The Reactivated Residual Strength: Laboratory Tests and Practical Considerations

Abstract

As is already known, some currently stable landslides may have been activated in the past along a pre-existing sliding surface and reached the residual strength there, as a consequence of high-cumulative displacements. After a fairly long period of quiescence, these landslides can reactivate due to a temporary increase in destabilising forces capable of mobilising the residual strength along the same sliding surface again. Some recent studies have suggested that, under certain conditions, the strength mobilised upon reactivation may slightly exceed the residual value and then decay towards the latter as the displacement progresses. Regarding this matter, many previous studies have hypothesised that some geotechnical variables could affect the recovered strength more significantly: the length of the ageing time, the vertical stress, the stress history, and the speed with which the reactivation occurs. The aim of this research is to confirm whether such recovery of strength upon reactivation is possible and which geotechnical parameters have the greatest influence on the process. To this end, laboratory tests were carried out with the Bromhead ring shear apparatus on normally consolidated saturated samples of both natural soils and clays provided by industry (bentonite and kaolin). The coupling effect of the ageing time, the vertical stress, and the reactivation speed on the mobilised strength upon reactivation were investigated, starting from a pre-existing residual state of these samples. Within the limits of this research, the results seem to confirm that all three geotechnical variables are influential, with a greater impact on the reactivation speed and, subordinately, on the ageing time for long quiescence periods. Therefore, it is concluded that a quiescent landslide could show a reactivated strength slightly higher than the residual value if the destabilising action could arise with a certain rapidity. Conversely, if the destabilising action occurs very slowly, the mobilised strength could correspond to the residual value. The experimental results of this research may find some application in the design of strengthening works for a stable quiescent landslide that could experience a fairly rapid increase in destabilising actions, such as in the case of seismic stress, morphological modification of the slope, or a rising water table.

1. Introduction

When a landslide undergoes large displacements along a sliding surface, the available soil strength reaches a minimum value, which is the residual strength. Under this condition, quiescence or reactivation may occur, depending on the extent the available soil strength is able to balance the increase of destabilising forces. However, predicting the future behaviour of a quiescent landslide is very complex: the landslide could reactivate with uniform or accelerated motions or with both, could creep, stop, and then reactivate again. Under this scenario, the recovered strength during quiescence could play a key role, especially if it could be different from the value reached in the previous active phase.

At the present time, the existence of a reactivated strength different from the residual one is still a matter of discussion, even though some researchers have highlighted the importance of the quiescence time, the stress history, the stress level, and the speed of reactivation on the amount of the mobilised strength upon reactivation.

For example, Alonso and Pinyol [1] hypothesised that ageing could cause the progressive increase in strength during the stability periods. In contrast, Skempton [2,3] stated that if a failure has already occurred in clayey soils, any subsequent displacement along the slip surface will be controlled by the residual strength; therefore, an old quiescent landslide could only reactivate by mobilising again the residual strength along the pre-existing sliding surface. To confirm Skempton’s hypothesis, Mesri and Huvaj-Sarihan [4] presented a comparison between secant residual strength angles determined from both back analyses of reactivated landslides and laboratory tests: this comparison did not show any strength regain at the reactivation.

Many other authors [5,6,7,8,9,10,11,12] expressed different opinions supporting the fact that the strength at reactivation could exceed the steady residual strength, in both laboratory tests and full scale observations.

D’Appolonia et al. [13] found that the mobilised strength for a West Virginia landslide (U.S.A.) was greater than the laboratory residual strength, and Hamel and Adams [14] stated that, in the Appalachian Plateau (U.S.A.), the strength gains are likely to be within the range of 20% to 50% of the shear strengths measured in laboratory tests of practical duration on small specimens.

The reactivation mechanism of ancient landslides in Southwest China was examined by Zhang et al. [15] and a healing mechanism was considered a plausible explanation for the stable status of these landslides for a long period.

The self-healing phenomenon of a red-bed landslide was studied by Yan et al. [16]: the relationship between the recovery strength of the shear surface and the healing time was analysed by reversal shear tests, and the law of the recovery strength was then analysed under different vertical stresses.

The self-healing of a landslide using laboratory ring shear tests with different shear rates and grain sizes was studied by Jiang et al. [17]. The authors found that the peak strength of the landslide that had undergone accelerated creep was greater than the previous peak strength.

Wang et al. [18] and Dong et al. [19] showed that the strength recovery increases as both the vertical stress and the healing time increase; however, the rate of growth decreases and ultimately approaches zero as the recovery time increases.

Miao et al. [20] and Miao and Wang [21] suggested that the residual shear strength of the soils within the sliding zone in the Jurassic red strata in Three Gorges Reservoir (China) could have had a certain recovery as a result of the secondary compression of the shear zone. Soils with a high clay content generally do not exhibit a significant strength recovery, while soils with a low clay content clearly recover their residual strength due to the volume change of the shear zone caused by secondary compression after a long period of reconsolidation. In this case, greater external load or a reduction in effective stress are needed to reactivate the landslide.

Referring to the effect of stress history, Zheng et al. [22] showed that the reactivated residual strength increased with the increase in OCR, even after a short resting time of one day. Moreover, the overconsolidation effect on reactivated residual strength was more prominent at lower vertical stress levels than that at higher vertical stress levels.

Qi et al. [23] asserted that the slip zones of ancient landslides have anomalous high shear strengths and the healing mechanism of the failure surfaces makes the evolution of the ancient landslides difficult to describe via traditional residual strength theory.

As considered by Stark and Hussain [10], a strength gain due to ageing could explain the behaviour of shallow landslides investigated by previous researchers [5,6,13]; the same authors suggested that the strength gain could also explain the reduction in slope creep until the complete cessation of movements.

The practical position regarding the reactivated residual strength is that the strength recovery should be considered with caution in the mitigation measures of landslides, because if this occurs, it could be lost as a result of very small displacements. Nevertheless, even if of limited intensity, Alvarado et al. [24] stated that the transient peak strength at reactivation may have an effect on the landslide stability, so this could have a significant implication in designing the stabilisation works.

In this research, we attempted to evaluate the coupling effect of ageing time, vertical stress, and reactivation speed on the mobilised strength upon reactivation, starting from a pre-existing residual state. Normally consolidated samples, both natural soils and clays provided by industry (bentonite and kaolin), were tested in fully saturated conditions by using the Bromhead ring shear apparatus. Although physical–chemical effects related to the interaction with the physical environment [24,25,26] could modify the reactivated soil strength, they have not been considered here.

Within the limits of this research, the results seemed to confirm that, in saturated normally consolidated soils, all three of the geotechnical variables mentioned above could cause a strength at reactivation slightly greater than the residual one, but decaying fast towards the latter as the displacement progresses.

2. The Database

Italy is particularly affected by slope instabilities in proximity of the Alpine and the Appennine chains. The samples under investigation were taken from landslides that occurred in 14 sites located on the slopes of these two long chains.

The sites of Recoaro, Fantoni, Tessina, Cortina, Rosazzo, and Montona fall into the south-eastern Alps, an area characterised by overlapping sedimentary layers delimited by the Padana plain at the southern margin.

The site of Arquà Petrarca belongs to the complex of the Euganean hills, an area characterised by eruptive bodies surrounded by sedimentary profiles gradually becoming part of the Padana plain.

The sites of Val Tidone, Castiglion de Pepoli, Val di Sambro, Buttoli, and Cecina fall into the Tosco–Emilian Apennines, while the sites of Calatabiano and Caltavuturo fall into the Sicilian Apennines.

The location of the aforementioned sites along the Italian peninsula is shown in Figure 1, along with the Italian landslide hazard map compiled by ISPRA [27]. At present, the ISPRA database reports about 630,000 landslides, many of which reactivated after several years, decades, or even centuries of quiescence.

The geotechnical data of 24 natural soils tested in this research are summarised in

Table 1. Geotechnical properties of all 26 samples tested in this research.

Sample Identification	Fine Fraction FF (%)	Clay Fraction CF (%)	Liquid Limit wL (%)	Plastic Limit wP (%)	Plasticity Index PI (%)	Activity Index AI	${\overline{\mathsf{\phi }}}_{\mathbf{r}}(°)$ (V = 0.089 mm/min)	Comparison Parameter $\frac{\mathbf{C}\mathbf{F}(\mathbf{\%})+\mathbf{P}\mathbf{I}(\mathbf{\%})}{{\mathbf{w}}_{\mathbf{p}}(\mathbf{\%})}$
Sodium Bentonite	98	75	346	68	278	3.71	7.7	5.19
Kaolin	100	22	46	24	22	1.00	25.4	1.83
Buttoli 1	77	25	38	18	20	0.80	11.0	2.50
Buttoli 2	81	30	45	22	23	0.77	15.3	2.41
Cecina	75	35	53	27	26	0.74	18.5	2.26
Val di Sambro 1	53	17	44	23	21	1.24	27.5	1.65
Fantoni S8	80	20	76	36	40	2.00	25.1	1.67
Fantoni S10	91	40	97	50	47	1.18	22.1	1.74
Fantoni S12	58	12	60	27	33	2.75	28.7	1.67
Fantoni A	68	13	48	31	17	1.31	31.3	0.97
Fantoni E	92	17	56	24	32	1.88	27.9	2.04
Fantoni I	79	25	66	39	27	1.08	26.9	1.33
Fantoni L	85	24	74	37	37	1.54	26.0	1.65
Fantoni M	81	24	69	44	25	1.04	28.3	1.11
Rosazzo	70	25	45	22	23	0.92	27.0	2.18
Rosazzo 1	85	22	47	27	20	0.91	29.8	1.56
Montona	75	40	51	24	27	0.68	27.3	2.79
Castiglion de Pepoli	58	18	46	26	20	1.11	29.0	1.46
Val Tidone C	97	34	52	28	24	0.71	20.8	2.07
Tessina S	93	21	41	26	15	0.71	27.4	1.38
Tessina C	75	17	37	23	14	0.82	27.3	1.35
Arquà Petrarca	53	5	34	29	5	1.00	35.3	0.34
Recoaro	47	7	25	20	5	1.00	33.5	0.60
Caltavuturo	63	18	48	25	23	1.28	24.1	1.64
Calatabiano	53	5	33	26	7	1.40	33.2	0.46
Cortina	96	44	69	35	34	0.77	17.2	2.23

; for comparison purposes, the data of two clays, a sodium bentonite and of a kaolin both provided by industry, are also shown.

The residual strength was measured with the standard Bromhead ring shear apparatus with outer and inner diameters of 100 mm and 70 mm, respectively. To avoid excessive settlement during consolidation, reconstituted specimens were made by hydrating at a water content sufficiently below the liquid limit. After consolidation, the reconstituted specimens had an initial thickness of about 5 mm. In order to generate the sliding surface in a short time, all the samples were subjected to an initial relative rotation of 360° (final relative displacement of 270 mm) at a displacement rate of 11 mm/min.

After pore overpressure dissipation, the stabilised residual strength was evaluated for all the samples at a constant rate of 0.089 mm/min.

The 26 mean secant residual strength angles, ${\overline{\phi }}_{\mathrm{r}}$, reported in Table 1 were evaluated by averaging the results obtained for three vertical stresses, σ_v, of 27.6 kPa, 52.1 kPa, and 101.1 kPa at the sliding speed of 0.089 mm/min.

The effect of ageing was studied for 10 samples (Sodium Bentonite, Buttoli 1, Val di Sambro 1, Fantoni S10, Rosazzo, Rosazzo 1, Montona, Castiglion de Pepoli, Caltavuturo, and Calatabiano) for which reactivations were performed after cycles of ageing ranging from fifteen minutes to, at most, one month.

Finally, the effect of three rate of shearing, v, of 0.018 mm/min, 0.089 mm/min, and 0.445 mm/min was investigated for Calatabiano and Caltavuturo clays only.

In order to draw a general picture of the 26 samples under study, all the secant residual strength angles have been reported in Figure 2 in relation to the clay fraction, CF% (Figure 2a) and by using a new comparison parameter, (CF + PI)/w_P (Figure 2b), being w_P (%) the plastic limit and PI% the plasticity index. All the data in Figure 2 refer to the three aforementioned vertical stresses and to a rate of shearing of 0.089 mm/min.

Compared with the representations making use of CF or PI alone, it was found that the parameter (CF + PI)/w_P involves less dispersion of the data. Looking at Figure 2b, all the data are placed within a band limited by a lower and an upper envelope: the upper envelope delimits the samples with the largest residual strength angle, characterised by an interplay between lower plasticity, lower clay fraction, and lower vertical stress, whereas the lower envelope delimits the samples with the smallest residual strength angles, characterised by an interplay between greater plasticity, greater clay fraction, and greater vertical stress. The evidence that the secant residual strength angle decreases as the vertical stress increases proved that the residual strength envelopes are affected by non-linearity, especially at a low stress level.

3. Steady-State and Reactivated Residual Strength

Generally, the effect of the displacement speeds on the steady residual strength has been subjected to extensive studies throughout the last few decades, considering both low [2,3,28] and high displacement speeds [29,30,31,32].

Referring exclusively to the effect of the low reactivation speed, which concerns the object of this study, it was deemed essential to recall some results available in the scientific literature: Skempton [3] stated that, at a sliding speed of less than 0.01 mm/min, the residual strength can be considered as drained, i.e., not influenced by neutral pore pressure. At greater displacement speed, but not exceeding 1.0 mm/min, the residual strength can oscillate between ±10% of the drained residual value obtained at a shearing speed of 0.01 ÷ 0.025 mm/min [30].

Further authors [33,34,35] suggested that, irrespective of the clay fraction content, the kinematics of a landslide could occur basically drained, if the displacement speed is less than 0.50 mm/min along the failure surface.

As sketched in Figure 3, the drained residual strength, τ_r(v), comes out as a reaction to a viscous–frictional behaviour, in which the viscous component of strength is related to the sliding speed, v.

If the relative displacement is stopped, a progressive decay of the residual strength is observed over time until its stabilisation on τ₀, a value for which no further stress decay should occur.

Cruden and Varnes [33] pointed out that shear creep may occur even at rates as low as 0.001 mm/min, thus requiring a very long time of observation; however, these observations were omitted from this research and the strength decay was considered concluded within the 30 days of the relaxation stage. Keeping this simplification in mind, the parameter τ₀ corresponded to a zero displacement speed and the shear creep was considered almost completely attenuated.

Later, τ₀ was used as a reference value in the quantification of the strength recovery upon reactivation.

The time spent in the relaxation stage represented an ageing period, t_age, during which the sample could have experienced variation in strength. Actually, ageing may occur under shear stresses also below or slightly above τ₀, as investigated by other researchers [36,37,38,39]; in this research, only ageing at τ₀ stress was considered.

When reactivation started at a constant displacement speed, an almost instantaneous growth in strength, τ_reac, occurred, followed by an equally rapid decay up to τ_r(v), as soon as the displacement proceeded. The transient increase in strength, ∆τ₁ = τ_reac − τ₀, configured rigid–fragile behaviour, which, in normally consolidated samples, could depend on three main factors: the vertical stress, σ_v, the sliding speed at reactivation, v, and the time spent during the quiescence phase, t_age. The increase in strength, ∆τ₂ = τ_r(v) − τ₀, could be considered a viscous strength component, related to both the vertical stress, σ_v, and the sliding speed, v.

The behaviour outlined above is discussed now with reference to the shear strength tests carried out for Caltavuturo and Calatabiano clays, for which the influence of the displacement speed upon reactivation was also investigated.

The Caltavuturo landslide occurred on 10 April 2015, in a flysch formation, as a result of heavy rainfall in locality Favara, Sicily. The Calatabiano landslide occurred the 24 October 2015, in a flysch formation, as a consequence of heavy rainfall in the centre of Calatabiano town, Sicily.

Figure 4 shows for both Caltavuturo (Figure 4a) and Calatabiano clays (Figure 4b) the trends of τ₀, τ_r(v), and τ_reac, for vertical stresses of 27.6 kPa, 52.1 kPa, and 101.1 kPa, shearing speed 0.089 mm/min, and ageing of one hour, while Figure 5 shows, for both Caltavuturo (Figure 5a) and Calatabiano clays (Figure 5b), the trend of τ_r(v) and τ_reac, for shearing speeds of 0.018 mm/min, 0.089 mm/min, and 0.445 mm/min, vertical stress of 27.6 kPa, and ageing of one hour.

From Figure 4 and Figure 5, both referring to the same ageing time, the influence of both vertical stress and reactivation speed on the reactivated strength is discernible, as is how the increase in strength, ∆τ₁, rapidly decays towards the stationary value τ_r(v).

For comparison purposes, the secant strength angle was evaluated: as shown in Figure 6, the secant angle of residual strength, φ₀, corresponds to the stress state τ₀ and σ_v, while the increments, ∆φ₁ and ∆φ₂, are related to the increments in shear stress ∆τ₁ and ∆τ₂.

The increments of ∆φ₁ after one hour of ageing and with varying vertical stresses and reactivation shearing speeds are reported in Figure 7 for both Caltavuturo (Figure 7a) and Calatabiano clays (Figure 7b). It is possible to notice how the reactivated strength grows in direct proportion to the shearing speed, whereas the relationship with the vertical stress is of inverse proportionality; this follows from the fact that the reactivated strength envelope slightly shifts upwards, with the result that ∆φ₁ increases more as the vertical stress decreases.

At the minimum speed of 0.018 mm/min, vertical stress of 27.6 kPa, and one hour of ageing, the increase in the strength angle at reactivation, ∆φ₁, was about 2.5° for Caltavuturo clay and about 3.5° for Calatabiano clay. At the maximum speed of 0.445 mm/min, this increase was about 5.5° for Caltavuturo clay and about 6.5° for Calatabiano clay.

The increase in strength at reactivation versus displacement speed is also highlighted in Figure 8 for both Caltavuturo (Figure 8a) and Calatabiano clays (Figure 8b), aged one hour under the vertical stress of 101.1 kPa. Both the magnitude of the reactivated strength and the displacement necessary to degrade the aged structure up to the steady condition depend on the shearing speed and the soil plasticity. The more plastic Catavuturo clay seems to require larger displacements to reach the steady residual condition, whereas the non-plastic Calatabiano clay shows smaller displacements under the same conditions. Moreover, the percentage increase in the reactivated strength angle (Figure 8) seemed to be greater in the more plastic samples.

From both Figure 7 and Figure 8, it can be deduced that quiescent landslides reactivated at very slow displacement speed may not show a significant increase in residual strength at reactivation; however, a quiescent landslide subjected to a seismic event or quick destabilising forces could mobilise a reactivation strength higher than that mobilised at very slow reactivation speed.

Figure 9 shows, for both Caltavuturo (Figure 9a) and Calatabiano clays (Figure 9b), the increase in strength, ∆τ₁, for a reactivation speed of 0.089 mm/min by considering the influence of both the vertical stress and the quiescence time, the latter extended up to one month. The equivalent representation in terms of secant strength angle, ∆φ₁, is shown in Figure 10 for both Caltavuturo (Figure 10a) and Calatabiano clays (Figure 10b).

Most of the time-dependent strength recovery takes place within the first 48 h, whereas the strength recovery for longer ageing periods appears to be slower. After one month of ageing, the increase in the reactivated secant strength angle for a reactivation speed of 0.089 mm/min and vertical stress of 27.6 kPa was about 7.5° for Caltavuturo clay and about 8.5° for Calatabiano clay. As already stated, passing from the representation in terms of ∆τ₁ to that one in terms of ∆φ₁, the role of vertical stress reversed: due to the envelope curvature, more accentuated at low stress, the secant strength angle increases more as the vertical stress decreases.

Figure 11 summarises the secant strength angles at reactivation, φ_react, for the 10 samples tested up to one month of ageing at shearing speed of 0.089 mm/min and vertical stress of 101.1 kPa.

In the same Figure 11, the reactivated strength angles are compared with the corresponding steady residual, φ_r(v), also obtained at the same shearing speed and vertical stress as the first ones. As already stated by Miao and Wang [21], it was observed that less plastic samples tend to develop a slightly larger increase in the reactivated strength angle in comparison to the more plastic ones. This fact is better highlighted in Figure 12, which shows the increase in the secant strength angle at reactivation, φ_reac − φ_r(v), as a function of clay content, CF, and considering both the minor and the major vertical stresses employed in the experiments, it is possible to note how the recovered strength angle seems to increase as the clay fraction decreases.

4. Some Possible Reasons to Explain the Strength Recovery upon Reactivation

Changes in the residual strength may occur as a result of two different classes of phenomena, the first related to the interaction between the soil and the physical environment [24,25,26] and the second related to the mechanics of the particle medium. Leaving aside the first class of phenomena, which is not the object of this research, some aspects relating to viscosity, creep, and thixotropy will now be discussed, keeping in mind that a rigorous quantification of the impact of these three soil properties on the reactivated strength is very complex and not foreseen by the aims of this research; creep and thixotropy, in particular, may require very long and extensive laboratory investigations carried out by means of specifically designed equipment.

4.1. Transition from Static to Kinetic Strength: The Role of Viscosity

In the framework of the friction theory, the transition from static to kinetic conditions is described in terms of static friction at detachment and the subsequent kinetic friction during the sliding phase at a constant rate of displacement. For low sliding speeds, the former kind of friction is usually greater than the latter and is the result of both interlocking and adhesion of the shared micro-roughness between the surfaces in contact.

Referring to the case of soil, the reactivated strength, τ_reac, plays a role analogous to that of static friction at detachment, whereas that of the steady residual strength, τ_r(v), is analogous to kinetic friction. However, the frictional mechanism in soil may be quite different: the reactivation starts with the deformation of the soil fabric, which then dislocates as soon as the relative displacement increases. The previous ageing phase causes some increase in the density of the particle-to-particle contacts along the shear band: the strong viscosity of the absorbed water at the particle contacts (edge-to-face hinge) may explain the initial reaction at the start of displacement. In order to explain the strength decrease following reactivation, it should be kept in mind that the displacement occurring along the shear band is orthogonal to the direction along which the volumetric creep occurs during ageing; therefore, the initial aged fabric may become destructurated as the displacement increases and the strength may quickly decay towards τ_r(v).

In this mechanism, the reactivation speed may play an important role: as shown in Figure 8, the reactivated strength increases with the displacement speed and conversely decreases if the reactivation speed is low. If the displacement speed approaches zero, the reactivated shear strength could approach the reference value, τ₀. This latter circumstance may occur irrespective of the amount of time spent in the previous ageing phase, and could be explained if the increase in strength at reactivation depended only on the viscous properties of the edge-to-face hinge so that ∆τ₁ may be imperceptible if the reactivation speed is almost null.

The strength increment upon reactivation may be expressed in terms of the viscous properties of soil:

$${\mathsf{\tau }}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}}-{\mathsf{\tau }}_0={\mathrm{c}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}}\mathrm{v}$$

(1)

with c_reac being the viscous constant of soil at reactivation.

Similarly, the strength mobilised in the steady condition may be expressed as:

$${\mathsf{\tau }}_{\mathrm{r}}\left(\mathrm{v}\right)-{\mathsf{\tau }}_0=\mathrm{c}\mathrm{v}$$

(2)

with c being the viscous constant of soil in the residual steady condition.

The shear strength, τ(s,v), mobilised during the transition from the reactivation up to the residual steady condition, may be modelled with a softening law which takes into account both the cumulated displacement, s, and the reactivation speed, v:

$$\mathsf{\tau }\left(\mathrm{s},\mathrm{v}\right)=\left[{\mathsf{\tau }}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}}-{\mathsf{\tau }}_{\mathrm{r}}\left(\mathrm{v}\right)\right]{\mathrm{e}}^{\left(-\mathsf{\beta }{\mathrm{s}}^{\mathsf{\delta }}\right)}+{\mathsf{\tau }}_{\mathrm{r}}\left(\mathrm{v}\right)$$

(3)

with β and δ being soil constants depending on both the vertical stress, σ_v, and the time of ageing, t_age.

Recalling the relationships (1) and (2), Equation (3) may be rewritten in terms of the viscous coefficients of soil:

$$\mathsf{\tau }\left(\mathrm{s},\mathrm{v}\right)=\left({\mathrm{c}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}}-\mathrm{c}\right){\mathrm{v}\mathrm{e}}^{\left(-\mathsf{\beta }{\mathrm{s}}^{\mathsf{\delta }}\right)}+\mathrm{c}\mathrm{v}+{\mathsf{\tau }}_0$$

(4)

where the frictional strength component is provided by τ₀.

For example, the data of Figure 8a have been replicated in Figure 13 using Equation (4) with the parameters reported in

Table 2. Parameters used in Equation (4) to model the reactivated strength of Caltavuturo clay at various reactivation speeds: σ_v = 101.1 kPa and t_age = 1 h.

v (mm/min)	τreac (kPa)	τr(v) (kPa)	τ0 (kPa)	τreac/τr(v)	creac (kPa)/(mm/min)	c (kPa)/(mm/min)	β	δ
0.018	36.50	35.70	34.30	1.022	122.22	77.78	1.10	1.30
0.089	39.70	36.30	34.30	1.094	60.67	22.47	0.55	1.28
0.445	43.40	37.00	34.30	1.173	20.45	6.07	0.31	1.22

.

From the data in Table 2 it is deduced that as the reactivation speed increases from 0.018 mm/min to 0.445 mm/min, the viscous constant at the reactivation of soil ranges between 1.6 and 3.4 times larger than the viscous constant of soil under the steady condition.

4.2. Ageing and Creep

Ageing may involve some creep deformation of the soil fabric, which enables the soil itself to stiffen and strengthen [40].

Time-dependent deformations under constant mean stress are referred to as volumetric creep, whereas those related to a constant deviatoric stress are referred to as deviatoric creep [41].

The secondary compression of a clay, mainly induced by volumetric creep under constant load in an oedometer, can delineate the role of the loading rate: the quasi-preconsolidation effect is an example of how the soil fabric can react more rigidly if reloaded rapidly after a period of ageing [42].

Referring instead to what could happen in a quiescent landslide, it seems reasonable that compressive creep may have developed along the shear surface during ageing, giving rise to recovered strengths proportional to both the normal stress and the ageing time (Figure 9). However, as already anticipated, the strength recovery can only be evidenced by a certain level of reactivation speed: if reactivation occurs at a very low speed, it is likely that no strength higher than τ₀ could be seen (Figure 7).

Deviatoric creep refers to a viscous displacement induced by a constant shear stress. If deviatoric stress is low, the creep displacement evolves at a decreasing rate (primary creep). When the deviatoric stress exceeds certain levels, the creep displacement may occur at a constant rate, even for a long time (secondary creep), or it may accelerate until failure (tertiary creep).

The important role in the kinematics of deviatoric creep has been highlighted by some fundamental studies [43,44], whereas experimental investigations have been performed by using both the ring shear and the direct shear devices [36,37,38,39]. The evolution of creep into accelerated motion has been approached through consideration of a rate-dependent sliding-block model [45,46].

In this investigation, the ageing cycles were performed at the reference stress, τ₀, for which the creep displacement would have ended within the primary phase; therefore, no influence of deviatoric creep on reactivated strength could be outlined.

4.3. Thixotropy

If ageing takes place under constant volume and soil composition, the subsequent increase in strength and stiffness is classified as a thixotropic effect [47,48,49]. As stated by Barnes [49], if a thixotropic material is subjected to a constant shearing speed, its viscous resistance will decrease until stabilisation at a steady value. If shearing is stopped and an ageing cycle is carried out, the measured strength at reactivation will be initially higher, but will then decrease again towards the steady value previously attained. The recovered initial strength mainly depends on the time spent in the rest condition.

Thus, thixotropic hardening is a time-dependent processes that may explain some increase in strength at reactivation after ageing has occurred at constant volume.

5. Conclusions

In this paper, the drained residual strength at reactivation has been discussed on the basis of laboratory tests carried out with the Bromhead ring shear apparatus in some normally consolidated saturated samples, both of natural soils and of clays provided by industry (bentonite and kaolin). Two different classes of phenomena may account for changes in the residual strength, the first related to the interaction between the soil and the physical environment [24,25,26], while the second related to the mechanics of the particle medium. The aim of this research was to assess the coupling effect of ageing time, vertical stress and reactivation speed on the mobilised residual strength upon the reactivation of displacement. Ten samples were subjected to different ageing cycles at various time amplitudes and vertical stress levels; the samples were then sheared after each ageing cycle. For two soil samples, the effect of different displacement rates was also investigated.

The following conclusions were drawn:

• The stress condition, τ₀, reached after relaxation under zero displacement speed should identify a reference condition for which shear creep can attenuate within the primary phase;
• After quiescence at τ₀ stress, the strength at reactivation could exceed the residual value, τ_r(v), depending on the ageing time, the shearing speed, and the vertical stress. This could be the consequence of some causes, such as viscosity, volumetric creep, and thixotropic hardening, which can account for an initial reactivated strength proportional to the ageing time and the reactivation speed;
• The reactivated strength rapidly falls towards τ_r(v) as the displacement increased at constant speed. This would mean that the aged soil fabric undergoes destructuration;
• If reactivation occurred at a displacement speed approaching zero, the reactivated shear strength approached the reference value,τ₀, irrespective of the amount of time spent in the previous ageing phase; this could occur if the strength at reactivation depended only on the viscous reaction of the particle edge-to-face hinges.

The mechanisms discussed in this work outline how a landslide that is already moving, even at very low speed, could not develop an age-induced strengthening along the sliding surface, so that no further recovered strength would be opposed to a new destabilising event. This latter point suggests how knowing the real kinematics of a landslide is strongly necessary; in fact, shear creep displacements can occur with velocities even lower than 3 × 10⁻⁵ mm/min (16 mm/year) [33], difficult to highlight but capable of preventing the benefit of volumetric creep along the sliding surface.

However, if it is certain that the quiescent landslide is stable, the experimental results of this research can provide methodological guidance on the design of reinforcement works to counteract a rather rapid increase in destabilising actions, such as in the case of seismic stresses, morphological changes of the slope, or as a consequence of a rising water table. Furthermore, the triggering speed of a landslide may also depend on the landslide morphology and on the boundary conditions, both difficult to reproduce in the laboratory.

Beyond the geotechnical parameters studied in this research, it may be important to further investigate the influence of both the stress history (OCR) and the partial saturation on the mobilised strength upon reactivation. Partial saturation, in fact, could arise from the interaction of the landslide body with the meteorological environment of the area.

Despite the limitations of this research, which certainly require further investigation and confirmation, the important role of reactivation speed in the kinematics of quiescent landslides is emphasised.