Landslide dams formed by rock avalanche processes usually fail by seepage erosion. This has been related to the complex sedimentological characteristics of rock avalanche dams which are mostly dominated by fragmented and pulverized materials. This paper presents a comprehensive experimental programme which evaluates the critical hydraulic and geometrical conditions for seepage-induced failure of landslide dams. The experiments were conducted in a flume tank specifically designed to monitor time-dependent transient changes in pore-water pressures within the unsaturated dam materials under steady-state seepage. Dam models of different geometries were built with either mixed or homogeneous materials. Two critical hydraulic gradients corresponding to the onset of seepage erosion initiation and collapse of the dam crest were determined for different upstream inflow rates, antecedent moisture contents, compactive efforts, grain size ranges, and dam geometries.
Results
Two major types of dam failure were identified: Type I and Type II. These were further subdivided into minor failure processes which include exfiltration, sapping, downstream toe bifurcation, and undermining of the downstream face. The critical hydraulic gradients for seepage erosion initiation varied from 0.042 to 0.147. Experiments conducted with the mixed materials indicate that the critical hydraulic gradients for collapse of the dam crest increased with an increase in uniformity coefficient.
Conclusions
The deformation behaviour of the dams was significantly influenced by particle density, pore geometry, hydraulic conductivity, and the amount of gravel and pebbles present in the materials. The results indicate that the critical seepage velocity for failure of the dams decreased with an increase in downstream slope angle, but increased with an increase in pore geometry, dam height, dam crest width, upstream inflow rate, and antecedent moisture content.
Keywords
ExfiltrationSappingHydraulic gradientCritical seepage velocityWetting front propagationDownstream slope saturation
Background
Landslide dams and other natural river blockages such as moraine dams and glacier-ice dams are formed in narrow valleys bordered by oversteepened slopes. Active geological processes in these settings such as erosion and weathering often lead to the availability of highly fractured and hydrothermally altered bedrock which constitute source materials for hillslope processes and landslide dam formation (Costa and Schuster 1988; Clague and Evans 1994; Korup et al. 2010). These potentially dangerous natural phenomena occur mostly in seismically-active regions where high orographic precipitations on rugged mountain terrain associated with frequent earthquakes and snowmelt contribute to several geological processes that lead to mass wasting and river-damming landslides (Korup and Tweed 2007; Allen et al. 2011; Evans et al. 2011; Crosta et al. 2013). Failure of landslide dams could trigger the sudden release of stored water masses from lakes created by these damming events. This consequently produces catastrophic outburst floods and debris flows that inundate the downstream areas, causing loss of lives and infrastructural damage (O'Connor and Costa 2004; Bonnard 2011; Plaza et al. 2011). For example, the worst recorded case of landslide dam disaster occurred during the 1786 Kangding-Luding earthquake in Sichuan Province, southwest China (Dai et al. 2005). The earthquake triggered a huge landslide which dammed the Dadu River but failed ten days later and generated a catastrophic outburst flood that drowned more than 100,000 people. Similarly, Chai et al. (2000) presented a comprehensive account of the catastrophic failure of three landslide dams (Dahaizi, Xiaohaizi, and Deixi), triggered by the August 1933, Ms 7.5 earthquake in Diexi town, Sichuan Province, China. These landslide dams failed two months later, triggering catastrophic outburst floods that traveled more than 250 km downstream, and claimed about 2,423 lives. Therefore, timely evaluation of landslide dams is important for prevention of catastrophic dam failures and mitigation of disasters caused by downstream flooding of the released water masses.
Seepage erosion is one of the undermining factors affecting the stability and long-term performance of landslide dams and embankment dams. Many civil engineering and geoenvironmental studies have defined subsurface erosion processes by several terms such as piping, heave or blowout, seepage erosion, tunneling or jugging, internal erosion and sapping or spring sapping (Zasłavsky and Kassiff 1965; Jones 1981; Higgins 1982, 1984; Hutchinson 1982; Hagerty 1991; Wörman 1993; Terzaghi et al. 1996). However, a few researchers have made clear distinctions between the different processes involved in soil destabilization caused by seepage and piping (Jones 1981; Bryan and Yair 1982; Dunne 1990). The role of seepage in increasing positive pore-water pressure and causing apparent reduction of matric suction (ua-uw) in unsaturated soils has been documented in the literature (Fredlund et al. 1978; Lam et al. 1987; Fredlund et al. 2012). Generally, landslide dams, stream banks and soil slopes are composed of unconsolidated materials which exist in unsaturated conditions. The stability of landslide dams in unsaturated conditions depends on the presence of matric suction which increases the shear strength of the soil τ, as described by the equation proposed by Fredlund et al. (1978):
where c’ = effective cohesion of the soil, (σn-ua) = net normal stress on the failure plane, ϕ’ = effective friction angle with respect to the net normal stress, (ua-uw) = matric suction, ϕb = angle that denotes the rate of increase in shear strength relative to matric suction. Transient changes from unsaturated to saturated conditions under steady-state seepage initiate high hydraulic gradients that accentuate subsequent reduction of apparent cohesion of the soil. This, in turn, increases seepage forces that accelerate soil mobilization, exfiltration and downstream entrainment of the eroded soil particles, as described by the equation:
$$ {F}_s={\gamma}_wi $$
(2)
where Fs = seepage force per unit volume, i = hydraulic gradient, γw = unit weight of water. Detailed research on seepage erosion processes in unsaturated soils and the effects of pore-water pressure on the stability of soil slopes have been carried out by Hutchinson (1982), Iverson and Major (1986), Howard and McLane (1988), Fredlund (1995), Skempton and Brogan (1994), Crosta and Prisco (1999), Rinaldi and Casagli (1999), Dapporto et al. (2001), Lobkovsky et al. (2004), Wilson et al. (2007), Fox et al. (2007), Cancienne et al. (2008), and Pagano et al. (2010).
The concept of hydraulic criteria for assessing the likelihood of initiation of internal erosion in soils is based on the hydraulic load acting on a soil particle which must exceed the drag forces of the seeping water. This is related to the critical hydraulic gradient ic, defined as the hydraulic gradient at which the effective stress of the soil becomes negligible. Apparently, a large number of theoretical and experimental approaches have been used to obtain critical hydraulic gradients in embankment dams, levees, dykes and other water-retaining structures. For example, Terzaghi (1943) obtained ic value of 1 for upward directed seepage flow as described by the following equation:
$$ {i}_c=\frac{\gamma \hbox{'}}{\gamma_w} $$
(3)
where γ’ = submerged unit weight of soil, and γw = unit weight of water. However, Skempton and Brogan (1994) observed selective erosion of fines in internally unstable cohesionless soils for upward flow conditions at critical hydraulic gradients (ic = 0.2 ~ 0.34) lower than that obtained from Terzaghi’s classical approach. Similarly, Den Adel et al. (1988) carried out tests for horizontal seepage flow and obtained critical hydraulic gradient values of 0.16 to 0.17 and 0.7 for unstable and stable soils, respectively. Ahlinhan and Achmus (2010) performed experiments with unstable soils for upward and horizontal seepage flows and obtained critical hydraulic gradient values of 0.18 to 0.23. Ke and Takahashi (2012) obtained critical hydraulic gradients of 0.21 to 0.25 for internal erosion with binary mixtures of silica sands under one-dimensional upward seepage flow.
Whilst a lot of research has been done on critical hydraulic gradients for internal erosion, problems still exist in defining and ascribing limit values of hydraulic gradients for seepage erosion. For instance, Samani and Willardson (1981) proposed the hydraulic failure gradient if, defined as the hydraulic gradient at which the shear strength of a confined soil is reduced by the drag forces of the seeping water. Wan and Fell (2004) introduced istart and iboil to represent critical hydraulic gradients for the onset of internal erosion and boiling, respectively. However, the conventional one-dimensional upward seepage tests can only be used to determine the hydraulic criteria for seepage erosion in granular materials with the exclusion of other factors such as dam geometry (dam height, dam crest width, upstream and downstream slope angles), and rate of inflow into the upstream reservoir. Hence, elaborate evaluation of the influence of these geometrical and hydraulic factors on seepage processes in landslide dams would require carrying out flume experiments where the characteristic deformation behaviour of the dam models would allow for accurate determination of the limit values of these hydraulic parameters.
Brief review of seepage erosion in soils
Comprehensive research on seepage erosion and piping mechanisms in landslide dams (Meyer et al. 1994; Davies and McSaveney 2011; Wang et al. 2013; Okeke and Wang 2016; Wang et al. in press), levees and earth embankments (Richards and Reddy 2007), hillslopes (Ghiassian and Ghareh 2008), and stream banks (Fox and Wilson 2010), have all been completed. Variations in experimental results and opinions are strictly based on the design and method of experiment adopted, coupled with size and scale effects arising from the nature of material tested.
Seepage erosion involves the detachment and entrainment of finer soil particles through a porous medium under a hydraulic gradient caused by the seeping water (Cedergren 1977). The various processes involved in seepage erosion mechanisms in hillslopes and landslide dams have been identified. For example, sapping, as defined by Hagerty (1991) involves exfiltration over a broad area on a sloping surface such that large lenticular cavities appear as a result of concentrated seepage which removes soil particles at the exit point and increases the diameter of the evolving channel over time. Iverson and Major (1986) derived a generalized analytical method for the evaluation of seepage forces considering static liquefaction and Coulomb failure under steady uniform seepage in any direction within a hillslope. They observed that slope destabilization occurred as a result of seepage force vector, which represents a body force that corresponds to the hydraulic gradient potential. They concluded that slope stability will invariably occur when the direction of the seepage flow is such that λ = 90°-ϕ, whereas the existence of a vertically upward seepage component results in Coulomb failure at similar conditions required for static liquefaction, especially when the slope angle is more or less equal to φ. Howard (1988) used flume experiments and numerical simulations to evaluate sapping processes and sapping zone morphology in homogeneous, isotropic sand mixtures. His experiments identified three distinct zones at the sapping face: mass wasting zone, sapping zone and fluvial transport zone, whereas numerical simulations performed by Howard and McLane (1988) revealed that the rate of mass wasting at the sapping face is dependent on the rate of sediment transport through the fluvial transport zone.
Perzlmaier et al. (2007) presented an overview of empirically-derived critical hydraulic gradients for initiation of backward erosion in a range of soil types based on field experience in several dams and levees (Table 1). Richards and Reddy (2010) evaluated piping potential in earth structures using a modified triaxial system, referred to as the true triaxial piping test apparatus (TTPTA). This apparatus was designed for controlling confining stresses and determining critical hydraulic gradients and critical velocities required for initiation of internal erosion. Their tests found that the critical hydraulic gradient and the critical seepage velocity for internal erosion in uniform fine-grained quartz sand varied from 1.8 × 10−3 to 2.4 × 10−3 and 8.1 × 10−3 to 1.1 × 10−3 m/s, respectively. They concluded that the critical seepage velocity is an essential parameter for evaluation of piping potentials in non-cohesive soils. Moffat et al. (2011) used a rigid wall permeameter to study internal erosion susceptibility in widely graded cohesionless soils by imposing a unidirectional flow in either upward or downward directions such that a constant average hydraulic gradient was maintained across the specimen. They found that suffusion occurred by ‘episodic migration’ of the finer fraction when the imposed average hydraulic gradient was increased. Chang and Zhang (2012) determined the critical hydraulic gradients for internal erosion under complex stress states using a computer-controlled triaxial testing apparatus which allowed for independent control of hydraulic gradient and stress states. They found that under isotropic stress states, the initiation hydraulic gradient istart increased with an increase in effective mean stress. They further observed that under the same confining stress, the initiation gradients obtained under compression stress states were higher than those obtained under extension stress states. These findings may have cleared up some of the ambiguities associated with critical hydraulic gradients determined under one-dimensional seepage tests as noted by Fell and Fry (2013), due to the inability of the conventional method to monitor stress states of soils.
Table 1
Comparison of empirically-derived critical average gradients ic for initiation of backward erosion and piping in different soil types (Perzlmaier et al. 2007)
However, despite the wealth of research done so far, not much has been reported on the influence of geometrical and hydraulic conditions for seepage erosion development in landslide dams. This paper presents a comprehensive experimental programme conducted to investigate transient pore-water pressure variations and the critical hydraulic gradients for seepage-induced failure of landslide dams. A series of experiments were conducted in a flume tank modified to accurately determine the limit values of hydraulic gradients at the various stages of the dam failure process. This is in contrast to the conventional one-dimensional upward directed seepage tests performed in a modified triaxial chamber. The main objectives of this research are summarized as follows: (1) to determine the critical hydraulic gradients required for initiation iini and failure if of landslide dams under different geometrical and hydraulic conditions, as well as the critical seepage velocities for erosion and debris flow mobilization; (2) to investigate the effects of pore-water pressure during seepage processes and its role in initiating seepage erosion and dam failure; and (3) to identify the various failure mechanisms of landslide dams under steady-state seepage conditions.
Experimental Methods
Testing facility
The experiments were conducted in a rectangular flume tank 2 m long, 0.45 m wide and 0.45 m high. The flume tank was made of 5 mm-thick acrylic sheets (plexiglass) of high transparency which enables visual observation of wetting front propagation, deformation and failure mechanism of the dam models. The flume was tilted to make a bed slope of ψ = 5°. The downstream end of the flume was equipped with two 4 cm-diameter holes for outflow of fluidized sediments. The water entering the upstream reservoir was provided by a rubber hose attached to a water tap while discharge into the upstream reservoir was controlled by a flowmeter connected to the drainage hose. The generation and dissipation of pore-water pressures during the experiments were monitored with three pore-water pressure sensors, hereafter referred to as p1, p2, and p3, with rated capacity of 50 kPa each (Fig. 1a). The sensors were fixed underneath the center of the flume bed through three 10 mm-diameter holes drilled on a horizontal line at the center of the flume bed. The sensors were separated by horizontal distances of 0.1 m and 0.103 m, respectively. Each of the pore-water pressure sensors was equipped with an L-shaped manometer attached to the outer wall of the flume to ensure an equal balance between the fluid pressure and atmospheric pressure. Transient variation in upstream reservoir level was monitored with a water level probe positioned near the toe of the upstream slope. Deformations and settlements caused by seepage and pore-water pressure buildup were monitored with two 0.1 m-range CMOS multi-function analog laser displacement sensors attached to a wooden overboard (Fig. 1b). The two sensors, hereafter referred to as Hd1 and Hd2, were separated by a distance of 0.04 m.
Fig. 1
a Experimental setup. Hd Laser displacement sensors; Ups Upstream water level probe; p1, p2, and p3 Pore-water pressure sensors. b Side view of the flume tank before the commencement of an experiment
Soil characteristics
A series of experiments were conducted using different soils and testing conditions. Table 2 shows a summary of all the experiments conducted under different testing conditions while the results of the critical pore-water pressures and critical seepage velocities obtained from the tests are summarized in Table 3. Uniform commercial silica sand no. 8 was used to build the dam models, except in Exp 1 to 3 where the dam models were composed of different proportions of silica sand nos. 5 and 8, including industrial pebbles and gravel, hereafter referred to as sandfill dam (SD), gravelly dam I (GV-I), and gravelly dam II (GV-II), respectively. The grain size distribution curves of all the materials used are shown in Fig. 2. The mechanical and hydraulic characteristics of the materials used in the experiments are summarized in Table 4. Silica sand nos. 5 and 8 are generally composed of subangular to angular grains with dry repose angles of 32 and 35°, respectively. Constant-head permeability tests and other soil property tests were carried out on the soils based on the physical conditions (bulk density and antecedent moisture content) used in building the dam models in accordance with standards of the Japanese Geotechnical Society (JGS).
Table 2
Summary of all the experiments at different testing conditions
Test specification
Test no.
Dam geometry
Qin (m3/s)
\( \rho \)dry (Mg/m3)
eo
iini-1
iini-2
if1
if2
Tb (s)
Hd (m)
Dcrw (m)
α (deg)
β (deg)
Dam composition
Exp 1
0.25
0.1
40
55
2 × 10−4
1.10
1.41
0.119
0.101
0.77
0.61
340
Exp 2
0.25
0.1
40
55
2 × 10−4
1.56
0.71
0.092
0.123
1.82
0.87
920
Exp 3
0.25
0.1
40
55
2 × 10−4
1.44
0.84
0.053
0.101
1.48
1.20
1360
Rate of inflow into the upstream reservoir (filling rate)
Exp 4
0.25
0.1
35
50
1.67 × 10−5
1.07
1.48
0.097
0.099
1.38
0.90
1750
Exp 5
0.25
0.1
35
50
5 × 10−5
1.07
1.48
0.122
0.089
1.50
0.94
1300
Exp 6
0.25
0.1
35
50
1 × 10−4
1.07
1.48
0.115
0.067
1.48
0.99
1100
Exp 7
0.25
0.1
35
50
1.67 × 10−4
1.07
1.48
0.103
0.08
1.36
1.32
890
Antecedent moisture content at low compactive effort (eo = 1.76)
Exp 8
0.25
0.1
35
55
1.5 × 10−4
0.96
1.76
0.118
0.08
1.70
0.92
800
Exp 9
0.25
0.1
35
55
1.5 × 10−4
0.96
1.76
0.094
0.084
1.59
0.94
720
Exp 10
0.25
0.1
35
55
1.5 × 10−4
0.96
1.76
0.104
0.085
1.57
1.00
680
Exp 11
0.25
0.1
35
55
1.5 × 10−4
0.96
1.76
0.103
0.053
1.40
1.07
620
Antecedent moisture content at high compactive effort (eo = 1.21)
Exp 12
0.25
0.1
35
55
1.3 × 10−4
1.20
1.21
0.087
0.133
1.17
0.64
980
Exp 13
0.25
0.1
35
55
1.3 × 10−4
1.20
1.21
0.147
0.123
1.22
0.70
840
Exp 14
0.25
0.1
35
55
1.3 × 10−4
1.20
1.21
0.093
0.125
1.28
0.95
760
Exp 15
0.25
0.1
35
55
1.3 × 10−4
1.20
1.21
0.042
0.103
1.30
1.00
740
Downstream slope angle
Exp 16
0.25
0.15
35
30
1 × 10−4
1.01
1.62
0.123
0.091
1.01
0.73
2300
Exp 17
0.25
0.15
35
40
1 × 10−4
1.01
1.58
0.091
0.099
1.03
0.74
1500
Exp 18
0.25
0.15
35
50
1 × 10−4
1.01
1.52
0.128
0.053
1.39
0.61
1150
Exp 19
0.25
0.15
35
60
1 × 10−4
1.01
1.48
0.099
0.092
1.37
0.58
900
Dam height
Exp 20
0.15
0.15
40
50
1.2 × 10−4
1.10
1.41
0.111
0.063
1.17
0.55
890
Exp 21
0.20
0.15
40
50
1.2 × 10−4
1.10
1.41
0.045
0.133
1.30
0.79
1020
Exp 22
0.25
0.15
40
50
1.2 × 10−4
1.10
1.41
0.103
0.043
1.33
0.82
1080
Exp 23
0.30
0.15
40
50
1.2 × 10−4
1.10
1.41
0.116
0.071
1.35
0.85
1280
Dam crest width
Exp 24
0.25
0.20
35
55
1.67 × 10−4
1.14
1.32
0.086
0.083
1.60
0.86
1380
Exp 25
0.25
0.25
35
55
1.67 × 10−4
1.14
1.32
0.118
0.081
1.78
0.89
2600
Hd = dam height; Dcrw = dam crest width; α = upstream slope angle; β = downstream slope angle; Qin = inflow rate into the upstream reservoir; \( \rho \)dry = dry bulk density; eo = initial void ratio; iini-1 = critical hydraulic gradient for seepage erosion initiation (between sensors p1 and p2); iini-2 = critical hydraulic gradient for seepage erosion initiation (between sensors p2 and p3); if1 = critical hydraulic gradient for collapse of the dam crest (between sensors p1 and p2); if2 = critical hydraulic gradient for collapse of the dam crest (between sensors p2 and p3); Tb = time of collapse of the dam crest
Table 3
Summary of results of critical pore-water pressures and critical seepage velocities obtained from the tests
Test specification
Test no.
Qin (m3/s)
pcrit-1 (kPa)
pcrit-2 (kPa)
pcrit-3 (kPa)
Vcrit-1 (m/s)
Vcrit-2 (m/s)
Characteristic failure mechanism
Dam composition
Exp 1
2 × 10−4
1.30
1.24
1.08
7.10 × 10−6
5.68 × 10−6
Type I
Exp 2
2 × 10−4
1.64
1.49
1.38
1.14 × 10−6
5.39 × 10−7
Type II
Exp 3
2 × 10−4
1.45
1.35
1.34
1.49 × 10−6
1.21 × 10−6
Transitional: Type II to Type I
Rate of inflow into the upstream reservoir (filling rate)
Exp 4
1.67 × 10−5
1.47
1.35
0.98
1.05 × 10−6
7.39 × 10−7
Type I
Exp 5
5 × 10−5
1.65
1.18
0.96
1.14 × 10−6
7.15 × 10−7
Type I
Exp 6
1 × 10−4
1.68
1.20
1.01
1.18 × 10−6
7.85 × 10−7
Type II
Exp 7
1.67 × 10−4
1.52
1.50
1.19
1.07 × 10−6
1.01 × 10−6
Type II
Antecedent moisture content at low compactive effort (eo = 1.76)
Exp 8
1.5 × 10−4
1.50
1.06
1.03
1.37 × 10−6
7.60 × 10−7
Type II
Exp 9
1.5 × 10−4
1.39
1.11
1.01
1.44 × 10−6
8.49 × 10−7
Type I
Exp 10
1.5 × 10−4
1.49
1.10
0.87
1.59 × 10−6
1.02 × 10−6
Type I
Exp 11
1.5 × 10−4
1.43
1.12
0.83
1.30 × 10−6
9.52 × 10−7
Type I
Antecedent moisture content at high compactive effort (eo = 1.21)
Exp 12
1.3 × 10−4
1.41
1.20
1.15
1.29 × 10−6
7.60 × 10−7
Type II
Exp 13
1.3 × 10−4
1.40
1.19
1.02
1.28 × 10−6
7.50 × 10−7
Type II
Exp 14
1.3 × 10−4
1.38
1.22
0.99
1.08 × 10−6
8.50 × 10−7
Type II
Exp 15
1.3 × 10−4
1.40
1.20
0.96
1.03 × 10−6
7.98 × 10−7
Type II
Downstream slope angle
Exp 16
1 × 10−4
1.52
1.32
1.29
9.50 × 10−7
6.75 × 10−7
Type II
Exp 17
1 × 10−4
1.40
1.20
1.08
9.35 × 10−7
6.64 × 10−7
Type II
Exp 18
1 × 10−4
1.44
1.06
0.83
1.30 × 10−6
4.60 × 10−7
Type I
Exp 19
1 × 10−4
1.50
1.03
0.99
1.28 × 10−6
5.30 × 10−7
Type I
Dam height
Exp 20
1.2 × 10−4
1.13
0.78
0.98
1.24 × 10−6
5.99 × 10−7
Type I
Exp 21
1.2 × 10−4
1.48
1.21
1.22
1.38 × 10−6
8.40 × 10−7
Type II
Exp 22
1.2 × 10−4
1.60
1.40
1.29
1.40 × 10−6
8.90 × 10−7
Type II
Exp 23
1.2 × 10−4
1.72
1.37
1.01
1.43 × 10−6
9.10 × 10−7
Type II
Dam crest width
Exp 24
1.67 × 10−4
1.70
1.40
1.10
1.53 × 10−6
8.20 × 10−7
Type I
Exp 25
1.67 × 10−4
2.01
1.68
1.48
1.69 × 10−6
8.55 × 10−7
Type I
Qin = inflow rate into the upstream reservoir; pcrit-1 = critical pore-water pressure for collapse of the dam crest at p1; pcrit-2 = critical pore-water pressure for collapse of the dam crest at p2; pcrit-3 = critical pore-water pressure for collapse of the dam crest at p3; Vcrit-1 = critical seepage velocity (between sensors p1 and p2); Vcrit-2 = critical seepage velocity (between sensors p2 and p3)
Fig. 2
Grain size distribution curves of the dam materials. GV-I Gravelly dam I, GV-II Gravelly dam II, SD Sandfill dam, SS-8 Silica sand no. 8
Table 4
Mechanical and hydraulic characteristics of the materials used in the experiments
Sample name
Test no.
Sediment mixture (%)
D50 (mm)
Cu
Cc
Gravel (%)
Sand (%)
Fines (%)
K (m/s)
Sandfill dam (SD)
Exp 1
Silica sand 5 (100)
0.799
2.474
1.385
-
99.5
0.5
5.5 × 10−4
Gravelly dam I (GV-I)
Exp 2
Silica sand 8-gravel mix (40:60)
0.284
79.870
0.069
34
49.6
16.4
3.8 × 10−5
Gravelly dam II (GV-II)
Exp 3
Silica sand 8-pebbles-gravel mix (30:30:40)
0.201
3.520
1.047
22.6
62.9
14.5
6.0 × 10−5
Silica sand no. 8
Exp 4 ~ 25
Silica sand 8 (100)
0.124
1.726
1.195
-
67.1
32.9
5.8 × 10−5
D50 = median grain size; Cu = coefficient of uniformity; Cc = coefficient of curvature; K = coefficient of permeability
Landslide dam model construction and experimental procedure
Landslide dam models of different geometries were built approximately 0.4 m downslope from the upstream water inlet (Fig. 3a). Effort was made in building the dam models so as to simulate naturally existing landslide dam prototypes. Mechanically mixed soils were placed in the flume tank in equal lifts using the moist tamping method. Initially, oven-dried soils were mixed with a known volume of water and then compacted to obtain the desired moisture content and bulk density. All the experiments were conducted with an antecedent moisture content of 5 %, except in Exp 8 to 15 where the antecedent moisture content was varied from 5 to 20 %. The geometrical characteristics of the dam models are shown in Fig. 3b. The dam height Hd and the dam crest width Dcrw were varied from 0.15 to 0.3 m and 0.1 to 0.25 m, respectively. The angles α and β representing the upstream and downstream slope angles were varied from 35 to 40° and 30 to 60°, respectively.
Fig. 3
a Plan view of the flume tank indicating the position of the dam model and monitoring sensors. b Schematic diagram of the dam geometry (not to scale)
Seven different series of experiments, all summing up to 27 runs of tests, were carried out, each with intent to assess transient pore-water pressure variations and the critical hydraulic gradients for seepage erosion initiation and dam failure under steady-state seepage. The main experiments were conducted after carrying out a series of initial tests which were mostly done to check sensor reliability, result validation, test repeatability and selection of appropriate mixtures of materials. However, the results of experiments conducted on dams built with dam crest width Dcrw of 0.1 and 0.15 m are excluded in this paper due to some challenges posed by the monitoring sensors. The initial conditions set for all the tests assumed that the upstream reservoir was empty. Filling of the upstream reservoir was carried out with a rubber hose attached to a water tap, and connected to a manually-operated flowmeter. A steady-state seepage through the dam models was achieved by ensuring that the upstream reservoir level remained constant at approximately two-thirds of the dam height. Real-time data was acquired by connecting all the sensors to a standard high-speed monitoring and recording workstation comprised of two synchronized universal recorders (PCD-330B-F) and a laptop computer. Sampling frequency was set at 50 Hz for all the tests.
At the beginning of each experiment, discharge into the upstream reservoir was set at the desired value using a manually-operated flowmeter. The discharge was maintained until the upstream reservoir level equaled two-thirds of the dam height. Afterward, an equilibrium hydraulic head was established by ensuring that the upstream reservoir level remained constant prior to the collapse of the dam crest. The change from unsaturated to saturated state began during the filling of the upstream reservoir. Consequently, loss of matric suction due to positive pore-water pressure buildup under steady-state seepage, as observed from sensor p3 (Fig. 4), marked the onset of static liquefaction and exfiltration of water from the downstream toe, which further led to debris flow mobilization and dam failure.
Fig. 4
Schematic diagram for the determination of hydraulic gradients
Determination of critical hydraulic gradients
Variations in hydraulic gradients (i1 and i2) through the dam models were determined from pore-water pressure values obtained from the experiments. Darcy (1856) in Fredlund et al. (2012) postulated that the rate of water flow through a soil mass was equal to the hydraulic gradient, as described by the equation:
where vw = flow rate of water (m3/s), kw = coefficient of permeability with respect to the water phase (m/s), ∂hw/∂z = hydraulic gradient in the z-direction. Hydraulic heads, h1, h2, and h3 at three different locations within the dam models were computed from pore-water pressure values using the following equation (Fig. 4):
$$ h=\frac{u_w}{\gamma_w{ \cos}^2\psi } $$
(5)
where uw = pore-water pressure (kPa), γw = unit weight of water (kN/m3), ψ = flume bed slope angle (degree). Therefore, hydraulic gradient i1 between sensors p1 and p2 was determined as described by the equation below:
where h01, h02 and h03 represent corresponding vertical distances between the flat firm base and the slope bed, whereas L1 and L2 are horizontal distances between p1 and p2, and p2 and p3, respectively. Two limit values of hydraulic gradients, corresponding to the onset of initiation of seepage erosion iini and collapse of the dam crest if, were determined based on results obtained from the initial tests.
Results and discussion
General characteristics of the experiments
Two characteristic types of dam failure (Type I and Type II) were observed during the experiments and were found to depend on the geometry and hydromechanical characteristics of the dam materials. These were further subdivided into several interrelated failure processes which included wetting front propagation, downstream slope saturation, exfiltration, sapping/seepage-face erosion, toe bifurcation, undermining and progressive sloughing of the downstream face, and late-stage overtopping.
Type I involves failures which could be related to static liquefaction of the soil mass under steady-state seepage that reduced the apparent cohesion of the soil and led to debris flow mobilization. This type of failure was primarily initiated by sapping erosion which occurred as a result of steady exfiltration of water from the downstream toe; which by extension, triggered gradual undercutting and debuttressing of the downstream slope as the mobilized mass ‘flowed’ downstream, thus lowering the dam height (Fig. 5a). Dam failure occurred by overtopping as the upstream reservoir level reached the tip of the partially saturated dam material, eroding the entire crest to form a wide breach channel. This type of failure was characteristic of experiments conducted with low upstream inflow rates, low compactive effort (eo = 1.76), high downstream slope angle (β ≥ 40°), and dam crest width greater than 0.15 m.
Fig. 5
Typical failure mechanisms of the dams. a Type I - Upslope propagation of wetting front, exfiltration, sapping and sloughing of the fluidized soil mass. b Type II - Downslope propagation of wetting front, bifurcation, and undermining of the slope toe
Type II involves failures triggered by downslope propagation of the wetting front and subsequent mobilization of the fluidized material at the upper part of the downstream face. This failure mechanism was characterized by downstream toe bifurcation and abrupt collapse of a large flank of the slope due to intense saturation which originated from the dam crest and progressed towards the downstream toe (Fig. 5b). Dam failure occurred by the formation of a hydraulic crack aligned perpendicular to the downstream face due to the reduction of the effective stress of the soil. This type of failure occurred mostly in dams of low downstream slope angle (β ≥ 40°), high shear strength of the soil relative to the shear stress of the seeping water, and high compactive effort (eo = 1.21).
Influence of dam composition
Three types of materials (SD, GV-I, and GV-II) were used to investigate transient changes in pore-water pressures and variations in hydraulic gradients under steady-state seepage through the dam models (Exp 1 ~ 3; Table 2 and 3). The dam models were built to obtain initial void ratios of 1.41, 0.71 and 0.84 for SD, GV-I, and GV-II materials, respectively. The resulting trends of pore-water pressures within the dam models indicate gross anisotropy and heterogeneity in dams composed of GV-I and GV-II, whereas the low critical pore-water pressures obtained in the dam built with homogeneous SD material demonstrates the liquefaction potential of cohesionless and isotropic sands (Fig. 6). The failure mechanism of the SD dam was basically characteristic of the Type I failure pattern. Enlargement of the sapping zone was characterized by occasional mass failures which were enhanced by a decrease in the effective stress of the soil as the energy of the exfiltrating water increased. In contrast, GV-I material showed Type II failure mechanism, whereas the failure mechanism of GV-II material evolved from Type II to Type I (Fig. 7). Critical pore-water pressure values (pcrit-1) determined at p1, which correspond to the onset of failure of the dams were 1.30, 1.64 and 1.45 kPa for SD, GV-I, and GV-II, respectively. The observed trends of pore-water pressures within the dams were found to be inversely proportional to the initial void ratio eo (Table 3), and directly proportional to the coefficient of uniformity Cu of the dam materials (Table 4). This could be potentially caused by capillary rise within the materials which depends on the grain size distribution and bulk density of the constituent soil mass that, in itself, affected the porosity of the soil. Thus, the stability and deformation characteristics of the dams increased as the grain size distribution changed from poorly to well graded. Similarly, the critical hydraulic gradients for seepage erosion initiation iini, increased with a decrease in pore size, while the critical hydraulic gradient for collapse of the dam crest if, was influenced by the grain size distribution. The effect of grain size distribution on the development of seepage in the dams was evidenced by the variations in seepage velocity as the dynamics of the seeping water changed from laminar flow to turbulent flow (Table 3; Additional file 1: Video S1). The fact that the longevity of the dam built with GV-II material (vcrit-2, 1.21 × 10−6 m/s) was higher than those built with SD and GV-I materials (vcrit-2, 5.68 × 10−6 and 5.39 × 10−6 m/s, respectively) demonstrates that other physical parameters such as particle density, hydraulic conductivity and gravel content affect seepage development in landslide dams and soil slopes (Kokusho and Fujikura 2008).
Fig. 6
Time-dependent transient changes in pore-water pressures and trends of hydraulic gradients in dams built with (a) Sandfill dam (b) Gravelly dam I and (c) Gravelly dam II
Fig. 7
Images of seepage-induced failure of dams built with (a) Gravelly dam I and (b) Gravelly dam II
Rate of inflow into the upstream reservoir
Exp 4~7 were conducted to evaluate the influence of inflow rate Qin into the upstream reservoir. The dam models were built with uniform geometrical and physical characteristics (Table 2). Figure 8 shows the variations in pore-water pressures through the dams at steady-state inflow rates of 1.67 × 10−5 m3/s, 5 × 10−5 m3/s, 1 × 10−4 m3/s, and 1.67 × 10−4 m3/s. The filling rate of the upstream reservoir initiated seepage processes that changed the dynamics of the pore-water pressures. The critical hydraulic gradients for initiation of seepage erosion (iini-1 and iini-2) varied from 0.067 to 0.122. A low pcrit-1 value of 1.52 kPa was determined in the experiment conducted with Qin of 1.67 × 10−4 m3/s, relative to Qin of 5 × 10−5 m3/s (pcrit-1 = 1.65 kPa) and 1 × 10−4 m3/s (pcrit-1 = 1.68 kPa) (Table 3). This could be attributed to a rapid increase in the hydraulic head which initiated high seepage gradients that reduced the effective stress of the soil, leading to differential settlement, hydraulic cracking, and lowering of the dam crest. Thus, the rate of reduction of the shear strength of the soil due to a decrease in matric suction depends on the rate of inflow into the upstream reservoir Qin and the rate of propagation of the wetting front. Trends of hydraulic gradients through the dams indicate that if1 decreased with an increase in Qin, whereas if2 increased with an increase in Qin, suggesting a corresponding increase in seepage velocity between sensors p1 and p2 (Table 2; Fig. 13 in Appendix 1). Critical seepage velocities determined from the tests show that vcrit-2 increased from 7.39 × 10−7 m/s for Qin of 1.67 × 10−5 m3/s to 1.01 × 10−6 m/s for Qin of 1.67 × 10−4 m3/s. Exfiltration, sapping and undercutting of the downstream toe, characteristic of Type I failure mechanism, occurred at low inflow rates as a result of low seepage processes that led to liquefaction and collapse of the dam crest (Exp 4 and 5). In contrast, hydraulic cracking, downstream face saturation, and toe bifurcation characteristic of Type II failure mechanism, occurred in experiments conducted with high inflow rates (Exp 6 and 7). The experimental results demonstrate that the stability and time of collapse of the dam crest Tb decreased with an increase in inflow rate into the upstream reservoir. This was evidenced by the characteristic failure mechanism of the dam models which evolved from Type I to Type II with a corresponding increase in Qin (Table 3).
Fig. 8
Transient variations in pore-water pressures in experiments conducted with upstream inflow rates of (a) 1.67 × 10−5 m3/s (b) 5 × 10−5 m3/s (c) 1 × 10−4 m3/s (d) 1.67 × 10−4 m3/s
Influence of material condition
Soil wetting is a major cause of shear strength reduction and volume change in unsaturated soils and is a common occurring factor in collapsible soils and expansive soils. Exp 8~11 were conducted to assess the influence of antecedent moisture content w on the deformation behaviour of landslide dams under steady-state seepage. Antecedent moisture contents of the soils were increased by 5 % during soil preparation and dam model construction. Figure 9 shows the resulting trends of hydraulic gradients through the dams. A linear relationship was observed between the antecedent moisture content and the rate of deformation and collapse of the dam models (Fredlund 1999). It is noteworthy to mention that the critical hydraulic gradients (if1 and if2) coincided with the onset of dam deformation and crest settlement. Measured critical hydraulic gradients for seepage erosion initiation varied from 0.053 to 0.118, while the critical hydraulic gradient for failure of the dams increased with an increase in antecedent moisture content. Similarly, the reduction of capillary forces due to an increase in soil moisture content caused the critical seepage velocity to decrease from 1.31 × 10−6 m/s for w = 5 % to 9.52 × 10−7 m/s for w = 20 %. The failure mechanism of the dams evolved from Type II to Type I as antecedent moisture content increased through the dams. The rate of exfiltration and sapping erosion at the downstream toe increased from low saturated soils to highly saturated soils. This was attributed to the reduction of matric suction caused by wetting resulting in high void ratios that accentuated the abrupt collapse of the dams.
Fig. 9
Trends of hydraulic gradients in dams built with an eo of 1.76 and antecedent moisture contents of (a) 5 % (b) 10 % (c) 15 % (d) 20 %
Figure 10 shows trends of hydraulic gradients and the failure mechanism of dam models built with the same antecedent moisture contents (5, 10, 15 and 20 %), but packed at a higher compactive effort, eo= 1.21 (Exp 12~15). The characteristic trends displayed by the hydraulic gradients, as well as the low critical seepage velocities determined from the experiments indicate, that the initial void ratio eo of the soil affected the failure mechanism of the dams. It may be important to note that if1 and if2 increased with an increase in antecedent moisture content, thus suggesting that the dynamics of the seeping water were mainly characteristic of a laminar flow. The stability of the dam models increased as antecedent moisture content decreased from 20 to 5 %, as observed from Tb and pcrit-3, and thus indicates the effect of pore-water pressures in reducing the effective stress of the soil (Tables 2 and 3). This effect can be related to the influence of matric suction on the liquefaction potential and shear strength reduction in partially saturated soils (Simon and Collison 2001; Okamura and Soga 2006). Comparison between Exp 8 ~ 11 and Exp 12 ~ 15 shows that the deformation and collapse mechanism of the dam models were more pronounced in dams with an eo of 1.76 (Exp 8 ~ 11) than in those with an eo of 1.21 (Exp 12 ~ 15) (Figs. 16 and 17 in Appendix 2). Similarly, a comparison between the critical hydraulic gradients measurements in Exp 8 ~ 11 and Exp 12 ~ 15 shows that the critical hydraulic gradient decreased with a decrease in initial void ratio. The observed trends of wetting front propagation and the transient changes in pore-water pressures suggest that seepage flow through the dam materials was not essentially controlled by matric suction but by a hydraulic head gradient (Fredlund and Rahardjo 1993).
Fig. 10
Trends of hydraulic gradients in dams built with an eo of 1.21 and antecedent moisture contents of (a) 5 % (b) 10 % (c) 15 % (d) 20 %
Influence of dam geometry
The geometry of landslide dams is one of the major factors contributing to seepage erosion and slope instability. The two major factors that control the critical hydraulic gradient for instability in soil slopes are the downstream slope angles β and the gradient of the soil layer ψ (Iverson and Major 1986; Budhu and Gobin 1996). Basically, the internal friction angle of a dry cohesionless soil, at zero external pressure, is equal to the maximum stable slope angle of the soil. However, the soil mass collapses to a lower slope angle if steady-state seepage occurs. A series of experiments were conducted to evaluate the effects of downstream slope angle β on the critical hydraulic gradients for failure of landslide dams (Exp 16~19). The downstream slope angles were varied from 30 to 60°. A close examination of the results indicates that the stability of the dams increased as the downstream slope angle decreased from 60 to 30° (Table 2). The time of collapse of the dam crest increased from β = 60° (Tb, 900 s) to β = 30° (Tb, 2300 s). Similarly, if1 increased with an increase in β, whereas if2 decreased with an increase in β (Fig. 14 in Appendix 1). Also, the critical seepage velocity decreased with an increase in β, indicating high failure potentials in dams of high downstream slope angles (Table 3). The variations in pore-water pressures and the failure mechanism of the dams are shown in Fig. 18 (Appendix 2). The failure mechanism of the dams built with β in the range of 30 to 40° was initiated by the bifurcation of the downstream toe (Type II), whereas exfiltration, sapping and undermining of the downstream toe were characteristic of dams with β in the range of 41 to 60° (Type I). Budhu and Gobin 1996 remarked that for a soil which has ϕ of 30°, the exit hydraulic gradient at the slope face increases from 1 (when λ = β) to a limit value of sin β (when λ = 90°).
The influence of dam height on the stability and longevity of landslide dams under steady-state seepage was evaluated in dams built with different dam heights Hd, ranging from 0.15 m to 0.3 m (Tables 2 and 3). The experiments were conducted at a constant upstream inflow rate of 1.2 × 10−4 m3/s (Exp 20~23). A positive correlation was observed between the critical hydraulic gradients for dam failure (if1 and if2) and the dam height. The values of if1 and if2 increased from 1.17 and 0.55 for Hd = 0.15 m, to 1.35 and 0.85 for Hd = 0.30 m (Table 2; Fig. 15 in Appendix 1). Critical pore-water pressure values correlating with the onset of failure of the dams increased from 1.13 kPa (Hd = 0.15 m) to 1.72 kPa (Hd = 0.30 m) (Fig. 19 in Appendix 2). The results show that at constant α and β, the stability of the dams increased with a decrease in dam height Hd. This was further evidenced by the failure mechanism of the dams which evolved from Type I for Hd = 0.15 m to Type II for Hd = 0.30 m. The results indicate that the height of landslide dams is an important parameter for assessing the stability of natural river blockages.
Exp 24~25 were conducted to evaluate the influence of dam crest width Dcrw on the failure mechanism of landslide dams. A steady-state seepage was maintained at a constant upstream inflow of 1.67 × 10−4 m3/s. The results of transient variations in pore-water pressures and the corresponding trends of hydraulic gradients in the dams built with Dcrw of 0.20 m and 0.25 m (Exp 24 and 25) are shown in Fig. 11. The critical hydraulic gradients for seepage erosion initiation (iini-1 and iini-2), varied from 0.081 to 0.118. Exfiltration, sapping and debuttressing of the downstream toe, characteristic of Type I failure pattern, were the major failure mechanisms of the dams (Fig. 12). The rate of propagation of the wetting front through the dams was strongly influenced by Dcrw/Hd. High Dcrw/Hd resulted in high values of if1, if2, and vcrit. The continual propagation of wetting front through the dams resulted in a gradual reduction of the effective stress of the soil, and subsequent mobilization of the liquefied mass which travelled downstream with an initial speed of 1.2 × 10−5 m/s. The episodic occurrence of hydraulic cracks and undermining and sloughing of the fluidized slope mass continued until the dam breached by overtopping. The results demonstrate that at constant hydraulic and geometrical conditions (Hd, α and β), if1 and if2, as well as vcrit, increased with an increase in Dcrw, indicating that the critical seepage velocity and the critical hydraulic gradient for seepage erosion in landslide dams are influenced by dam crest width Dcrw and Dcrw/Hd.
Fig. 11
Evolution of pore-water pressures and hydraulic gradients in dams built with dam crest widths of (a) 0.20 m (b) 0.25 m
Fig. 12
Exfiltration, sapping and downstream toe debuttressing under steady-state seepage in dams built with dam crest widths of (a) 0.20 m (b) 0.25 m
Conclusions
An extensive experimental programme was carried out to investigate the effects of transient variations in pore-water pressures and the critical hydraulic gradients for seepage-induced failure of landslide dams using a flume tank specifically designed for accurate determination of these hydraulic parameters. A steady-state seepage was maintained by ensuring that the upstream reservoir level remained constant prior to the collapse of the dam crest. Limit values of hydraulic gradients and seepage velocities were determined for different hydromechanical and geometrical conditions. Based on the experimental results, the following conclusions can be drawn:
1.
Sapping was the most dominant mechanism of slope destabilization observed in all the experiments. Other significant interrelated failure processes of the dam models included wetting front propagation, downstream face saturation, exfiltration, hydraulic cracking, toe bifurcation, downstream slope undercutting, sloughing and late-stage overtopping.
2.
Two characteristic types of failure, which depend on the geometrical and hydromechanical properties of the dams were observed: Type I and Type II. Type I commonly occurred in dams built with low compactive effort (eo = 1.76), high downstream slope angle (β ≥ 40°), crest width greater than 0.15 m, and moisture content lower than 15 %. This type of failure was initiated by exfiltration, sapping, and upslope propagation of the wetting front towards the dry upper region of the dam crest. Type I failure mechanism shares similar characteristics to the three distinct zones of slope deformation triggered by sapping, which are: fluvial, sapping and undermining zones, as reported by Howard and McLane (1988). In contrast, Type II was found in dams of low downstream slope angle (β ≥ 40°), dam height greater than 0.25 m, high upstream inflow rates and high compactive effort (eo = 1.21). Failure in these dams was triggered by downslope propagation of the wetting front, bifurcation of the damp lowermost part of the downstream toe, sapping erosion and sloughing of the fluidized slope material.
3.
The build-up of positive pore-water pressure under steady-state seepage and its effects on the apparent cohesion of the soil were evaluated for different upstream inflow rates and antecedent moisture contents. The results indicated that the stability and longevity of the dam models increased with a decrease in upstream inflow rate and antecedent moisture content. Thus, demonstrating the significance of pore geometry, particle density, gradation, and hydraulic conductivity of materials forming landslide dams in the development of seepage processes.
4.
In all the experiments, the critical hydraulic gradients for seepage erosion initiation (iini-1 and iini-2) ranged from 0.042 to 0.147. The critical hydraulic gradient for collapse of the dam crest if was strongly influenced by several factors, such as the initial void ratio (compactive effort), antecedent moisture content, particle density, grain size distribution, inflow rate into the upstream reservoir and the geometrical characteristics of the dams.
5.
In the dams built with mixed materials, if1 and if2 increased with an increase in uniformity coefficient. The critical hydraulic gradient for collapse of the dam crest if increased with an increase in inflow rate into the upstream reservoir (filling rate). Similarly, if1 and if2 were controlled by the combined effects of antecedent moisture content and porosity of the soil. At low void ratios, if1 decreased with an increase in antecedent moisture content, whereas if2 increased as antecedent moisture content increased through the dams. However, at high void ratios, under the same antecedent moisture contents, if1 and if2 increased with an increase in antecedent moisture content, suggesting seepage flow dynamics typical of laminar flows.
6.
Furthermore, both if1 and if2 increased with an increase in Hd and Dcrw, whereas if1 increased with an increase in β, and if2 decreased as β increased. This indicates that the critical hydraulic gradient for dam failure for near-horizontal flow (Ψ = 5°), depends on β.
7.
These experiments demonstrate that seepage mechanisms in landslide dams comprised of unsaturated homogeneous and isotropic cohesionless materials are influenced by the hydraulic properties of the materials, as well as the geometrical characteristics of the dams.
8.
The textural characteristics of the materials used in these experiments are typical of landslide dams formed by rock avalanche processes where fragmentation and pulverization of the rock materials cause seepage processes to develop in the upper blocky carapace layer.
9.
However, further research should be done considering a wide range of sediment sizes and the addition of commercially available kaolinite clay to evaluate the mechanism of shear strength reduction under steady-state seepage. It is believed that performing unsaturated seepage analysis and limit equilibrium analysis, with regards to the results and conditions set for these experiments, could give further insights into the critical conditions for stability of landslide dams under steady-state seepage.
Notation
Cc = coefficient of curvature
Cu = coefficient of uniformity
Dcrw (m) = dam crest width
D50 (mm) = median grain size
eo = initial void ratio
Fs (kN/m3) = seepage force per unit volume
Hd (m) = height of the dam
i1 = hydraulic gradient (between sensors p1 and p2)
i2 = hydraulic gradient (between sensors p2 and p3)
iini-1 = critical hydraulic gradient for seepage erosion initiation (between sensors p1 and p2)
iini-2 = critical hydraulic gradient for seepage erosion initiation (between sensors p2 and p3)
if1 = critical hydraulic gradient for collapse of the dam crest (between sensors p1 and p2)
if2 = critical hydraulic gradient for collapse of the dam crest (between sensors p2 and p3)
K (m/s) = coefficient of permeability
pcrit-1 (kPa) = critical pore-water pressure for collapse of the dam crest at p1
pcrit-2 (kPa) = critical pore-water pressure for collapse of the dam crest at p2
pcrit-3 (kPa) = critical pore-water pressure for collapse of the dam crest at p3
Qin (m3/s) = inflow rate into the upstream reservoir
Tb (s) = time of collapse of the dam crest
uw (kPa) = pore-water pressure
Vcrit-1 (m/s) = critical seepage velocity determined at p1
Vcrit-2 (m/s) = critical seepage velocity determined at p2
w (%) = antecedent moisture content
α (degree) = upstream slope angle
β (degree) = downstream slope angle
γ’ (kN/m3) = submerged unit weight of soil
w (kN/m3) = unit weight of water
λ = seepage direction
\( \rho \)dry (Mg/m3) = dry bulk density
ϕ (degree) = internal friction angle
ψ (degree) = flume bed slope angle
Declarations
Acknowledgements
This investigation was financially supported by JSPS KAKENHI Grant Number A-2424106 for landslide dam failure prediction. Dr Solomon Obialo Onwuka (University of Nigeria, Nsukka) is gratefully acknowledged for his valuable comments and suggestions. The authors would like to thank the anonymous reviewers for reviewing the draft version of the manuscript.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
(1)
Department of Geoscience, Graduate School of Science and Engineering, Shimane University
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