Use of Vacuum for the Stabilization of Dry Sand Slopes

Transcription

1 Use of Vacuum for the Stabilization of Dry Sand Slopes B. Bate, A.M.ASCE 1 ; and L. M. Zhang, M.ASCE 2 Downloaded from ascelibrary.org by Hong Kong Univ Of Science & on 01/12/13. Copyright ASCE. For personal use only; all rights reserved. Abstract: Vacuum is proposed as a means for rescuing soil slopes showing signs of impending failure. Two aspects associated with the proposed method were studied; namely, the theory of airflow through dry soils and the effectiveness of vacuum for enhancing the stability of soil slopes. A model test device was developed, and two series of tests were carried out using this device. One was a series of tests on pore-air pressure distributions in dry sand slopes, and the second series involved dry sand slope stability tests. The results revealed that a vacuum (negative pore-air pressure) even as small as 20.4 kpa significantly increased the stability of the model slopes with dimensions of m (length 3 width 3 height). The pore-air pressure distributions in the model slopes were simulated using a finite-element partial differential equation solver, FlexPDE. Fick s law and mass conservation were used to formulate the airflow through dry soils. Good agreement was achieved between the experiment results and the numerical simulations. A computer routine, called Slope-Air, was developed for slope stability analysis using Bishop s simplified method and considering the pore-air pressure distributions in the slope. The calculated factors of safety of the model slopes at failure were consistent with the results of the model slope stability tests. DOI: /(ASCE)GT American Society of Civil Engineers. CE Database subject headings: Airflow; Slopes; Slope stability; Vacuum; Seepage; Sand (soil type). Author keywords: Airflow; Slopes; Slope stability; Stabilization; Vacuum; Seepage. Introduction Many analyses in geotechnical engineering assume that the soil is fully saturated or that the pore air in the soil is fully connected to the, and in this way the gauge pore-air pressure is zero. Such analyses may not be applicable to a range of practical problems where the pore-air pressure is not equal to atmospheric pressure, such as vacuum stabilization, methane hydrate exploration, and soil vapor extraction. In response to elevated pore-air pressures in soil, the net normal stress decreases. Accordingly, the shear strength and stiffness of the soil can be significantly reduced (Wheeler et al. 1991; Fredlund and Rahardjo 1993; Duffy et al. 1994). Consequently, the short-term stability of slopes or the load capacity of foundations will be decreased, while the slope deformations will be larger. Fredlund and Rahardjo (1993) estimated the pore-air pressures in a dam at the end of construction and analyzed the stability of the dam. It was found that ignoring the influence of pore-air pressure could result in a 15e34% overestimate of the factor of safety and thus lead to an unsafe design. Previous studies have emphasized the adverse effects of pore-air pressure on the stability and deformation of soil masses. Yet, it is possible to apply pore-air pressure in a positive way. In fact, vacuum technology has been used successfully to improve soft soil foundations 1 Assistant Professor, Dept. of Civil, Architectural, and Environmental Engineering, Missouri Univ. of Science and Technology (formerly Univ. of Missouri-Rolla), Rolla, MO (corresponding author). bate@mst.edu 2 Professor, Dept. of Civil and Environmental Engineering, The Hong Kong Univ. of Science and Technology, Clear Water Bay, Hong Kong. cezhangl@ust.hk Note. This manuscript was submitted on May 2, 2011; approved on March 13, 2012; published online on March 15, Discussion period open until June 1, 2013; separate discussions must be submitted for individual papers. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 139, No. 1, January 1, ASCE, ISSN /2013/1-143e151/$ (Harvey 1997; Shang et al. 1998; Chu et al. 2000; Tang and Shang 2000). Vacuum technology was also reported to have been applied to rock slopes at a surface mining site to enhance the slope stability (Brawner and Cavers 1986), as well as to horizontal drains to stabilize landslides (Arutiunian 1983; Arutjunyan 1988; Pakalnis et al. 1983a; Brawner 2003). Early applications of the vacuum technique in slope stability, however, did not gain enough attention, and have not led to further employment of vacuum techniques in recent decades. The reason may be attributed to the heterogeneous nature of the groundwater system and the soil stratum, the insufficient techniques of sealing, and the complex field operation, which make it hard to distinguish the effect of vacuum from other means, that is, local stress relief by a dragline in a tar sand mine (Pakalnis et al. 1983b). However, because the vacuum consolidation technique and the development of geomembrane liners have become more mature in recent years (Thevanayagam et al. 1994), vacuum-assisted slope stabilization has promising applications. In this study, the mechanisms of vacuum technology in the stabilization of dry soil slopes were investigated, and vacuum technology was proposed for the emergency rescue of active landslides. The concept involves a proposed vacuum rescue system that applies a vacuum to an enclosed soil mass (e.g., cut slope, fill slope, or fill behind a retaining wall). The enclosure can be formed by existing protection layers (e.g., shotcrete, chunan, masonry, or concrete walls) or a geomembrane that can be quickly installed in the field. Once prefailure signs are diagnosed on a slope or a retaining wall, the vacuum rescue system can be mobilized immediately to stabilize the slope or retaining wall and to avert disastrous consequences. The vacuum technique provides temporal support of the slope, although conventional approaches to slope improvement, such as slope modification, earth buttresses, and restraining structures (Mitchell 1981; Turner and Schuster 1996) are still needed. A preliminary study was undertaken to better understand the poreair pressure distributions caused by external vacuum points and the effect of applied vacuum on slope stability. This preliminary study had the following objectives: (1) to perform numerical analysis of JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013 / 143

2 two-dimensional (2D) steady-state airflow through dry sand, (2) to investigate the influence of vacuum on the stability of soil slopes and to quantify the influence using a limit equilibrium method, and (3) to conduct model tests to verify the numerical analyses and estimate the effectiveness of vacuum stabilization. Theories of airflow through dry soils, mechanisms of using vacuum for soil slope stabilization, and slope stability analysis that consider the influence of pore-air pressures were studied first. Then a series of model tests was conducted to investigate steady-state flow of air in dry sand slopes and the stability of dry sand slopes subjected to vacuum. Finally, 2D numerical analyses were conducted to simulate the airflow in the models, and the slope stability analyses were performed to calculate the factors of safety of the model slopes. Numerical Simulation Scheme Theory of Airflow in Dry Soils The rate of airflow through soil can be related to the air pressure gradient according to Fick s law (Fredlund and Rahardjo 1993) m t ¼ 2 k a u a g z where m= t 5 mass of air flowing through a unit area of air-filled pore space in unit time; k a 5 air coefficient of permeability; u a 5 pore-air pressure; u a = z 5 pore-air pressure gradient through the soil along the z-direction; and g 5 gravitational constant. An experimental study of airflow by Blight (1971) has shown that Fick s law gives a satisfactory approximation of test results. The air coefficient of permeability of a dry soil is usually much larger than its water coefficient of permeability (Fredlund and Rahardjo 1993; Ba-Te 2005). Therefore, under constant flux conditions, steady-state airflow can be reached in a relative short time in dry soil. The following assumptions were made: (1) the soil is nondeformable or there is no change in total stresses, (2) the soil is homogeneous and isotropic, and (3) the airflow through the dry soil only involves single-phase flow. Based on the conservation of mass and Fick s law, the 2D airflow continuity equation can be expressed as 2 u a x 2 ð1þ þ 2 u a z 2 ¼ 0 ð2þ where x and z 5 coordinates. Eq. (2) was used as the governing equation for numerical simulation of pore-air pressure distributions in model soil slopes. Also, a finite-element partial differential equation solver, FlexPDE (PDE Solutions Inc. 2011), was used to obtain a solution. Mechanisms for Use of Vacuum in Soil Slope Stabilization Vacuum can help stabilize a soil slope by two mechanisms, namely, an increase in the shear strength of soil and the acceleration of drainage. The shear strength of an unsaturated soil can be expressed in terms of two independent stress-state variables ðs 2 u a Þ and ðu a 2 u w Þ as follows (Fredlund et al. 1978): t f ¼ c9 þðs 2 u a Þ f tan f9 þðu a 2 u w Þ f tan f b ð3þ where t f 5 shear strength; c9 5 effective cohesion intercept; ðs 2 u a Þ f 5 net normal stress at failure; u a 5 pore-air pressure; u w 5 pore-water pressure; f9 5 effective angle of shearing resistance; f b 5 angle indicating the rate of change in shear strength relative to the change in matric suction ðu a 2 u w Þ f.eq.(3) is known as the extended Mohr-Coulomb failure criterion. In vacuum stabilization, there is no increase in total stresses (Leong et al. 2000). However, when vacuum (i.e., negative pore-air pressure) is applied to asoilmass,the net normal stress ðs 2 u a Þ increases. As a result, in the case of the vacuumstabilized dry sand slopes where the suction term does not contribute, this leads to an increase in the shear strength t f,asshownineq.(3).the shear-strength increment will increase the stability of the slopes against shallow failure. In the case of vacuum-stabilized unsaturated soil slopes, in addition to the increase in the net normal stress, ðu a 2 u w Þ will also increase because of the accelerated drainage of the pore water by vacuum. In the matric suction range that vacuum can create (,100 kpa), it is most likely that the friction angle f b associated with matric suction is not zero (Fredlund et al. 1978; Vanapalli et al. 1996). As a result, the shear strength of the soil will increase. Furthermore, the shear strength can also be enhanced by possible density increase as aresultofthecompressionofthesoilundervacuumpressure. Slope Stability Analysis Considering Pore-Air Pressure Effects Fredlund and Rahardjo (1993) derived a general limit equilibrium method for calculating the factor of safety of soil slopes, including the effect of pore-air pressure. In a general limit equilibrium formulation, the factor of safety is defined as the factor by which the cohesion and the coefficient of friction must be divided to drive the slope to a limit equilibrium state (Duncan 1996). The slip surface can usually be assumed to be circular, with little inaccuracy, unless there are geological controls that constrain the slip surface to a noncircular shape (Duncan 1996). Adopting assumptions made by Bishop (1955), the resultant interslice shear forces can be ignored. The Fredlund-Rahardjo formulation (Fredlund and Rahardjo 1993) can then be simplified as FS ¼ where N i ¼ Pi5n i ¼ 1 ( c i 9 b i R þ W i 2 c i9 b i sin a i FS " N i 2 u wi b i tan f b i tan f i 9 2 u ai b i Pi5n i ¼ 1 W i x i 1 2 tan fb i tan f i 9!# R tan f i 9 ) ð4þ b þ u i sin a i ai tan f9 FS i 2 tan f b b i þ u i sin a i wi tan f b i FS cos a i þ sin a i tan f9 i FS where n 5 number of slices; FS 5 factor of safety; R 5 radius for a circular slip surface; W i 5 total weight of the ith slice with a base sloping distance of b i ; N i 5 total normal force on the base of the ith slice; u ai and u wi 5 pore-air and pore-water pressures at the base of the ith slice; a i 5 angle between the tangent to the center of the base of the ith slice and the horizontal; c i 9, f i 9, and f b i 5 effective cohesion intercept, effective angle of shearing resistance and angle related to the change in matric suction at the base of the ith slice, respectively; and x i 5 horizontal distance from the centerline of the ith slice to the center of rotation. The angle f b begins to deviate from the effective friction angle as the soil desaturates at suctions greater than the air-entry value (Vanapalli et al. 1996). As the soil suction reaches the residual suction, f b appears to approach a value close to zero. For the dry clean sand, ð5þ 144 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013

3 the residual suction must have been exceeded. Therefore, f b is set to zero. Pore-water pressures in the dry sand are also set as zero. In this study, a computer routine called Slope-Air (Ba-Te 2005) was developed to analyze the stability of unsaturated soil slopes, by which distributed pore-air and pore-water pressures could be considered simultaneously. The method of slices, as shown in Eqs. (4) and (5), was used, and circular slip surfaces were assumed for uniform soil. The results of pore-air pressure distribution, calculated using FlexPDE, are mapped onto the soil slope profile. The pore-air pressures along a slip surface can be used to calculate the factor of safety along that surface. A grid-and-radius scheme was adopted to find the location of the center of the critical slip surface and the radius corresponding to the minimum factor of safety. An effective peak friction angle of 34 (corresponding to the relative density of 75%) was selected based on Cai s (2001) triaxial test results. Materials and Experimental Setup of Model Slope Tests Model Testing Devices A rotatable box was designed and built for the experimental study. The main components are a rotatable acrylic model box ( m, length 3 width 3 height), a stand on which the box could rotate, a vacuum supply system, and measuring devices. The model soil slope was prepared in the box. Dry sand was used to form the model and simulate the steady-state condition of the vacuum drainage of a slope. The omission of capillary water in the model box singled out the effect of vacuum on net normal stress and got rid of the effect of matric suction. A latex membrane was applied to cover the top of the slope to hold the vacuum. During testing, negative pore-air pressures were applied to the model soil slope. The negative air pressure was supplied by a vacuum pump and controlled by pressure regulators. The box could be rotated and fixed at any angle between 0 and 40. 2D airflow conditions were simulated by using perforated strips as vacuum inlets and outlets. Air pressure measuring tips were installed inside the model soil slope through predrilled holes that were aligned in two rows in the acrylic wall. A digital pressure switch (SMC series ZSE40F) was used to display the pore-air pressure. The resolution of this vacuum gauge was 0.1 kpa. Two video cameras were installed orthogonal to each other to record the failure of the soil slope. Soil Properties and Sample Preparation Uniform Leighton Buzzard sand (Fraction E) was used to form the model slope. This soil was fine and uniform uncrushed silica sand whose grain size ranged between 0.09 and 0.15 mm (Table 1). A dry pluviation method was used to prepare the model sand slope. Two main factors affect the density of the sand; namely, mass pouring rate and pouring height (Takemura et al. 1998; Ueno 1998). The pouring rate was carefully controlled using a scoop. Calibration between the free fall height and the relative density was conducted at four different free-fall heights. The average density values from those test results are plotted in Fig. 1. A free-fall distance of 790 mm was selected for final model preparation. The corresponding relative density of the sand was 75%. Based on Cai s (2001) triaxial test results, the extrapolated peak friction angle of the sand at a relative density of 75% was approximately 34. This was also assumed to be the effective angle of internal friction, f9, for Eqs. (4) and (5). The critical state friction angle of this sand was 29.7 (Cai 2001). The prepared rectangular trapezoidal model slope was 0.9 m in length and 0.28 m in height, with an initial slope angle of Table 1. Properties of Leighton Buzzard Sand (Fraction E) (data from Cai 2001; Haigh et al. 2000) Property Pore-Air Pressure Distribution Tests Pore-air pressure distribution tests were carried out at the boundary conditions as shown in Fig. 2 and Table 2. These boundary conditions differed in the magnitude of the applied vacuum, the locations of the vacuum sources, and the location of the vent to the. Readings were taken after the pore-air pressures had reached a steady state (normally less than 1 min). Slope Stability Tests Value Specific gravity, G s Uniformity coefficient, C u Maximum dry density (kg/m 3 ) 1, Minimum dry density (kg/m 3 ) 1, Minimum void ratio Maximum void ratio Coefficient of water permeability at e 5 0:72ðm=sÞ Critical friction angle, f crit ðdegreesþ Effective friction angle, f9ðdegreesþ Effective cohesion, c9ðkpaþ Grain size D 10 (mm) Grain size D 50 (mm) Grain size D 60 (mm) Fig. 1. Calibration of the relationship between free-fall height and relative density of dry Leighton Buzzard sand (Fraction E) First, a reference model Test T1, in which the slope was exposed to the, was brought to failure by rotating the model box. Then, one slope stability test was performed with a uniformly distributed vacuum inside the soil slope (T2), followed by two model slope tests with nonuniform pore-air pressure distributions (T3 and T4). During Tests T2 and T3, a suitable vacuum pressure was first applied to the model. After the steady-state pore-air pressure distributions had been measured, the models were tilted slowly in stages to failure or to the maximum slope angle (58 ). The slope angle increment in each stage was approximately 5. In model Test T4, a large vacuum ( 15 kpa) was first applied to the model. The model was then raised to a slope angle of 45 in stages, and after that, JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013 / 145

4 the magnitude of the applied vacuum was reduced in stages until the slope failed. The test conditions for the four model slope stability tests are summarized in Table 2. Results and Discussions Pore-Air Pressure Distribution Fig. 2. Model soil slope dimensions and points of air pressure source and measurement Table 2. Pore-Air Pressure Distribution Tests and Model Slope Stability Test Schemes Model slope test number The 2D flow condition was checked by measuring the air pressures at the 2D coordinate of (0.51, 0) and three different positions normal to the 2D plane (Fig. 2). The results of pore-air pressure measurements are shown in Fig. 3. The differences among three pressure values at three positions normal to the 2D plane were 0.1 kpa for Test A1 and 0 kpa for Tests A2, A3, and T3. The 2D flow condition, created by the perforated strip vacuum source, was validated. Figs. 3(a and b) show the pore-air pressure distributions at source vacuums of 24.0 and kpa, respectively. The boundary conditions were the same. The resulting pressure contours were similar in shape and different in magnitude. The magnitude of air pressure was proportional to the magnitude of the applied vacuum. This behavior occurred because Eq. (2) is a linear partial differential Air pressure distribution (kpa) a b c d e equation. As long as the boundary conditions do not change, the computed steady-state pressure at any point will be linearly proportional to the source pressure. Fig. 3 also indicates that the measured air pressure values were generally in good agreement with the calculated ones. Fick s law is capable of describing the steady-state airflow through the dry homogeneous sand. A few mismatches between the measured and calculated air pressure results were observed. The largest mismatch was at coordinate (0.28, 0.05) in Test A1. The measured vacuum was 21.3 kpa, while the calculated one was between 21.6 and 21.7 kpa. The problem may be associated with connections of the tubings. However, the difference of all of the rest of the measurements was no larger than 0.2 kpa. This difference was primarily caused by the limited resolution of the digital vacuum gauge, which was 0.1 kpa. The resolution was of high precision for normal usage. However, the vacuum in the soil slopes at failure was less than 0.6 kpa. A higher precision vacuum gauge is recommended for future research. Slope Stability Slope angle at failure (degrees) Air pressure Test A Open to the Sealed boundary Sealed boundary Sealed boundary Air pressure Test A Open to the Sealed boundary Sealed boundary Sealed boundary Air pressure Test A3 Sealed boundary Sealed boundary Open to the Slope stability Test T1 Sealed boundary Open to the Open to the Open to the Sealed boundary 34 Slope stability Test T2 Sealed boundary 20.4 Sealed boundary Sealed boundary Sealed boundary 58 Slope stability Test T3 Open to the 20.5 Sealed boundary Sealed boundary Sealed boundary 58 Slope stability Test T4 Sealed boundary Sealed boundary Open to the 45 Note: The locations of points a, b, c, d, and e are shown in Fig. 2. The inclination of the model slope was represented by both the angle between the base of the slope and the horizon (BSA) and the angle 146 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013

5 Fig. 3. Pore-air pressure distributions in (a) Test A1; (b) Test A2; (c) Test T3; (d) Test A3 between the slope surface and the horizon (SSA). The SSA before failure was the sum of the BSA before failure and the initial slope angle (18.4 ). In Test T1, the slope was stable until the BSA reached 15.6 (i.e., the SSA reached 34 ). When the box was lifted higher, the sand on the slope surface started to slide down until the SSA was restored to 34 [Fig. 4(a)]. The slip surface was essentially planar and shallow throughout the process. In Test T2, a uniformly distributed vacuum of 20.4 kpa was applied to the slope and maintained using a latex membrane. At a BSA of 15.6 (SSA of 34 ), the model slope was stable. When the BSA was further increased, the slope remained stable until the BSA reached 39.6 (SSA at 58 ). At an SSA of 58, the soil on the crest settled by 25 mm [Fig. 4(b)], but no signs of sliding failure were obvious. Compared with the reference test, T1, the stability of model Slope T2 was greatly enhanced by the applied uniform vacuum, even though the magnitude of the vacuum was only 20.4 kpa. The pore-air pressure distribution in Test T3 is shown in Fig. 3(c). As the model was tilted, there was no appreciable slope movement at a BSA of 15.6 (SSA at 34 ). As the BSA reached 35.6 (SSA at 54 ), the soil on the crest started to settle. As the BSA reached 39.6, a large amount of soil on the crest moved downward toward the toe of the slope, as shown in [Fig. 4(c)]. The stability enhancement effect of the nonuniformly distributed vacuum was again significant. The other model, T4, was also subjected to nonuniformly distributed vacuum. There were two vacuum sources on the slope, as shown in Fig. 3(d), and the average vacuum of the two sources was taken as the magnitude of the applied vacuum. The slope was initially subjected to a large vacuum of 210 kpa and was tilted to absaof26.6 (or an SSA of 45 ). Afterward, the vacuums at the two sources were gradually reduced. The vacuum distribution shortly before the onset of failure is shown in Fig. 3(d), where the average applied vacuum was 20.6 kpa. When the average applied vacuum was further reduced to 20.3 kpa, a rupture surface starting from the crest developed rapidly. The sand in the lower middle of the slope moved toward the toe, and the soil near the crest settled substantially. Retrogressing slope failure was recorded. Within 5 min, the slope surface had become parallel to the box base. Fig. 4(d) shows a circular slip surface observed during the failure progress. Failures in dry cohesionless slopes are generally planar. Under the applied vacuum, the dry sand in the models exhibited an apparent cohesion (i.e., a shear-strength increment because of the increased net normal stress). Therefore, failure along a circular shear zone could develop. After the failure occurred, the pre-embedded strips and tips deviated from the original locations, and the readings were no longer reliable. The stabilizing effect of the nonuniform vacuum in this model was also evident. Another practical implication that can be drawn from this research is that vacuum should be applied to the potential slip failure zone to maximize its effect. In summary, an applied vacuum, whether uniformly distributed or nonuniformly distributed, greatly enhanced the stability of the model slopes. Slope Stability Analysis The stability of model slopes of various inclinations, as shown in Table 2, was analyzed using a self-coded computer program, Slope- Air. In model Test T1, the calculated factor of safety was 1.06 at an SSA of 32 and 1.0 at an SSA of 34, and the predicted slip surface was planar and cut the slope surface. In model slope Tests T2, T3, and T4, the centers of possible slip surfaces were plotted in the region to the upper left of the slope (Fig. 5). The minimum factor of safety corresponding to each center was determined by varying the radius of the possible slip surface. Then, the contours of the factor of safety at each grid point in the region were plotted, as shown in Figs. 5(aec). The critical slip surfaces corresponding to the minimum factor of safety were also plotted. The computed relationships between the factor of safety and the SSA for Models T1, T2, and T3 are shown in Fig. 6. With a particular pore-air pressure distribution, the factor of safety decreased with the SSA. At a particular SSA, the factors of safety of the slopes stabilized by vacuum were predicted to be much higher than those at zero poreair pressure. When the SSA reached 34, a slope without vacuum stabilization would fail, and the factor of safety was equal to unity. However, when a uniform vacuum of 20.4 kpa was applied, the slope would not fail until an SSA larger than 45 was reached. Similarly, when the nonuniform vacuum field of T3 was applied [Fig. 3(c)], the model predicted that the stability of the slope would be greatly enhanced and the slope would not fail until the SSA was close to 50. The calculated factors of safety for model Tests T2 and T3 at failure (SSA of 58 ) were 0.91 and 0.90, respectively. The JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013 / 147

6 Fig. 4. Failure of model slope: (a) Test T1, angle between the base of the slope and the horizon ; inset: transverse view; (b) Test T2, angle between the base of the slope and the horizon ; (c) Test T3, angle between the base of the slope and the horizon ; (d) Test T4, angle between the base of the slope and the horizon ; note the circular slip surface in T4 critical slip surfaces are shown in Figs. 5(a and b). The calculated failure patterns and the locations of the slip surfaces were similar to those seen in the model tests [Figs. 4(b and c)]. However, the calculated factors of safety were slightly smaller than 1.0. Side friction and restraint from the latex membrane were two possible reasons, as subsequently discussed. In Test T4, a slope was initially subjected to a large vacuum and tilted to an SSA of 45. Failure of the slope was then obtained by reducing the applied vacuum in stages. The computed relationship between the average applied vacuum at the two sources and the factor of safety is shown in Fig. 7. As expected, the factor of safety decreased as the vacuum decreased. At the onset of failure of the slope, the measured average applied vacuum was 20.3 kpa. Because of the rapid development of failure, the pore-air pressure distribution in the slope at the applied vacuum level could not be measured. As a result, the calculated pore-air pressure distribution corresponding to the measured applied vacuum (20.3 kpa) was used in the slope stability analysis. The calculated pressures were essentially proportional to those shown in Fig. 3(d). The calculated factor of safety at failure was 1.01, which was consistent with the test results. Slope-Air predicted deep slip surfaces, which were close to the toe of the slopes (Tests T2, T3, and T4). The model test results agreed with this prediction in general. However, the failure surface was slightly shallower than predicted, especially in the case of Test T4 (Fig. 5). Two factors led to this observation; namely, the vacuuminduced side friction and the membrane effects. The vacuum-induced side friction was most significant at the toe and in the crest region, where the height of the soil column was small. When the soil was about to move, tensile stresses of the membrane developed near the toe, while relatively smaller tensile stresses developed near the crest because of the geometry of the soil slope. Therefore, the soil in the toe area was restrained, and the slip surface was slightly shallower. Boundary Effects of Model Slope Tests To account for side boundary effects in the model slope tests, a threedimensional slope stability analysis was conducted on each of the test models (T2, T3, and T4). A closed-form solution developed by Gens et al. (1988) for cohesive soils was adopted as the starting point of this analysis. The solution assumed that the model side boundaries were vertical surfaces, which was the case in this study. The threedimensional factor of safety ðf 3 Þ as a function of the 2D factor of safety ðf 2 Þ is expressed as F 3 ¼ F þ 2M E A bqc 5 ð6þ R L where M E 5 first moment of area of each side plane of slip soil about the center of the circular slip surface; L 5 length of the slip surface in the transverse direction (0.5 m in the model tests); R 5 radius of the slip surface; and ðabqcþ 5 length of the circular slip surface. Results of calculations using Eq. (6) indicated that the factors of safety from the three-dimensional analysis were 7.57, 7.65, and 7.44% higher than those from the 2D analysis for model slope Tests T2, T3, and T4, respectively. The side boundary effects were consistent for Tests T2, T3, and T4, and yielded an average of 7.5% increase in factors of safety / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013

7 Eq. (6) is for cohesive soils, where undrained shear strength was used for the strength of soil and soil-boundary interface. For cohesionless soil, the results needed to be adjusted as shown in Eq. (7) 2 3 2M F 3 ¼ F 2 41 þ E A bqc s h tan u95 ð7þ s v tan f9 R L Downloaded from ascelibrary.org by Hong Kong Univ Of Science & on 01/12/13. Copyright ASCE. For personal use only; all rights reserved. Fig. 5. Factor of safety contours of model (a) Slope T2; (b) Slope T3; (c) Slope T4; the critical slip surface corresponds to the minimum factor of safety where s v tan f9 5 strength along the slip surface; s h tan u9 5 shear strength along the side boundary; f9 5 friction angle of soil; and u9 5 friction angle between the soil and the side boundary. From the angle of repose in Test T1, f9 and u9 do not deviate much. Therefore, they are assumed to be equal. Horizontal stress s h along a vertical slice of the soil column can be approximately related to the vertical stress at the slip surface, s v, by s h 5 ð2=3þs v K 0, where K 0 is the coefficient of earth pressure at rest. According to Jaky s rule, K sin f sin :44. Therefore s h 5 ð2=3þs v 3 0:44 5 0:29 s v. As a result, ðs h tan u9þ=ðs v tan f9þ in Eq. (7) equals 0.29, and 0:29 3 7:5% 5 2:2%. Therefore, the side boundary effects will lead to underestimation of the three-dimensional factors of safety by only 2.2% compared with the 2D factors of safety. Eq. (7) also needs modification to account for the effect of vacuum. The vacuum effect can be evaluated taking model Test T2, for example. The vacuum is 0.4 kpa uniformly in Test T2. The ðs h tan u9þ=ðs v tan f9þ term becomes ðs h þ 0:4 kpaþtan u9 ðs v þ 0:4 kpaþtan f9 The average height of the soil slices is m. Given a relative density of 75% and a specific gravity of 2.65, the density of the soil slope is about 2,000 kg/m 3. Consider a soil slice m in height, the average magnitude of the vertical stress at the slip surface is s v 5 2;000 kg=m 3 3 9:8kN=kg 3 0:156 m 5 3:1 kpa. Then the horizontal stress s h is 0.9 kpa. Substituting s v and s h in Eq. (8) yields Therefore, the side boundary accounts for about 0:37 3 7:5% 5 2:8% increase in the factor of safety in the three-dimensional analysis. Near the toe and crest of the slope, the vacuum effect would become more marked because of the smaller heights of the soil slices, and the side friction would be larger. The calculated results of the factors of safety in Tests T2 and T3 were 0.91 and 0.90, respectively. Considering the side boundary effects (2.8% increase), values of the three-dimensional factors of safety for Tests T2 and T3 became 0.94 and 0.93, respectively. Thus, the calculated factors of safety improved. Implications on Engineering Practice This study investigated the effects of vacuum on the stability of dry soil slopes. Whereas unsaturated soils were most likely encountered in the field, either the in situ soil was unsaturated initially, or the soil was saturated initially but became unsaturated as the vacuum was applied. As vacuum was applied to the soil, the soil-water content decreased first, then equilibrium was reached with the applied vacuum that could be pinpointed in the drying cycle of a soil-water characteristic curve (Fredlund and Xing 1994). Sand usually possessed higher hydraulic conductivity than clay, and therefore the vacuum reached equilibrium faster, and the stabilization effect was quicker. On the other hand, the sealing of vacuum in sand was more difficult. If top fine-grained soils were not present, a sealing layer might be required. Experimental justification for unsaturated soil ð8þ JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013 / 149

8 Fig. 6. Factor of safety of model Slopes T1, T2, and T3 at different slope surface angles Fig. 7. Factor of safety of model Slope T4 at different applied vacuum values slopes with both air and water flows are not provided, but appropriate experiments should be conducted before the new technique is applied. Conclusions The following conclusions can be drawn: Vacuum is proposed as a means for rescuing soil slopes that show signs of impending failure. Two aspects of the proposed method, airflow through dry soils and the effectiveness of vacuum stabilization, were studied. Pore-air pressure distribution tests and slope stability tests were carried out at model scale to study these two aspects, and numerical procedures were developed to analyze these problems. Two series of 2D pore-air pressure tests were carried out. The first series of experiments was performed keeping the locations of vacuum sources and vents to the unchanged, while changing the magnitude of the vacuum pressure. The observed pore-air pressure at a particular location in the model slope was approximately proportional to the applied vacuum level. The second series of experiments was performed by changing the boundary conditions. The measured pore-air pressure distribution was strongly influenced by the boundary conditions. The 2D airflow through dry sand was simulated numerically based on Fick s law and the law of mass conservation. The governing partial differential equation was solved using a finite-element solver, FlexPDE. The calculated pore-air pressure distributions at various vacuum levels and the three boundary conditions were in good agreement with those measured in the model tests. Four series of slope stability tests, including models subjected to uniform vacuum and nonuniform vacuum distributions, were performed to study the influence of vacuum on the stability of the soil slopes. Vacuum dramatically increased the stability of the model slopes. In Model T2, the application of a uniform vacuum of 20.4 kpa increased the failure slope angle from 34 to 58. In model Tests T3 and T4, which were subjected to distributed vacuums, the model slopes were also significantly stabilized, failing at large slope angles of 45 and 58, respectively. A computer program, Slope-Air, was written to analyze the stability of the model soil slopes subjected to airflow. Bishop s simplified method of slices and the extended Mohr-Coulomb shear-strength criterion were used. The pore-air pressures predicted through finite-element analysis were mapped for the slope stability analysis. The calculated factors of safety at failure were consistent with the results of the model slope stability tests. This study provides a theoretical framework of numerical analysis of soil stability involving air and water flows. The framework for dry soil slopes with air pressures was examined and validated. Further justification for unsaturated soil slopes with both air and water flows should be conducted before the application of this framework. The methodology has a broad range of applications in geoenvironmental engineering and clean energy, such as soil vapor extraction, carbon dioxide sequestration, and methane hydrate exploration. Acknowledgments The Research Grants Council of Hong Kong SAR (Project No ) and the Materials Research Center at the Missouri University of Science and Technology are gratefully acknowledged for their substantial support. References Arutiunian, R. N. (1983). Vacuum-accelerated stabilization of liquefied soils in landslide body. Proc., 8th Eur. Conf. Soil Mech. Found. Eng.: Improve. Ground, A.A. Balkema, Rotterdam, Netherlands, 575e576. Arutjunyan, R. N. (1988). Prevention of landslide slope process by vacuuming treatment of disconsolidated soils. Proc., 5th Int. Symp. Landslides, A.A. Balkema, Rotterdam, Netherlands, 835e837. Ba-Te. (2005). Flow of air-phase in soils and its application in emergent stabilization of soil slopes. Master of Philosophy thesis, The Hong Kong Univ. of Science and Technology, Hong Kong. Bishop, A. W. (1955). The use of the slip circle in the stability analysis of slopes. Geotechnique, 5(1), 7e17. Blight, G. E. (1971). Flow of air through soils. J. Soil Mech. Found. Div., 97(4), 607e624. Brawner, C. O. (2003). Engineer Around the world in fifty years, Bitech, Richmond, British Columbia, Canada. Brawner, C. O., and Cavers, D. S. (1986). Recent developments in rock characterization and rock mechanics for surface mining. Proc., Int. Symp. Appl. Rock Character. Mine Design, Society of Mining Engineers of AIME, Littleton, CO, 43e55. Cai, Z. Y. (2001). A comprehensive study of state-dependent dilatancy and its application in shear band formation analysis. Ph.D. dissertation, The Hong Kong Univ. of Science and Technology, Hong Kong. 150 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING ASCE / JANUARY 2013

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