Geotechnical Testing Journal

Geotechnical Testing Journal J. Israr,1 B. Indraratna,2 and C. Rujikiatkamjorn3

DOI: 10.1520/GTJ20150288

Laboratory Investigation of the Seepage Induced Response of Granular Soils Under Static and Cyclic Loading VOL. 39 / NO. 5 / SEPTEMBER 2016

Geotechnical Testing Journal

doi:10.1520/GTJ20150288

/

Vol. 39

/

No. 5

/

September 2016

/

available online at www.astm.org

J. Israr,1 B. Indraratna,2 and C. Rujikiatkamjorn3

Laboratory Investigation of the Seepage Induced Response of Granular Soils Under Static and Cyclic Loading Reference Israr, J., Indraratna, B., and Rujikiatkamjorn, C., “Laboratory Investigation of the Seepage Induced Response of Granular Soils Under Static and Cyclic Loading,” Geotechnical Testing Journal, Vol. 39, No. 5, 2016, pp. 795–812, doi:10.1520/GTJ20150288. ISSN 0149-6115

ABSTRACT Manuscript received December 11, 2015; accepted for publication May 19, 2016; published online July 1, 2016.

Experimental observations of the seepage induced response of soils under static and cyclic loading are reported. Hydraulic tests were performed using a modified filtration apparatus designed to capture the response of soils subjected to an upward flow. This apparatus could

1

2

3

Univ. of Wollongong, Wollongong NSW 2522, Australia, e-mail: [email protected] Centre for Geomechanics and Railway Engineering, Univ. of Wollongong, Wollongong NSW 2522, Australia (Corresponding author), e-mail: [email protected]

conveniently monitor various factors influencing the onset of seepage induced failures such as spatio-temporal variations in porosity, average and local hydraulic gradients, and the mean effective stress distribution with depth. Under static conditions, heave and heavepiping failures occurred in densely compacted uniform fine-gravels and fine-sands, respectively, and excessive washout (i.e., suffusion) was observed in gap-graded sandygravel soil. Despite this gap-graded soil failing in a similar way under static loading, relatively premature suffusion occurred under cyclic loading that could be attributed to the

Univ. of Wollongong, Wollongong, NSW 2522, Australia, e-mail: [email protected]

constant agitation of fines and the development of pore pressure within the pore spaces. The reported results and published data under cyclic loading were compared with various static filtration criteria to assess their potential instability, and they revealed that none could accurately capture their cyclic filtration response. However, at the onset of instability, a unique hydro-mechanical correlation could be observed between the magnitudes of local hydraulic gradients and effective stresses calculated using a proposed stress reduction model. Nevertheless, this correlation governing the inception of instability in reported tests established a clear hydro-mechanical boundary with possible implications for practical filter design under cyclic loading conditions. Keywords seepage failure, granular soils, hydraulic gradient, static, cyclic loads

C 2016 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. Copyright V

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Notation CSD, PSD ¼ constriction size and particle size distributions Cu ¼ coefficient of uniformity d ¼ sample depth (m) f d85;SA ¼ representative size for finer fraction from PSD by surface area technique (mm) eC1 ¼ constant of integration f ¼ cyclic loading frequency (Hz) ia and iij ¼ average applied and local hydraulic gradients, respectively icr;a ¼ average critical hydraulic gradient icr;ij ¼ local critical hydraulic gradient in ij-layer iDu ¼ pore pressure induced local hydraulic gradient k ¼ saturated hydraulic conductivity of soil (cm/sec) pw and pw;ij ¼ average and local hydraulic pressure difference, resepectively (kPa) Qf and Te ¼ effluent flow rate (lit/min) and turbidity (Nephelometric Turbidity Unit, NTU) and ru ¼ normalized pore water pressure ratio with mean effective confining stress. Du ¼ excess pore water pressure developed (kPa) Dy ¼ depth of discrete layer (m) lf and gf ¼ surface friction coefficient and frictional constant, respectively 2a ¼ axial strain (%) r0vm ; r0vt ; and r0vb ¼ mean, top and bottom vertical effective stresses, respectively (kPa) r0vmi and r0vmo ¼ initial mean effective stress and that at the onset, respectively (kPa) 0 rz ¼ effective stress at depth z (kPa)

Introduction Seepage induced failures in granular soils (e.g., downstream filters in dams) were observed to be the major causes of hydraulic structure failures worldwide, reportedly contributing more than 46 % to the failure of all embankment dams so far (Richards and Reddi 2007). These failures are generally recognized as internal instability phenomena that could be categorized as: (a) heave or piping (i.e., sand boiling), (b) suffusion or washout, and (c) external or internal erosion. These failures could lead to the formation of sinkholes in dams, subsidence in railroads and highway substructures due to pumping of fines through pipe formations, and embankment breaching (Trani and Indraratna 2010b; Selig and Waters 1994; Skempton and Brogan 1994). A layer of soil could be susceptible to any of the aforementioned

phenomena along its depth in the direction of seepage that may be unique for a set of associated hydro-geo-mechanical characteristics (Fig. 1). For instance, Indraratna et al. (2015) observed during hydraulic tests that seepage failures commenced with spatial variability along the depth of the samples. Moffat and Fannin (2011) reported the onset (i.e., inception) of instability as being spatio-temporal in nature that was governed by some unique relationships between effective stresses and the accompanying hydraulic gradients. Some studies highlighted that the downstream filters in embankment dams experience complex stress states such that their physical and mechanical properties deteriorate significantly as a result of suffusion and internal erosion in variable stress conditions (e.g., Smith and Bhatia 2010; Fourie et al. 1994; Chang and Zhang 2013; Xiao and Shwiyhat 2012). In practice, the potential internal instability of soils is assessed through various approximate particle size distribution (PSD) based geometrical criteria that were established on the basis of phenomenological observations from laboratory piping tests (e.g., Indraratna et al. 2015; Kenney and Lau 1985; Kezdi 1979). Nonetheless, these methods conservatively demarcate boundaries between stable and unstable gradations such that internal instability is believed to be only occurred in the latter (Li and Fannin 2012). However, under cyclic loading conditions, geometrically assessed internally stable gradations experienced washout of their skeletal fines (i.e., suffusion), similar to internally unstable soils (Trani and Indraratna 2010b). Granular soils are commonly used as capping and drainage layers in railway and highway substructures as subballast and subbase, respectively, where filtration occurs under significant magnitudes of cyclic loading caused by traffic (e.g., heavy haul freight and high speed passenger trains). The current criteria for filter design and assessment of internal stability used to select rail subballast gradations were originally established for filtration under static conditions, e.g., in dams (Selig and Waters 1994). As a result, an internally stable soil selected as a subballast layer could exhibit suffusion under dynamic conditions (e.g., Trani and Indraratna 2010b). As a consequence, this phenomenological discrepancy between static and cyclic internal instabilities could result in designing an inappropriate/ ineffective filter yielding excessive erosion from the substructure and subsequent ballast fouling and track deterioration. Therefore, in order to explain these phenomena scientifically, and enhance our understanding of important factors governing the onset of seepage induced failures in soils subjected to static and cyclic loading, a hydraulic apparatus was designed and commissioned at the University of Wollongong, Australia. A number of tests were performed on granular soil specimens to assess their internal instability potentials and the repeatability of tests. Typical cases of downstream inverted filter in a medium size embankment dam (static conditions) under an effective stress of 50 kPa, and subballast under heavy haul loading (cyclic

ISRAR ET AL. ON FILTRATION UNDER STATIC & CYCLIC LOAD

FIG. 1 Illustration of various seepage induced failures in granular soils.

conditions) at speeds up to140 km/h were simulated and results were presented.

Test Apparatus The test apparatus (Fig. 2) consisted of the following major components, namely: (1) a test chamber, (2) a servo-controlled hydraulic actuator system, (3) an automated hydraulic pump with a sedimentation tank, (4) a portable turbidity meter, and (5) data loggers. These components are described as follows: The test chamber was a purpose built, low friction polycarbon cell that was 300 mm long by 13 mm thick, and with a 240 mm TFE-fluorocarbon or polytetrafluoroethylene (PTFE) coated inside diameter; the cell can accommodate a 200 mm high specimen (Ridout Plastics, San Diego, CA). A test specimen was divided into seven distinct layers, between which 8 pore pressure transducers were placed at different depths (Fig. 2), with an accuracy of 0.05 kPa. Two 50-mm diameter load cells (LC) were placed in the middle and the bottom of the specimens to monitor effective stress variations to an accuracy of 0.1 kPa. Seepage induced spatial and temporal variations in the porosities could be monitored using 3 amplitude domain reflectometry (ADR) probes type ML2x (accuracy: 0.05 %) inside the sample. The filtration cell is considered to be large enough to avoid any boundary effects on soil erosion and preferential flow channels along the walls (Zou et al. 2013), as well as the effects of instrumentation on seepage response of test samples (Moffat and Fannin 2011). Confirmed by comparing the results of tests performed with and without the load cells,

reported in a later section, it was revealed that the presence of the load cells had negligible effects on the test results. A purpose designed servo-controlled hydraulic actuator that can apply high magnitude static and cyclic loads at higher frequencies through a flexible loading platen was used in this study (see Fig. 2a). The details of the loading system can be obtained from Trani and Indraratna (2010a). In the static tests, a uniform vertical stress of 50 kPa was applied, while for cyclic tests, a sinusoidal stress with a mean of 50 kPa (i.e., rmin ¼ 30 kPa and rmax ¼ 70 kPa) was applied using wave-based force controlled servo to simulate heavy haul dynamic loading with axle loads of 12 and 28 tons during unloading and loading, respectively (Trani and Indraratna 2010b; Esveld 2001). A fully automated hydraulic pump was used to apply the pre-requisite hydraulic pressure difference across a test sample in an upward direction (accuracy: 0.05 kPa). The average hydraulic gradient (ia ) applied along the depth of the sample (hf ) was deduced by the difference in the applied hydraulic pressure (pw ), and is given by Eq 1a (after Indraratna and Radampola 2002; Kassif et al. 1965). The local hydraulic gradients within each layer (Dy) were determined using the differi;j ential hydraulic pressure applied (pw ), given by Eq 1b. The erodible fines washing out of the soil samples could be captured inside a large effluent collector for post-test forensic analysis. out ia ¼ ðpin w pw =hf cw Þ

(1a)

iij ¼ ðpðiþ1Þðjþ1Þ pijw =Dy cw Þ w

(1b)

where cw ¼unit weight of water. The variations in effluent flow rates were deduced by intercepting the outflow at different

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FIG. 2 Schematics of test setup, apparatus and the instrumentation (Not according to scale).

intervals in a measuring cylinder for a given period of time and the turbidity readings (in NTU) were determined using the portable turbidity meter. The data coming from all 15 channels (8 pore pressure transducers, 3 ADR probes, 2 load plates, 1 LVDT and 1 load actuator) at various output voltages (3–15 V) were recorded. The low pass Butterworth filter design technique was used to remove any unwanted noise from the raw data (after Guo et al. 2004).

Experimental Investigation TEST PROCEDURE

A slightly modified test procedure from Indraratna et al. (2015) was adopted, and that involved applying an upward hydraulic flow to a uniform, fully-saturated, and densely compacted specimen (Rd 95%) subjected to either an axial static or cyclic load (Fig. 2). The hydraulic gradient was applied in increments of Di 6 8 for samples C and F, and Di 2 4 for Sample G, depending upon the specimen response that was allowed to come to stability before next increment and hence the rate of hydraulic loading was not uniform. The spatio-temporal variations in the average (ia ) and local (iij ) hydraulic gradients defined by Eqs 1a and 1b, respectively (using pore pressure measurements), vertical effective stress distribution (using load

cells), variations in porosity (using ADR probes) and the effluent turbidity in NTU (in lieu of temporal mass loss) were monitored to capture the onset of seepage induced failures. In this paper, the “onset” is referred to the point of initiation of seepage failure (i.e., washout, piping or heave) that occurs at unique values of icr depending on the soil type (Xiao and Shwiyhat 2012; Moffat and Herrera 2014). At the onset, the seepage dislodges the fine particles and increases the soil’s permeability, thereby reducing the hydraulic head loss (hence hydraulic gradient) and increasing the volumetric flow (Indraratna et al. 2015). Thus, the onset could be quantified on the basis of a number of observations such as: (a) marked variations in the slope of hydraulic gradient versus volumetric flow, (b) excessive increase in effluent turbidity readings beyond 60 NTU for an extended period of time, (c) sudden reduction in the magnitude of hydraulic gradient, and (d) a sudden variation in specimen’s porosity, increased volumetric compression, and visual tell-tale signs of pipes, horizontal channels, and fine particle erosion, etc. (e.g., Skempton and Brogan 1994; Moffat and Fannin 2006; Trani and Indraratna 2010; Indraratna et al. 2016). The tested specimens were retrieved from the top, middle, and bottom layers, and the corresponding particle size distributions were obtained in order to assess the internal stability that can be reflected by any changes in the gradation of soil in the middle layer.


FIG. 3 Particle size distributions for tested soil gradations (Note: The shaded region represents the typical range for subballast selection in practice in Australia (after Trani and Indraratna 2010a,2010b)).

was used to obtain the target compaction levels. This required compacting five layers (40 mm each) at an optimum moisture content (ASTM D698-12e2) under a 10 kg surcharge applied for 10 min per layer over a vibrating table (at 50 Hz). The uniformity of each specimen with regards to the particle size distribution and compaction was assessed using the procedure outlined by Indraratna et al. (2015). Saturation was completed in three steps to avoid any potential disturbance before the test: (1) de-airing the sample by applying 100 kPa suction, (b) filling the cell with filtered and de-aired water, and (c) saturating the samples for a minimum period of 24 h under a 50 mm constant head. Complete saturation was assured when the readings from all 3 ADR probes became uniform, i.e., 80 F/m (the apparent permittivity of water at 20 C) indicating that all the pores were filled with water, and zero excess pore pressure due to the application of target r0vt (Trani and Indraratna 2010a).

Effective Stress Reduction TEST SAMPLE PREPARATION AND SATURATION

Soils with three different gradations were tested including uniform medium sand (sample-F), uniform sandy-gravel (sample-C), and a gap-graded sand-gravel mixture (sample-G), as shown in Fig. 3. The selected gradations conformed to the current industry practice guides in selecting subballast and subbase (capping layers) soils in NSW, Australia (Trani and Indraratna 2010b). The current sample-G represents typical gap-graded soils suitable for hydraulic dams (Moffat and Fannin 2006). These moist soil samples were thoroughly mixed beforehand to obtain homogenous mixtures. The target compaction level (Rd 95%) was reached by compacting the predetermined bulk mass of soil to a sample depth of 200 mm to achieve the minimum void ratio emin (ASTM D4254-16). The compaction procedure used by Trani and Indraratna (2010b)

FIG. 4 Schematic illustrations of (a) the soil sample, the limit equilibrium of stresses in a discretized soil layer and the effective stress distribution under hydrostatic condition and (b) effective stress distribution under hydrodynamic condition.

The magnitude of vertical effective stress (r0 ) applied at the top of the specimen varies along its length by virtue of: (1) Skin friction from the cell walls (e.g., Moffat and Fannin (2006) observed more than 30 % reduction in stress due to skin friction from the walls of an acrylic cell), and (2) Seepage flow (Tanaka and Toyokuni 1991). This variation in stress would be a function of soil-wall frictional properties, seepage characteristics, and the direction of soil movement (Fig. 4a). For instance, a higher frictional coefficient (lf ) at the cell boundary would result in a greater loss of r0 in the specimen due to larger skin friction in an opposite direction to the tentative direction of soil movement. Similarly, upward seepage would decrease and downward seepage would tend to increase r0 (Moffat and Fannin 2011). However, once the upward seepage, interface skin friction, and effective stress

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are in equilibrium (Fig. 4b), the sample would start to move upwards under the influence of buoyancy (heave) with downward boundary friction. By considering the limit equilibrium within a soil layer (Dy) inside the specimen subjected to effective stress (r0 ) at the top, the boundary friction sf , and the hydraulic gradient i (Fig. 4), the equation governing stress reduction is given by (see the Appendix for the derivation): @r0 ¼ c0 þ ii cw þ gf r0mv @y

(2)

where: r0mv ¼ 0:5 ðr0vt þ r0vb Þ ¼ the mean effective stress within the soil layer, gf ¼ 4lf K0 =D ¼ a frictional resistance factor that evolves from the coefficient of earth pressure at rest (K0 ¼ 1 sin [0 ), and The coefficient of friction at the soil-wall interface (lf ) and D ¼ the diameter of test specimen. Given that the initial tendency of soil movement due to the application of r0 is downwards (i.e., axial compression) the frictional resistance would act upwards. Equation 2 can be modified for a case of upwards or downwards flow, as well as in the direction of frictional resistance. For instance, the layer of soil experiencing an upward flow with the frictional stresses acting in an upward direction against the applied mechanical loading at the top (r0 > 0), means that Eq 2 can be modified to read: @r0 ¼ c0 ii cw gf r0mv @y

0 r0v;iþ1 r0v;i rv;iþ1 þ r0v;i 0 (6) ¼ c i i c w gf Dyi 2 1 For Xi ¼ 1 0:5gf Dyi and Yi ¼ 1 þ 0:5gf Dyi , the effective stress on top of the next layer reads:

r0v;iþ1 ¼ r0v;i Xi Yi þ Dyi c0 Yi Dyi ii cw Yi

(7)

Using, r0v;iþ1t ¼ r0v;ib , the mean vertical effective stress within a soil layer-i is given by: r0mv;i ¼ 0:5 r0v;i ð1 þ Xi Yi Þ þ Dyi c0 Yi Dyi ii cw Yi (8) presents the results of static friction tests conducted to estimate the lf -values, i.e., the contact coefficients of friction between various surfaces (e.g., steel on dry gravel, polycarbon on wet gravel, PTFE coated polycarbon on wet gravel, and gravel on wet gravel etc.). A horizontal bed of soil was prepared and levelled within a box (600 by 300 by 50 mm) and 150 by 150 by 5 mm sheets of various materials were placed on the surface and then dragged across it under pre-requisite normal stress levels (rn ) to determine the peak frictional resistance (sf ) at the state of impending motion (ASTM D1894-14). This test procedure was then standardized by the results of consolidated drained direct shear tests performed on current test samples (ASTM D3080/D3080M-11), plotted with dotted lines in 0 Fig. 5a. A good agreement between lf and tan [ -values of sample-C estimated from these tests could calibrate the surface friction test results quite well. Fig. 5a

(3)

Effect of Instrumentation The first order form of partial differential in Eq 3 defines a boundary value problem for which there is no unique solution in current form with two variables (i.e., gf and r0mv ). However, for the case with no seepage flow (i ¼ 0), the solution would be a function of gf (Fig. 4b). In this case, the exact solution for Eq 3 reads as (see details in the Appendix): r0z

" #4lf Dy=D c0 D c0 D 0 ¼ þ rvt 4lf 4lf

(4)

The approximate solution based on finite differencing is given by: r0z ¼

1 r0vt ð1 Nf Þ þ c0 Dy ; ½1 þ Nf

Nf ¼ 2lf Dy=D (5)

Assuming that lf is constant along the boundary with a known r0vt , Eq 3 can be solved for the effective stress at the bottom of a soil layer. In a progressive sense and with a simple assumption of no variations in stress at the interface (i.e., r0vb;i ¼ r0vt;iþ1 Þ, a finite difference discretization of the soil column yields:

STATIC LOADING

Tests were carried out under static loading conditions for two reasons: i.e., to study how test specimens responded under static loading compared to cyclic loading, and to assess the effects of instrumentation on the response of test specimens. Given that the total volume of two load cells (39.27103 mm3 ) was 5 times greater than the overall volume of the ADR probe needles, wires and transducer sensors (i.e., 7.63103 mm3 ) was nearly 0.43 % of the total soil volume in a sample (i.e., 9047.8103 mm3 ), only the effect of load cell (LC) placed inside the test samples was assessed. For this purpose, a total of 6 tests were carried out under a 50 kPa static load; 3 tests without LC and 3 with LC. The hydraulic pressure, and hence theia -value, was increased in steps in small increments of 0.5 for sample-G, unlike those of samples-C and –F from 3 to 5 based on the response of the test samples. As Fig. 5b shows, there was good agreement between the predictions from the middle and bottom effective stress estimates from Eqs 4 and 5, while those with LC (i.e., load cells) showed a similar reduction in stress (10%) due to interface friction. Similarly, Fig. 6 presents the time histories of porosities


FIG. 5 (a) Interface friction coefficients from direct shear test and surface frictions tests and (b) comparisons between calculated and observed effective stresses under hydrostatic condition (Note: DST and LC define direct shear test and load cells, respectively).

captured from the ADR probes, where symbols and lines represent readings with and without load cells, respectively. The times for occurrence of onsets were not comparable because of difference of hydraulic loading rates employed during tests. Variations in porosity before and after the onsets were in good agreement for specimens with and without load cells. For example, no significant variations occurred in specimen porosity before the onset (Fig. 6a, 6b, and 6c); however, marked variations were observed after the onsets of washout and piping in Fig. 6b and 6c, respectively. Based on these observations, it could be concluded that there was only minimum interference by the load cells. For instance, at the onset of failure in samplesF and -G (heave-piping and washout, respectively), the spatial variations in the porosity of the samples were almost identical before the onset, and that meant the current tests had good repeatability.

CYCLIC LOADING

As shown in Fig. 6d, the specimens exhibited initial compression in the seepage tests under cyclic loading (i.e., sample-G at f ¼ 5, 10, 15, and 20 Hz, and samples-C and -F at f ¼ 5 Hz). The soil compression eventually decreased or even ceased after 40,000 cycles independent of loading frequency. It was noted that the washout failure at the critical onset was similar to that under static loading. Fig. 7 presents the comparisons between the observed and computed variations in effective stress magnitudes (from Eq 7) for samples-G and-C, where the close agreements between theory and measurements with and without LC could validate the proposed stress reduction model (Eq 3). Here, vertical lines represent effective stress distributions at the onset of washout in sample-G (Fig. 7a and 7b) and heave in sample-F (Fig. 7c and 7d). Nevertheless, the stress distributions were almost identical, e.g., samples G showed washout that

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FIG. 6 Porosity variations for; (a) sample-C, (b) sample-F, and (c) sample-G under static loading, and (d) sample-G under cyclic loading at f ¼ 20 Hz.

initiated in layer-23 at almost 16 kPa (Fig. 7a and 7b), while sample-F exhibited heave-piping that triggered in layer-12 at almost 8 kPa (Fig. 7c and 7d). Fig. 8 shows the stress distributions of all the test samples at the start and the onset of seepage induced failure; here the slightly non-linear initial (average) stress distributions became increasingly non-linear at the critical onset of instability. This behavior may be attributed to significant particle rearrangement due to internal erosion at the onset. Non-uniform erosion of particles may form clusters with particles having large number of contacts with the neighboring particles and empty pores with smaller less contacts, as shown by some recent discrete element studies (Langroudi et al. 2013). This may cause stress concentration in some portions and reduction in others, as shown by the variable stress distribution curves in Fig. 8.

Test Results and Discussions HYDRAULIC RESPONSE OF TESTED SAMPLES

presents the relationships between the hydraulic gradients and the volumetric flow rates (Qf ), indicating the onset of seepage induced failure in the test samples that was characterized by a marked variation in Qf -values (generally Fig. 9a

increasing). At the inception of failure, as indicated in and 9c, the effluent turbidities (Te ) were much more than the threshold of 60 NTU (Indraratna et al. 2015), followed by a marked increase in axial strain (2a ) that could be attributed to the washout of skeletal fines. The uniformly graded samples-C and -F were internally stable but they exhibited heave and composite heave-piping (development of small piping channels followed by heave) failures, at very highicr;a -values. Sample-C did not exhibit any marked increase in effluent turbidity and axial strain, but the initiation of heave development was an indication of failure. The onset of heave could be identified by a slight increase in the Qf -value when the companion r0mv -values within a soil layer were neutralized to a minimum value by the seepage and frictional forces. The onset of failure in sample-F was characterized by visual heavepiping, a marked rise in Qf and Te -values, and a substantial increase in the 2a -rate. Similar observations facilitated failure in sample-G at comparatively smallericr;a -values under both static and cyclic loading. For instance, sample-G subjected to static loading with and without LC showed internal instability at icr;a ¼ 16:3 and 15:3, respectively, but when subjected to cyclic frequencies of 5, 10, 15, and 20 Hz, internal instability occurred at smaller values of icr;a ¼ 12:8; 11:8; 11:5; and 11:2, Fig. 9b


FIG. 7 Seepage induced stress reduction for hydrodynamic cases under static loading: (a) sample-G with load cell, (b) sample-G without load cell, (c) sample-C with load cell, and (d) sample-C without load cell.

FIG. 8 Initial and final (i.e., at the onset) effective stress distribution for current test samples.

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FIG. 9 Current test results for select samples; (a) flow curves, i.e., relationships between applied hydraulic gradients and effluent volumetric flow rates and time histories for: (b) effluent turbidity and (c) axial strains.


FIG. 10 Illustration of (a) captured fines on top of loading piston due to piping failure (Test 3 in Table 1), (b) development of piping leading to the washout (Test 5), (c) onset of washout (Test 5), (d) development of washout failure under cyclic loading at 10 Hz (Test 8), and (e) onset of washout at 20 Hz (Test 9).

respectively (Fig. 9). These turbidity peaks evolving from the washout of finer fractions from the gap-graded sample-G continued to grow higher (NTU 60) when the hydraulic pressure increased, that eventually resulted in larger axial

strains (Fig. 9c). Fig. 10 presents a visual illustration of the apparatus, the test samples, and the development and onsets of seepage induced internal instability in selected samples (Table 1).

TABLE 1 Hydro-mechanical factors at the onset of seepage induced internal instability in current samples. Mean Effective Stress (kPa) Test Series Sample Loading Number ID Frequency (Hz)

Initial r0mvi

At Onset r0mvo

Hydraulic Gradient Average Local Du Induced icr;a iij iDu

ru

Internal Stability

Remarks

(Yes/No)

(Failure Type) Heave

1

C

0

46.7

9

50.2

52

0

0

Yes

2 3

C C

0 5

46.7 46.7

8 8.5

51.4 49

55 56.7

0 1.80

0 0.093

Yes Yes

4

F

0

47.1

10.1

44.5

41

0

0

Yes

5 6

F F

0 5

47.1 47.1

9.3 9.6

45.8 42.4

44 46.5

0 2.75

0 0.127

Yes Yes

7

G

0

47.4

13.5

15.3

27.5

0

0

No

8

G

0

47.4

14.7

16.3

26

0

0

No

9

G

5

47.2

19.1

12.8

29.8

5.08

0.117

No

10

G

10

47.3

18.7

11.8

30.7

6.77

0.160

No

11 12

G G

15 20

47.3 47.4

18.6 18.4

11.5 11.2

30.9 31.1

7.28 7.79

0.173 0.187

No No

Note: Here, the ru defines the pore pressure ratio normalized with local mean effective confining stress.

Heave-piping

Washout Excessive/Pre-mature washout

805

806


FIG. 11 Time histories of local hydraulic gradients and onset of seepage induced failures for selected internally: (a) stable and (b) unstable test samples.

HYDRO-MECHANICAL RESPONSE AND SEEPAGE INDUCED FAILURES Fig. 11 presents the time histories of local hydraulic gradients (icr;ij ) for the selected test samples, whereby the onsets of internal instability are indicated by the average critical hydraulic gradients (icr;a ). Fig. 11a presents the results of internally stable samples (i.e., C and F) with and without LC, in solid and dotted lines, respectively. The failure onsets in sample-C and -F were characterized by the development of heave and a visual heave-piping at high hydraulic gradients and relatively small corresponding mean effective stresses (i.e., r0mv 10 kPa), respectively. Note that irrespective of whether or not the load cells were placed inside the samples, the average and local icr -magnitudes obtained for samples-C and -F were consistent. This again confirmed the repeatability of tests and the fact that instrumentation had no significant effects on the test results

(see Fig. 11a). For instance, the average icr;a ¼ 51:4 and 50:2 were obtained for sample-C with and without the load cells within the samples with a corresponding r0mv ¼ 8:6 and 8 kPa, respectively. Fig. 11b presents the local hydraulic gradients for sample-G under static and cyclic loading conditions. Under static loading, the magnitudes of average icr;a at the onset of washout were 15.3 and 16.3 with local icr;23 ¼ 27:5 and 26 with associated r0mv ¼ 13:5 and 15 kPa, respectively. However, under cyclic loading conditions, the same sample-G exhibited slightly premature washout failures. For instance, under f ¼ 5 and 20 Hz, the washout initiated at icr;a ¼12.8 and 11.2, icr;ij ¼29.8 and 31 under companion r0mv ¼19.1 and 18.4 kPa, respectively (Table 1). Notably, the increase in loading frequency from 5 to 20 Hz resulted in an increasingly premature failure in terms of icr;a values, whereas the washout initiated within the same layer-23


and at an almost similar icr;ij r0mv;ij combination, which clearly defined the hydro-mechanical boundary for sample-G. The decrease in porosity resulted in marked reductions in permeability that were reflected by the development of significant pore pressure (Du) within the test samples under cyclic loading. Similar observations were reported by Trani and Indraratna (2010b) for their filters F-2 and F-4, which experienced internal instability under pseudo-static filtration tests at f ¼ 5 Hz. The probable explanations for this discrepancy would be: (a) the development of localized (transient) pore pressure inside the samples, as shown in Fig. 11b, and (b) the constant agitation causing significant alterations in constriction sizes and packing patterns as well as the vigorous movement of finer fractions in the pore spaces due to cyclic loading, as described elsewhere (Xiao et al. 2006). In the current study this component of pore water pressure (Du) could be estimated by comparing the magnitudes of average and local icr for sample-G under static and cyclic loading conditions. Here, the local iij combined with iDu and approached the hydro-mechanical boundaries governed by unique icr;ij r0mv;ij combinations such that: icr;ij ¼ iDu þ iij

(9)

iDu ¼ Du=cw Dy

(10)

Du ¼ ru

r0co

FIG. 12

Correlations for (a) Du; ðbÞ ru and ðcÞ iDu against the cyclic loading frequency f.

(11)

where: ru ¼ the normalized pore pressure, r0co ð¼ r0mv ð1 þ 2K0 Þ=3Þ ¼ the mean effective confining stress, K0 (¼ 1 sin [0 ) ¼ the coefficient of earth pressure at rest, and [0 ¼ the drained angle of internal friction. By using the relationship for r0co in Eq 11 and then substituting it in Eq 10, it takes the following form: iDu ¼

ru r0mv ð1 þ 2K0 Þ 3 cw Dy

(12)

Equations 11 and 12 indicate that iDu is dependent on the effective confining stress, which is likely to vary significantly with the magnitude of applied cyclic loading that in this study was kept constant between r0min ¼ 30 kPa and r0max ¼ 70 kPa. Fig. 12 shows the observed correlations for Du; ru ; and iDu against applied cyclic loading frequency for the current test results, respectively. Similarly, Tables 1 and 2 summarize the factors governing the hydro-mechanical boundaries for the tested samples. These factors include r0mv -values initially and at the onset, the average, local, and Du-induced icr , estimated ru , stability assessments after Indraratna et al. (2015) and observed failure types. In Fig. 13a and 13b, icr;a was plotted against the gef ometrical stability index (Dcc35 =d85f ) introduced by Indraratna et al. (2015) and the initial r0mvi -values, respectively. One can

clearly observe the difference between the response of the test samples under static and cyclic loading conditions, whereby no clear relationships could be deduced. However, a clear correlation between icr;ij and r0mv;ij governing the failure onsets can be seen in Fig. 13c, whereby all the data from the static and cyclic tests could be described by a single empirical correlation. This

807

808


TABLE 2 Summary of current test results and those adopted from published literature. Internal Stability (Assessed)

icr

Observations Reported Local

Du (kPa)

50.2 51.4

52 55

0 0

S

49

56.7

0.53

1.1

S S

44.5 45.8

41 44

0 0

1 1

Frequency (Hz)

Ie

KL

Ke

Sh

Observed

Average

0 0

S S

S S

S S

S S

S S

1.5

5

S

S

S

S

1.1 1.1

0 0

S S

S S

S S

S S

F

1.1

5

S

S

S

S

S

42.4

46.5

0.81

1.18

170

G G

9.5 9.5

0 0

U U

U U

U U

U U

U U

15.3 16.3

27.5 26

0 0

1 1

155 195

G

9.5

5

U

U

U

U

U

12.8

30

1.5

2.2

200

G G

9.5 9.5

10 15

U U

U U

U U

U U

U U

11.8 11.5

30.4 30.3

2 2.14

2.4 2.6

255 270

G

9.5

20

U

U

U

U

U

11.2

31

2.30

2.8

250

5 10

S S

S S

U U

U U

S S

— —

0.4 2.9

2.3 3.1

3 30

Sample

Cu

References

C C

1.5 1.5

Current study

C F F

Ip-12 Ip-12

12 12

F-1

5.4

F-2 F-3

9.1 9.4

Chung et al. 2012 Trani and Indraratna 2010a

— —

ki =kf ratio 1 1

Turbidity (NTU) 0 0 48 130 145

5

S

S

S

S

S

10.2

—

—

1.5

60

5 5

S S

S S

S S

S S

U S

10.2 10.2

— —

— —

1.5 1.2

520 80

5

U

S

S

S

U

10.2

—

—

1.5

950

F-4

18

C15(1)

15

10

S

S

S

S

S

—

—

—

1.6

30

C15(2)

15

10

S

S

U

S

S

—

—

—

1.9

50

C15(3) C15(4)

15 15

10 10

U U

S U

U U

U U

U U

— —

— —

— —

1.8 0

225 >1000

C25

25

10

U

U

U

S

U

—

—

—

2.9

150

C45

45

10

U

U

U

U

U

—

—

—

4.4

450 800

Kamruzzaman et al. 2008

H-12

12

2

U

S

U

U

S

—

—

—

2.2

H-12

12

5

U

S

U

U

S

—

—

—

2.3

950

H-12 H-12

12 12

10 15

U U

S S

U U

U U

U U

— —

— —

— —

2.3 2.2

>1000 >1000

2

U

S

S

S

S

—

—

—

2.7

220

10

U

S

S

S

U

—

—

—

2.8

250

K-15

15

K-15

15

Haque et al. 2007

Kabir et al. 2006

Note: Here, Du; ki =kf ; Cu ; S; and U define pore pressure developed, ratio between initial and final (before failure) saturated hydraulic conductivities, uniformity coefficients, internally Stable, internally Unstable and Not-reported, respectively. Also, Ie, KL, Ke, and Sh represent Indraratna et al. (2015), Kenney and Lau (1985), Kezdi (1979) and Sherard (1979), respectively.

shows that seepage induced failures in soils occur at unique icr;ij r0mv;ij combinations, which govern the hydro-mechanical boundaries for internal instability that may or may not be independent of the type of loading. Analysis of impact of loading condition on magnitudes of critical hydraulic gradients revealed that icr;a under cyclic loading was smaller than under static loading and its magnitude reduced further with the increase in loading frequency. For instance, internally stable samples C and F showed 4 and 6 % reductions in icr;a under cyclic loading at 5 Hz, respectively, while Sample G showed up to 19, 25, 27, and 30 % reductions in icr;a under cyclic loading at 5, 10, 15, and 20 Hz, respectively. In contrast the magnitude of icr;ij tended to be higher under cyclic loading that increased further at higher frequencies.

For example, samples C and F showed 6 and 9 % increase in icr;ij at 5 Hz, respectively, while Sample G showed almost 11, 14, 15, and 16 % increase at 5, 10, 15, and 20 Hz, respectively. Table 2 presents the filtration test data under cyclic conditions taken from published literature and data from this current study. Most of this data does not provide enough hydromechanical factors to prevent the hydro-mechanical boundaries governing the onset of seepage induced failures to be evaluated. Similarly, the lack of data regarding Du-development prevented iDu from being estimated, so the effects of cyclic loading on the filtration of test specimens could not be quantified properly. However, the reductions in permeability due to cyclic loading, followed by the very large effluent turbidity values at the onset could indicate that the washout failures were excessive and


FIG. 13 Relationships between; (a) average critical hydraulic gradient and stability index of Indraratna et al. (2015), (b) average critical hydraulic gradient and initial mean effective stress (r0mvi ) and (c) local critical hydraulic gradient and mean effective stress at the onset (r0mvo ) of seepage induced failure for current test samples (Note: See Table 1 for test series numbers and description).

sudden in nature. For instance, although stable, the dense samples F-2 and F-4 (Rd > 95%) reportedly experienced 20 and 50 % reductions in permeability, respectively, before exhibiting dramatic suffusion as a result of significant agitation and development of Du under dynamic conditions (Trani and Indraratna 2010b).

Given that the severity of the test conditions can affect the internal stability of soils, the reported data were geometrically assessed by some existing criteria, including criteria from Kenney and Lau (1985), Kezdi (1979), Sherard (1979), and the CP-CSD method of Indraratna et al. (2015), for which the results were presented in Table 2. The application of Kenney and Lau’s (1985) criterion resulted in 6 unsafe predictions, whereas the criteria of Kezdi (1979) and Sherard (1979) produced 3 and 4 unsafe and 3 and 5 conservative assessments, respectively. The CP-CSD method had a more distinct approach at assessing the potential internal instability of reported samples, with only 4 incorrect (3 conservative and 1 unsafe) assessments. Much of the reported data clearly indicated that the filtration of granular soils under cyclic loading was different and more complex than that of static loading. Notably, the CP-CSD method which was deemed accurate for static filtration by Indraratna et al. (2015) could capture the cyclic filtration of samples with enhanced rigor compared to the other methods which only relied on soil’s PSD. The above analysis showed that none of the existing geometrical criteria for static filtration could accurately capture the potential internal instability of reported data under cyclic conditions (i.e., no 100 % success). However, the current results could be represented by a unique correlation between the local icr;ij and r0mv;ij magnitudes defining a clearer hydromechanical boundary for internal instability. This unique icr;ij r0mv;ij correlation that defined the static and cyclic tests in tandem indicates that the internal instability in granular soils may or may not be independent of the type of loading. This also showed that the existing geometrical criteria for internal stability of filters could be unsafe under cyclic conditions, where hydromechanical factors would govern the stability of filters. Nevertheless, this study highlighted some of these factors (icr;ij , icr;a , and r0mv;ij ) and investigated the effects of frequency on their magnitudes that may be useful for understanding filtration of soils under severe cyclic loading conditions due to earthquakes and high speed trains. Given that a limited number of tests with single loading magnitude were conducted in this study, no firm conclusions could be drawn regarding the factors governing this unique hydro-mechanical combination. Nevertheless, it is likely that the filtration of soils may be affected by the change in loading magnitude, direction of seepage flow, and confining pressures that have not been covered in this study. The complexities arising from the reduction in permeability due to fabric compression, developments ofDu, variations in the effective stress, and the icr magnitudes, must be accounted for in the design of filters under cyclic loading conditions. In this respect, the current study should be regarded as a framework for future developments on the topic of internal instability in granular soils under dynamic conditions.

809

810


Conclusions A new testing facility capable of examining the seepage behavior of granular soils under static and cyclic loading conditions has been developed and a series of internal erosion tests was conducted on three soil samples. The following conclusions were drawn: (1) The initial distribution of effective stress in soils may have reduced linearly along the height of the sample due to seepage and then become increasingly non-linear near the onset of internal instability. In stable soils, the magnitude of effective stresses at the onset is likely to be very low compared to unstable soils that could still be carrying a significant magnitude of effective stresses. (2) The study revealed that internally stable (uniform) soils can have heave and heave-piping phenomenon under cyclic loading, whereas the gap graded soils showed washout failure under static loading that became excessively premature under cyclic loading. For instance, heave and heave-piping failures occurred in densely compacted uniform fine gravels and fine sands, respectively, and suffusion was observed in gap-graded sandygravel soil. (3) The samples-C and -F subject to initial r0vt ¼ 50 kPa, experienced heave failures at low mean vertical effective stresses (i.e., 10 kPa) with an icr;a more than twice that of sample-G, which exhibited severe washout at r0vmo 14 kPa and icr;a 16 under static loading conditions. Notably, gap-graded sample-G exhibited relatively premature washouts when subjected to cyclic loading (e.g., at icr;a ¼12.8 and 11.2 under f ¼5 and 20 Hz, respectively). (4) An analysis of local hydraulic gradients revealed that the washout in sample-G began within the range of r0vmo 14 20 kPa and companion icr;ij 26 31. The relationship between average critical hydraulic gradient was significantly lower for the gap-graded soils as compared to the uniformly-graded soils. Nevertheless, the relationship between local critical hydraulic gradient and local mean effective stress was found to be same for the static and cyclic loading. (5) Observing that the internal stability of soils was affected markedly by the severity of hydro-mechanical factors under cyclic loading, a comparison for potential internal instability assessments by various existing criteria was made. It was revealed that the method of Indraratna et al. (2015) that incorporates both PSD and CSD of soils in tandem could assess the reported results with enhanced rigor compared to many other existing criteria. However, none of these geometrical criteria claimed 100 % success in assessing the potential for internal instability. (6) The application of cyclic loading resulted in a significant development of Duthat in corroboration with marked vibration of fines within pore spaces facilitated the development of premature suffusion. Their effect was

quantified in terms of a normalized pore pressure ratio and the resulting iDu could be back-calculated, which was observed to be directly related to the cyclic frequency for current results under given cyclic loading magnitude (r0min ¼ 30 and r0max ¼ 70 kPa). It was observed that the seepage induced failures in soils occurred at unique hydro-mechanical boundaries that may or may not be independent of loading conditions (static or cyclic). For instance, the icr;ij r0mv;ij relationship for the current data obtained from the static and cyclic loading tests could be described by a single correlation. Nonetheless, it is likely that the observed hydro-mechanical combination may vary depending on the type of soil (cohesive and non-cohesive), its physical and geometrical properties (lf ; [0 ; PSD, Rd , and CSD), loading magnitude (r0vt ), and direction of seepage. Further research would be invaluable in determining the effects of varying the magnitudes of cyclic loading and confining pressure on hydro-mechanical boundaries that was not covered in this study. ACKNOWLEDGMENTS

The financial support from University of Engineering and Technology Lahore, Pakistan and the University of Wollongong, Australia, given in the form of a PhD scholarship to the first author is acknowledged. The technical support from High-bay laboratory staff of UoW is also appreciated.

Appendix Derivations of Eqs 1, 4, and 7. Applying limit equilibrium to the sum of all disturbing forces within the soil layer (Fig. 5(c)): FM þ FW þ Ff þ FS ¼ 0

(13)

where, FM , FW , Ff , and FS define the sum of forces due to vertical effective stresses, effective weight of soil layer, cell wall frictional resistance, and seepage stresses due to applied hydraulic gradient, respectively (see Eqs 14–17). pD2 @r FM ¼ dy 4 @y FW ¼

pD2 0 c dy 4

Ff ¼ pDlK0 r0mv dy

(14)

(15)

(16)

2

FS ¼

pD ii cw dy 4

(17)

Now using Eqs 14–17 in Eq 13 and simplifying: @r ¼ c0 þ ii cw þ gf r0mv @y

(18)


For hydrostatic case (i ¼ 0), the stress reduction is merely governed by the upward skin friction @r0v ¼ c0 gf r0 @y ! ðz 4lf 0 D dy

dr0v ¼ r c0 D 4lf 0 ! " !# D Dc0 0 0

drv ¼ r 4lf z 4lf z h i Taking, r0 Dc0 =4lf z ¼ r0v

4lf z ¼ ln r0v

D 4 z f 0 rv ¼ e D eC1 Using initial condition, i.e., at z ¼ 0, Eq 23 modifies to read: " # Dc0 C1 0 e ¼ rz 4lf

(19)

(20)

(21)

(22)

(23)

(24)

Using Eq 24 in Eq 23 and simplifying further, one can obtain Eq 4. Now, for a soil sample subject to axial stress from top and upward seepage, the finite discretization of Eq 3 yields Eq 4 that governs the effective stress reduction: Dyi gf 0 rv;iþ1 r0v;i ¼ Dyi ðc0 ii cw Þ 2

(25)

Dyi gf 0 Dyi gf 0 rv;iþ1 r0v;i þ rv;i ¼ Dyi ðc0 ii cw Þ 2 2

(26)

r0v;iþ1 r0v;i r0v;iþ1 þ

gf Dyi gf Dyi r0v;i 1 ¼ Dyi ðc0 ii cw Þ r0v;iþ1 1 þ 2 2 r0v;iþ1

1 r0v;i Xi ¼ Dyi ðc0 ii cw Þ Yi

(27)

(28)

Eq 28 can be simplified further to obtain Eq 7.

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