, slope-parallel flow is not justified. However, the role of slope-lateral flow in the long term cannot be assessed by our data, since sensors are concentrated in a small plot and more measurements would be needed at the toe of the slope or in areas of convergent topography.

6.4. Basal Boundary Conditions

[74] Direct measurements and monitoring data (no sensor response in the bedrock) indicate that the clay-shale bedrock is less permeable than the overlying clay cover. In such conditions, the rainfall water should accumulate at the bottom of the cover, promoting lateral subsurface flow [Haneberg, 1991]. On the other side, monitoring data show fast pore pressure drainage, and pressure head data can be reproduced using the semispace assumption (equation 3b) of the Iverson [2000] model. To investigate this apparent conflict, we consider a typical sensor response and apply three solutions of the linear-diffusion equation: 1) the original Iverson [2000] solution for a homogeneous slope (Kbedrock = Kcover), 2) the solution proposed by Baum et al. [2002, 2008] (TRGRS model) for a slope with an impermeable boundary at a finite depth (KbedrockKcover; depth of the bedrock = 2 m), and 3) a numerical finite-element solution for the intermediate case of partially leaking bedrock (Kbedrock ≈= 0.1 Kcover). Table 4 summarizes the parameters used in the analysis whose results are shown in Figure 17.

image

Figure 17. Comparison between observed (obs) and simulated (sim) pressure head (left) in the clay cover and (right) in the bedrock using different hydrologic models.

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Table 4. Soil Properties Used to Generate Figure 17
ParameterClay CoverBedrock
Homogeneous Slope Model (Iverson, 2000)
Ksat (m/s)1 × 10−71 × 10−7
C0 (1/m)1 × 10−31 × 10−3
D0 (m2/s)1 × 10−41 × 10−4
 
Impermeable Bedrock* Model (TRGRS)
Ksat (m/s)1 × 10−7\
C0 (1/m)1 × 10−3\
D0 (m2/s)1 × 10−4\
 
Leaking Bedrock* Model (Numerical Solution)
Ksat (m/s)1 × 10−71 × 10−8
C0 (1/m)1 × 10−31 × 10−2
D0 (m2/s)1 × 10−41 × 10−6

[75] Iverson's original [2000] solution (Figure 17a) provides better results than the impermeable boundary model (Figure 17c). TRGRS predicts water accumulation at the bottom of the cover and the development of a perched water table, never observed in the field. The Iverson solution, on the other hand, overestimates the pressure increase in the bedrock (Figure 17b) where sensors do not detect any appreciable pressure growth.

[76] The intermediate case of partially leaking bedrock provides good results (Figures 17e and 17f); the pressure increase in the cover (Figure 17e) is almost identical to that predicted by the Iverson model, and the response in the bedrock (Figure 17f) is strongly smoothed and attenuated. These results were obtained using low-hydraulic conductivity (Kbedrock = 10−8 m s−1; Kcover = 10−7 m s−1) combined with relatively high-moisture capacity at saturation (C0 bedrock = 10−2 m−1;C0 cover = 10−3 m−1) for the clay bedrock. The increase of C0 at the soil-bedrock transition has the dual effect of increasing available storage (thus avoiding water accumulation in the cover) and decreasing hydraulic diffusivity (which causes strong attenuation of the pressure wave, see equation (2)). A simple decrease of the hydraulic conductivity of the bedrock (leaving C0 unchanged) could not replicate the field data. The physical justification of this assumption is not straightforward (high-C0 values are typical of compressible soils, and this is not the case of the bedrock). Probably, C0 bedrock accounts for the water storage within the pervasive fissure network which characterizes the scaly clays. In this hypothesis, the rainfall water that reaches the bottom of the cover is stored (or drained) by the shallow fractured bedrock.

7. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

[77] Analysis of the hydrologic response to rainfall of an unstable clay slope allows the following conclusions to be drawn.

[78] 1. The hydrologic behavior of the examined clay cover is characterized by rainfall-induced pore pressure waves (short-term rainfall response) superimposed on a seasonal head level. The pressure waves advance vertically downward through the fully saturated soil at high speed (the observed velocity is, on average, 200 times greater than the advective front velocity) and become slower and smoother with depth.

[79] 2. The short-term behavior of the clay cover can be well reproduced using the 1-D linear-diffusion model proposed by Iverson [2000]. The model captures the essential physics of the phenomenon, and it is able to simulate the observed sensor response using realistic values of hydraulic parameters. The model loses its predictive capabilities when applied outside its validity domain (for example, in the case of infiltration through an unsaturated soil (dry season) or when surface ponding occurs during the rainfall event (wet season)). The same data cannot be reproduced using the kinematic-wave model based on lateral subsurface stormflow.

[80] 3. A diffusion model which accounts for an impermeable boundary at finite depth (TRIGRS) [Baum et al., 2002, 2008] predicts the accumulation of water at the bottom of the cover and the development of a perched water table, although evidence of this was never observed. Although some stratification of permeability may exist in the slope, the Iverson [2002] model for a homogeneous slope provides more realistic results. An explanation for this contrast may be the presence of a pervasive fissure network in the upper part of the bedrock which allows the storage (or deep drainage) of the water that reaches the bottom of the cover. A partially leaking bedrock model provides good results and supports this hypothesis.

[81] 4. At present, the utility of a linear-diffusion model in the framework of areal slope stability assessment is rather limited. Substantial uncertainty affects hydrologic analyses on a large scale because of the difficulty of predicting the initial condition of the slopes and the dramatic influence of hydraulic parameters in modeling results. For example, the increase of pressure head produced by a 12 h rainfall at a depth of 1 m varies by 80% (from 0.2 to 1 m), for a difference of hydraulic diffusivity of less than 1 order of magnitude (D0 from 10−5 to 6 × 10−5 m2 s−1). Within this context, we stress the importance of field monitoring and discourage the application of models not adequately supported by data to predict landslide susceptibility.

Notation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information

[82] 

A

upstream drainage area, m2.

C(ψ)

specific soil moisture capacity, 1/m.

C0

specific soil moisture capacity at saturation, 1/m.

dz

depth of the steady state water table in the Z direction, m.

D

hydraulic diffusivity, m2/s.

D0

hydraulic diffusivity at saturation, m2/s.

D0cal

hydraulic diffusivity at saturation calibrated against field data, m2/s.

Ef

Nash-Sutcliffe efficiency coefficient.

H

flow depth, m.

I

mean rainfall intensity, m/s.

Iz

surface boundary flux, m/s.

IP

plastic index, %.

K(ψ)

hydraulic conductivity, m/s.

Ksat

hydraulic conductivity at saturation, m/s.

Kz

saturated hydraulic conductivity in the vertical direction, m/s.

Klat

aturated hydraulic conductivity in the slope-parallel direction, m/s.

LL

liquid limit, %.

M

odometer modulus, kPa.

Sy

specific yield.

t

time, s.

T

rainfall duration, s.

Tnormal

reference time for slope-normal pore pressure transmission, s.

Va

advective water front velocity, m/s.

Vs

gravitational water front velocity, m/s.

x

downslope distance, m

Z

vertical distance below the ground surface, m.

Zbed

vertical depth of the impermeable bedrock, m.

α

slope angle, degree.

β

slope of the steady state pressure head distribution with depth, deg.

Δψpk

variation of pressure head at peak, m.

Δt0

lag time between rainfall onset and sensor response, s.

Δtpk

lag time between sensor response and pressure peak, s.

γd

dry unit weight of the soil, kN/m3.

ɛv

volumetric deformation.

θ

volumetric soil water content.

θsat

volumetric soil water content at saturation.

σv0

vertical effective stress, kPa.

ψ

pressure head, m.

ψ0

pressure head at the beginning of the rainfall event, m.

ψpk

pressure head at peak, m.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Rocca Pitigliana Test Site
  5. 3. Monitoring System
  6. 4. Observed Pore Pressure Response
  7. 5. Hydrologic Modeling
  8. 6. Discussion
  9. 7. Conclusions
  10. Notation
  11. Acknowledgments
  12. References
  13. Supporting Information
FilenameFormatSizeDescription
jgrf689-sup-0001-t01.txtplain text document0KTab-delimited Table 1.
jgrf689-sup-0002-t02.txtplain text document0KTab-delimited Table 2.
jgrf689-sup-0003-t03.txtplain text document0KTab-delimited Table 3.
jgrf689-sup-0004-t04.txtplain text document0KTab-delimited Table 4.

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