Keywords

1 Introduction

Large-scale creeping landslides often refer to massive mass movements that slide down the mountain slopes at a creeping rate of displacement, ranging from a few to tens of centimeters a year. Depending on the geohydrological conditions, the displacement rate fluctuates, but in many cases, it is found to be only a few centimeters a year. Such a slow rate of land sliding is often also referred to as creeping displacement, and the soil material in the slip surface of such landslides is often found to be clayey, which is generally found and considered to be in its residual state of shear due to continuous landslide displacement for a long time.

Even when the geohydrological conditions do not change, the landslide activity continues under the influence of gravitational force-produced shear component along the shear surface that can be considered almost equal to the amount of shear resistance produced along the shear surface, i.e., a condition of limit state failure. However, Patton (1984) describes that such landslides keep moving even when the slip surface shear resistance is slightly greater than the driving shear forces. If we consider that the stress conditions on the slip surface material do not change for a certain duration but the landslide is in constant downslope movement, we can compare this situation with creep phenomenon, which basically is time-dependent rise in strain under a constant applied stress. So, it is considered that the large-scale landslide displacement behavior can be understood through shear creep tests on clayey materials. However, due to already occurred large shear deformation (or displacement), the shear resistance along the slip surface cannot be treated as that of an only slightly sheared soil material. So, use of a ring shear machine has been in practice for the last several decades, especially when evaluating landslides and large deformation ground problems. The ring shear machine can shear an annular soil specimen for nearly infinite amount of shear deformation and helps to measure peak and residual shear resistances of a clayey soil material.

In general, the shear strength of a soil is defined as its maximum resistance to applied shear force (Skempton 1964; 1985; Bishop et al. 1971; Lupini et al. 1981, Giba and Egashira 1992; Gibo 1994; Nakamura et al. 2010). When a soil is sheared, the developed shear resistance first reaches a peak value at a comparatively short time or less deformation. During this process, the soil material undergoes volume change due to vertical movement of soil particles and depending on the outward (known as dilation) or inward (known as contraction) movement of the particles, the developed peak shear resistance is high or low. The peak shear resistance, especially for overconsolidated or dense materials, is attained when the rate of outward vertical movement (i.e., dilation) of soil particles is maximum. Immediately after the peak value, upon further shearing, the shear resistance drops gradually until fully softened shear resistance is achieved, which is generally known as critical state (refer to Fig. 1). Shearing beyond the critical state may result in slight volume change (normally contraction), which is basically due to reorientation of clayey particles in the shear zone, but after the reorientation process is over, no further volume change is theoretically supposed to take place, and the frictional resistance exhibited remains constant. This very state is referred to as residual state of shear for clayey soil materials (Skempton 1964, 1985; Lupini et al. 1981).

Fig. 1
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General trend of pre- and post-peak shear resistance and shear deformations in ring shear tests (based on Skempton 1985)

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So far, most creep tests on soil materials have employed a triaxial compression cell or an oedometer (such as Ter-Stepanian 1963; Yen 1969; Waker 1969; Campanella and Vaid 1974; Nelson and Thompson 1977; Patton 1984; Feda 1989; Picarelli et al. 2001; Picarelli et al. 2004; Augustesen et al. 2004; Leoni et al. 2008; Yin et al. 2010; Brandes and Nakayama 2010, etc.), but these methods largely differ from the state of shear explained above, i.e., creep shear behavior of the slip surface material or the landslide creep, which may be ideally defined as a time-dependent slow displacement under no change in driving forces or stresses and can be represented by creep displacement curves shown in Fig. 2.

Fig. 2
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Ideal creep displacement curves showing primary, secondary, and tertiary states of shear creep and primary creep not leading to secondary creep

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At residual state of shear, a clay material is supposed to have zero to negligible cohesion and no effect of dilation or contraction. What helps the slip surface material at this state develop shear resistance is the true inter-particle frictional force generated amongst the soil particles. So, the existing creep test methods do not truly help understand the mechanism of creeping landslide displacement. So, for this study, an existing torsional ring shear machine was modified to make it also capable of measuring residual-state creep displacement under any amount of applied constant shear stresses. A special care was taken not to let the residual-state slip surface material undergo strength recovery due to period of shear stagnation while changing from ordinary shear to creep shear. So, in this article, the focus mainly goes onto introducing the residual-state creep shear test method for the experimental simulation of landslide creep, understanding the residual-state creep displacement behavior of different types of clayey materials, and linking the findings of this experimental study with the creeping type landslide displacement behavior.

2 Material and Method

2.1 Modified Ring Shear Machine

A torsional ring shear machine (Bishop et al. 1971) was used in this study after a few special modifications. The annular specimen container of the ring shear machine measures 8 cm inner diameter and 12 cm outer diameter with a total depth of 3.2 cm. To perform the residual-state creep tests, the ring shear machine was modified based on the transitional change of the strain-controlled motor-driven shear into creep load shearing without completely releasing the applied shear stress, which is capable of measuring the creep displacement with respect to time under the application of a constant creep load, as shown in Fig. 3. The lower part of the ring shear machine has been designed to allow the applied creep load to act directly on the slip surface of the test specimen, and the displacement or deformation due to the creep load can be recorded in the displacement recorder unit. The deformation of the specimen with respect to time and the corresponding changes in the volume of the specimen, if any, during the creep tests can be recorded automatically. The testing process involves strained-controlled shearing, confirmation of residual state, application of various creep shear stresses (or stress-controlled shearing) and recording of time-displacement histories.

Fig. 3
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Modified ring shear machine and experimental setup for the residual-state creep tests

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2.2 Test Materials

Landslide slip surface materials generally are clayey soils composed of common clay minerals such as smectite, chlorite, and illite. These minerals generally have very high specific surface area, higher cation exchange capacity, and greater affinity to water. For this reason, large-scale creeping landslides have been extensively studied from clay mineralogical perspective and are often interpreted as a long-term geomorphological process influenced significantly by mineralogical changes (e.g., Yatabe et al. 1991; 2007, Torii et al. 2006). So, in this study, all tests were conducted using commercially available kaolin clay, Toyoura sand powder finer than 75 µm, and their mixtures with commercially available Na-bentonite powder (with about 50% smectite content) in different desired proportions. The mix proportion of Na-bentonite in kaolin and the sand powder was 5, 10, 15, 20, and 25% by weight. The main purpose of increasing the amount of Na-bentonite in the test samples was to achieve decreasing residual strength or residual friction angle (ϕr) of the test samples. The physical properties and ring shear results of the tested mix samples are presented in Table 1. In the ‘sample name’ column, SP refers to sand powder, K refers to kaolin powder, B refers to bentonite powder, and the figures after these notation letters refer to the percentage of the material mixed in that test sample. For example, SP100 refers to 100% sand powder, K100 refers to 100% kaolin while SP95+B5 refers to 95% sand powder and 5% bentonite, K75+B25 refers to 75% kaolin and 25% bentonite.

Table 1 Physical properties and ring shear results of the clayey soils
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2.3 Experimental Program

In the residual-state shear creep tests, two main steps were followed: (1) ordinary ring shear tests and (2) residual-state shear creep tests. The ordinary ring shear tests were conducted to achieve the soil materials residual state of shear. This state was confirmed when the shearing had reached a state of constant values for the load-cell reading and dial gauge reading after about 10 cm of shear displacement. In the residual-state shear creep tests, the first creep load was calculated on the basis that the applied shear stress was 90% of the residual-state shear resistance, which is referred in this study as ‘Residual-state Creep Stress Ratio’ and is denoted by RRCS. A 90% residual-state creep stress ratio is denoted by RRCS = 0.9. Then, the material specimen was left under creep loading for several hours and displacement was recorded with the passage of time. After one set of creep test was considered or observed to have been over, the creep load was increased in subsequent steps and time-displacement histories were recorded. The overall experimental flow of the residual-state shear creep tests is shown in Fig. 4. The applied RRCS values in case of all tested samples varied from 0.9000 to 1.0300 in a step of 0.005.

Fig. 4
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Overall experimental flow of residual-state creep test

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All material samples were prepared for the tests by first uniformly mixing them with appropriate amount of distilled water and then deairing for complete saturation. The deaired liquid samples were then poured into the specimen maker and consolidated under a pressure of 98.1 kN/m2 until the primary consolidation was confirmed to be over. Then, the specimen was transferred into the ring shear machine’s sample container and consolidated again under a pressure of 196.2 kN/m2. However, to avoid unwanted machine friction due to high normal pressure, all shear tests were conducted under a normal pressure of 98.1 kN/m2 (with an overconsolidation ratio of 2.0). The shearing condition was confirmed to be fully drained by allowing sufficient time to dissipate excess pore water pressure, for which the average rate of displacement through the slip surface was set at 0.15 mm/min. At first, strain-controlled shearing was conducted until the residual state of shearing was achieved and residual strength was obtained. Then, the strain-controlled shearing was stopped for about 10 min, and preparations for the creep test were made.

To avoid confusions and discrepancies due to unknown parameters, some important assumptions were made in this study, which are as follows:

  • At the residual-state of shear, there is no influence of further displacement on the shear resistance of the slip surface soil.

  • The amount of recovered shear strength, if any, due to reduction in the rate of shear (e.g., Bhat and Yatabe 2015; Scaringi et al. 2018) or due to the state of no shear is negligible.

  • The effect on the shear resistance due to lack of uniformity in sample preparation, if any, effective stress application accuracy, etc. is negligible.

  • The change in the shear behavior due to changes in the value of the RRCS, if any, is negligible.

  • There is no influence of any amount of displacement in the amount of shear resistance if the sheared material has already reached its residual state

3 Results and Discussion

Creep deformation in soil materials is often explained in three stages, as also illustrated in Fig. 2. In the beginning, the deformation increases rapidly but slows down to a certain value; this stage is known as primary creep. Then, the rate of deformation becomes constant; this is known as secondary creep. Finally, the deformation rate starts to increase exponentially leading to complete failure; this stage is known as tertiary creep. So, in this study, the test results are basically summarized in three stages of creep.

Of the residual-state shear creep test results of total 12 clayey material samples (refer to Table 1), four representative test results for the K100, SP100, K75+B25, and SP75+B25 samples are presented respectively in Figs. 5, 6, 7 and 8, and the basic parameters obtained from the test results in Figs. are summarized respectively in Tables 2, 3, 4 and 5. Owing to the space constraint, the test results for the other eight samples are not presented but all those results are used in interpreting the residual-state creep failure behavior in subsequent discussion. As indicated in the above figures and tables, t1 refers to the elapsed time up to the end of primary creep (or beginning of the secondary creep), δ1 refers to the amount of displacement corresponding to t1, tf refers to the time when secondary creep ends and tertiary creep begins (i.e., final stage of creep failure), and δc refers to the amount of displacement corresponding to tf.

Fig. 5
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A typical set of residual-state shear creep test results of the K100 sample (i.e., 100% kaolin powder)

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Fig. 6
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A typical set of residual-state shear creep test results of the SP100 sample (i.e., 100% sand powder)

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Fig. 7
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A typical set of residual-state shear creep test results of the K75+B25 sample (i.e., 75% kaolin powder and 25% bentonite powder)

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Fig. 8
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A typical set of residual-state shear creep test results of the SP75+B25 sample (i.e., 75% sand powder and 25% bentonite powder)

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Table 2 Summary of the residual-state creep tests on the K100 sample (refer to Fig. 5)
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Table 3 Summary of the residual-state creep tests on the SP100 sample (refer to Fig. 6)
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Table 4 Summary of the residual-state creep tests on the K75 + B25 sample (refer to Fig. 7)
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Table 5 Summary of the residual-state creep tests on the SP75+B25 sample (refer to Fig. 8)
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Particularly in the figures above, it is evident that for all cases of RRCS, the amounts of displacement at the time of failure, i.e., at the beginning of the tertiary creep, are more or less the same (also refer to Tables 2, 3, 4 and 5). It indicates that regardless of the amount of applied creep stress, the soil material in its residual state of shear fails only after a certain amount of displacement is achieved. So, in this study, this typical amount of displacement is named as ‘critical displacement’ and is denoted by δc. In case of the K100 sample (Fig. 5), an averaged critical displacement is around 1.758 mm. Likewise, it is 1.414 mm for SP100 sample (Fig. 6), 4.014 mm for K75+B25 sample (Fig. 7), and 2.89 mm for SP75+B25 sample (Fig. 8).

Although the test results of other eight samples are not presented, the critical displacements for the SP95 +B5, K95+B5, SP90+B10, K90+B10, SP85+ B15, SP80+B20, K85+ B15, and K80 +B20 samples were estimated to be 1.925 mm, 1.974 mm, 2.104 mm, 2.250 mm, 2.363 mm, 2.653 mm, 2.783 mm, and 3.136 mm, respectively. All these values of critical displacement are plotted against the values of angle of residual friction (ϕr) (as presented in Table 1) in Fig. 9. Except for a few points, the trend of decrease in critical displacement with increased angle of residual friction is quite linear. This trend clearly reveals that the critical displacement is inversely proportional to residual friction characteristic of a clay material.

Fig. 9
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Relation between critical displacement (δc) and residual friction angle (ϕr) of the clayey soils

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The concept of critical displacement may be understood further through coefficient of friction. Basically, any material exhibits two types of frictional behaviors as governed by coefficient of static friction µs (i.e., frictional resistance in rest) and coefficient of kinematic friction µk (i.e., frictional resistance while in motion). The coefficient of static friction is usually greater than the coefficient of kinematic friction, which means a stationary object always needs a greater force to move than to keep it in motion. In a soil material too, the initial force required shear it is always greater than the force required to keep it shearing. So, in this case too, in the beginning the coefficient of static friction (µs) governs the displacement, e.g., in primary and secondary stages of creep, but as soon as the displacement reaches its critical value, the coefficient of kinematic friction (µk) comes into scene to govern the frictional behavior, which leads to accelerated displacement and thereby to complete failure. So, the amount of displacement required for transitional change of µs to µk is understood as critical displacement in this study.

The test results also reveal that creep deformation for RRCS values equal to or below 1.0 does not progress to secondary and tertiary stages (e.g., first three test cases in Fig. 5), which means regardless of the length of time, the clay material does not fail in creep. However, as soon as the RRCS value gets greater than 1.0, the creep failure does take place, and the trend is greater the RRCS value, shorter the time up to failure. Moreover, amongst the tested samples, RRCS = 1.03 was found to be the upper limiting value revealing any greater value would result in instantaneous failure. This more or less indicates that creep failure in residual state of shear of clayey materials is exhibited from a shear loading equivalent to residual shear resistance to an increase in shear loading by 3% of the residual shear resistance.

Furthermore, variation of failure time (tf) with residual-state creep stress ratio (RRCS) for all tested samples is shown in Fig. 10. It is more than clear from this figure that the failure time (tf) is a function of residual-state creep stress ratio (RRCS) and residual friction angle (ϕr). For a particular sample, there is a fine trend of curvilinear decrease in logarithmic time of failure (i.e., log(tf)) with the increase in residual-state creep stress ratio (RRCS), while tf is seen to get longer with a greater angle of residual friction (ϕr). This tri-parametric relationship between failure time (tf), residual-state creep stress ratio (RRCS), and angle of residual friction (ϕr) can be well considered an important basis for predicting residual-state creep failure of clayey materials. Moreover, establishment of a numerical relationship between these three parameters is considered to help predict creeping landslide displacements. For example, if a landslide can be precisely assessed to give representative angle of residual friction of the slip layer clay and state of shear stress application, the time required up to complete sliding can be very well estimated.

Fig. 10
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Variation of failure time (tf) with residual-state creep stress ratio (RRCS)

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4 Concluding Remarks

Application of creep deformation theory in predicting deep-seated landslide failures has been a topic of interest to landslide researchers for a long time. However, most of the work done so far is focused on understanding creep failure behavior of soil materials within the range from strain hardening to strain softening, which does not adequately explain the creep failure mechanism of clayey materials that have already reached a state of residual friction, such as in large-scale creeping landslides. In this study, a modified ring shear machine was used to conduct ordinary ring shear tests and residual-state creep shear tests. Altogether 12 lab-prepared clay samples were used in the test sets, and the recorded time-displacement data series were interpreted to understand the residual-state creep deformation behavior of clayey materials. One of the most important understandings is when RRCS ≤ 1.0, no clay material exhibits creep failure in the state of residual shear, but it takes place only when RRCS > 1. In addition, the amount of displacement required for tertiary creep to begin in a particular clay material was found to be the same regardless of the amount of creep load applied. This amount of displacement (i.e., critical displacement) is inversely related with the residual shear strength (or the angle of residual friction) of clay materials. Furthermore, the time until complete failure or the failure time (tf) is a function of residual-state creep stress ratio (RRCS) and angle of residual friction (ϕr). Finally, a numerical relationship between these three parameters needs to be established for predicting landslide creep displacement and failure.