This work deals with the possibility of predicting the effects of drains as a stabilizing measure against landslides. The use of drains is becoming increasingly widespread in slope stabilisation. This technology is less costly than other types of control works and is suitable for a large number of situations, even when the landslide is very deep and structural measures are inadequate. Although drain trenches are widely used in engineering, our knowledge of design methods has advanced little in recent years and important aspects of the problem are yet to be investigated. When slope analysis is carried out, the increase in the safety factor, due to stabilising works, can be evaluated by taking into account the groundwater regime on the supposed slip surface, as modified by insertion of drains. Therefore, before performing the slope analysis, results of detailed, accurate calculation of pore pressures, in the presence of drains, must be available.
A key neglected aspect is the seasonal fluctuation of the groundwater in the subsoil  due to changes in atmospheric conditions. Methods available in the literature to quantify the increase in slope stability by drains often fail to take account of transient aspects of the groundwater regime connected to atmospheric changes. Generally, these methods analyse very schematic cases regarding hydraulic conditions at ground surface and the slope geometry. Moreover, water flow in the slope direction is rarely considered.
Due to such limitations, the evaluation of slope stability improvement is not accurate enough. There are also few pore pressure measurement data reported in the literature from sites where drain trenches have been constructed. Therefore, the limitations of design methods are unclear. This work is devoted to a more comprehensive analysis of drain effects: seasonal fluctuations in groundwater resulting from changes in atmospheric conditions are modelled. In Section 2 the role of water in slope stability is analysed. Moreover, in the same section we report equations and hydraulic boundary conditions useful for analysing transient water flow in subsoil and the techniques for modelling the presence of drains in a slope. On the basis of the equations described, new software has been developed. In Section 3 we describe a case history in southern Italy, in the Sele Valley, where a large landslide was stabilised by drains. The response of the groundwater regime was monitored for a long period of time, before and after drain construction. A detailed picture of the groundwater regime is presented through the measured data and a complex back analysis of the observed phenomenon.
Comparison of the results of this analysis with other methods available in the literature , , , ,  and site measurements show that, if the slip surface of the landslide is not particularly deep, slope safety is improved by drains more than was predicted by common methods of design. The scatter between them and the results of present analysis can be up to 30%–40%. This is very important in slope stability problems, where a safety factor FS=1.2–1.3 is considered to be large enough. We will show in the following that the main factor responsible for this scatter is the evaluation of the water flow infiltrating at ground surface, which was calculated with great accuracy in this work.
The analysis developed in this paper deals with a simple model of soil mechanics. However, the results and their comparison with experimental data encourage the generalisation to relatively more sophisticated nonlinear models available in the literature, among others , , , . Of course, the nonlinearity of problems may need relatively more sophisticated computational schemes.
The role of the groundwater regime on the slope stability of saturated soils
Groundwater regime in slopes
The stability of slopes is usually analysed in drained conditions. This means that pore pressure depends only on hydraulic conditions at the boundaries of the analysed volume and no connection exists with large strains occurring before the failure. Shear strength is expressed by the Coulomb failure criterion, ,
Here, is the shear strength, denotes the the total tension and the pore pressure; and are the strength parameters: the drained cohesion and the drained friction angle, respectively. Eq. (2.1) shows that if the total tension stays constant, as usually occurs in natural slopes, an increase in pore pressure implies a decrease in shear strength.
Painstaking investigation, carried out for more than a decade on some clay slopes in southern Italy , showed that pore pressures attain their maximum values during wet seasons. Obviously, in these periods landslides can be activated or reactivated due to the strength decrease described by Eq. (2.1). Nonetheless, when the stabilizing effect of drains is analysed, the groundwater regime in slopes is very often modelled as a steady phenomenon (seepage). This is a serious limitation in computing pore pressures at shallow depths, where the groundwater flow is strongly influenced by seasonal atmospheric conditions. Instead, it is likely that the pore pressures in deep regions of the slope keep substantially constant during all the year. Therefore shallow landslides, whose sliding surface is located some metres from the ground surface, exhibit seasonal behaviour regarding displacements. Indeed, all around the sliding surface, pore pressures fluctuate during the year and the safety factor varies correspondingly. Dealing with landslides influenced by seasonal fluctuations of pore pressures requires an analysis of groundwater referring to transient flow.
On the basis of the previous observations, it is clear that drains might prevent the rise of the water table up to values endangering slope stability during those weeks or months that could be critical for landsliding. Hence, the most important aspect to investigate is the capability of drains to control the transient rise of pore pressures as a consequence of atmospheric changes.
Equations of transient flow
Slopes are usually analysed in plane strain conditions. Thus, in modelling a groundwater regime too, it is enough to refer to two dimensions (coordinates and in Fig. 2.1(a)). If the subsoil is assumed to be an isotropic linearly elastic medium, characterized by permeability , Young’s modulus and Poisson index , the equation of transient flow is expressed by ,
where h is the piezometric head
Eq. (2.2) holds true if total stresses remain constant in all the volume subjected to the analysis. Two initial-boundary-value problems are considered for Eq. (2.2). The first concerns analysis of the whole volume and is summarized by the following equations:
Modelling the role of drains in slopes
Drain trenches must be deep enough to penetrate through the regions where ; thus the groundwater flows from the subsoil to the trenches and the pore pressures decrease inside the whole drained volume. The lowering of the water table caused by drains is not homogeneous in the slope: it depends upon the distances of the point in question from the trench boundary and from the ground surface.
The mathematical problem is similar to (2.5), (2.6), (2.7), (2.8), (2.9), (2.10), (2.11), but the hydraulic conditions along the trench boundaries also have to be specified. Given that the material constituting trenches has a saturation degree more or less equal to zero, water flows only from the subsoil to the trenches and not vice versa. In this case, a double boundary condition is necessary (Fig. 2.1(b)):
Some methods for the design of drain trenches and for pore pressure forecasting in the presence of drains are reported in the literature , , , , . They deal with the analysis of groundwater flow in steady and in transient conditions, in order to calculate the time from the start of drainage to the final steady condition in the groundwater regime. The analysed cases are very schematic: the ground surface is assumed to be horizontal and time variations of the hydraulic conditions at the ground surface, due to intermittent rainfall, are not considered. The water flow in the slope direction is also neglected.
Di Maio and Viggiani  showed that steady values of pore pressure in subsoil, in the presence of drain trenches, are regulated by infiltration at the ground surface. Therefore rainfall and, in general, atmospheric conditions are fundamental elements affecting pore pressure fields, both in natural conditions and when modified by drains.
New software was developed to solve the problem of drain trenches inside slopes, given all the aspects neglected by existing methods of design. This is based on the explicit finite-difference method for Eq. (2.5), e.g. , , ,
Eq. (2.14) is considered together with initial data and with boundary conditions, which can involve the unknown function or its derivatives. In this last situation and with reference, for example, to
The code for analysing these problems is written in C++ and has an easy to use Windows interface. As already mentioned in Section 1, nonlinear problems may require relatively more sophisticated schemes, e.g. , , , .
The case history
In 1990, in southern Italy, during highway works along the Sele river, some ancient landslides were reactivated as a consequence of trench excavations. After these events, further work was needed to assure the safety of the highway. In particular, in the urban district of Contursi, the highway crosses a huge unstable zone affected by several landslides. The unstable area was stabilised by drains, consisting of trenches in some zones (Fig. 3.1) and wells with horizontal drainage pipes in others. In the Sele Valley, as in much of the Southern Apennine chain, Varicoloured Clays outcrop. Varicoloured Clays are a marine formation of overconsolidated clay and marls enveloping limestone layers. Landslide bodies generally consist of remoulded and softened clay enveloping lapideous elements.
Groundwater regime in natural conditions
The groundwater regime was investigated before and after drain construction, using Casagrande piezometers installed inside boreholes over the whole area (Fig. 3.1). Recently, some wire vibrating piezometers, continuously linked to a data logger, were also installed. The effectiveness of drains was ascertained through comparison of the pore pressure regime in the slope, measured both far from the drained area and within it. Measurements before and after the construction of control works were also available. The investigation program was fairly extensive, aiming to measure pore pressure fluctuations inside and around the landslide body and in the substratum, in order to determine the hydraulic conditions at the boundary of the unstable area. Piezometer measurements were carried out continuously from 1991 onwards. Soils were investigated extensively both in the laboratory and in the field:
- the range of the effective stress variation (due to the water level fluctuation) is small,
– the event has occurred several times in the slope’s history (over-consolidation).
Typical aspects of the groundwater regime were detected through piezometric measurements. Regarding zones far away from drains, where the groundwater regime is affected by natural conditions, the typical behaviour of the water table is summarised as follows:
– Heads measured by the piezometer cells, installed at shallow depths, are usually higher than those measured by lower cells, with differences of up to half a metre during the whole year, causing a downward water flow; this is shown in Fig. 3.2, which reports measurements made by a piezometer installed above the drained area, at a large distance from the drainage.
- The envelopment of the piezometer heads, measured by the upper piezometric cells, is practically straight and parallel to the ground surface. Similarly, the envelopment obtained by the lower cells is parallel to the slope, but lower than the first.
- The piezometer heads undergo seasonal fluctuations of the order of some metres, more significant in the upper cells but also noticeable in the lower cells (Fig. 3.2).
Regarding the last point, the following phases can be identified: (a) a period with a pore pressure increase lasting from November to February (in March and April the pore pressure reaches and maintains its maximum level); (b) a period with a pore pressure decrease that usually occurs from May to October. The pore pressure increase is directly related to rainfall and therefore follows the random distribution of weather patterns. As the characteristics described have also been recognised in other slopes constituted by Varicoloured Clays , they may be considered to be typical of that geologic environment. Regarding the drained zone (Fig. 3.1), several trench systems spaced 20–22 m apart, with secondary segments, were constructed. Trenches were dug down to a depth of 7–8 m from the ground surface. Measurements at piezometers installed between trenches (Fig. 3.2) show that pore pressures are well below those measured far from drained area. Moreover, seasonal fluctuations more or less vanish. The latter shows the greater stabilising effect of drains, since the maximum pore pressure, attained during winter and early spring, is the cause of reactivation of seasonal landslides. This aspect of drain action has not been stressed in the literature, despite its great importance in slope stability.
Analysis of groundwater regime
The slope was modelled as a trapezium, constituted of homogeneous soil, whose bases are 105 and 70 m, and length 280 m . The slope is 7∘1′. The problem was analysed in two steps. The first consists of a hypothetical steady phase, during which hydraulic conditions at boundaries are supposed to be constant all year. This calculation was carried out to determine mean water flow through the boundaries of the volume examined. Steps of spatial integration are 14 m and 10.5 m, respectively, in the horizontal and vertical directions.
Numerous parametric analyses were performed in order to study the response of the water table to different conditions at the boundaries. It emerged that water flow through the ground surface is the hydraulic condition that much more than others influences pore pressures in subsoil around the slip surface. This result coincides with the fact that the slip surface is relatively shallow (its depth is always less than 9 m). Hence, major efforts were made to examine the hydraulic condition at the ground surface according to the following procedure.
The results were as follows:
– the flow-net, represented in Fig. 3.4(a), shows that water flow is inclined more than the ground surface with respect to the horizontal, as described in Section 3.2.1;
the envelopes of piezometric heights depend on the depth of the considered points from the ground surface, as stated in Section 3.2.1: (i) the envelope calculated at a depth of 6.20 m is more or less parallel to the ground surface and is located at a depth of 2.5 m from the ground surface (Fig. 3.4(b)), (ii) the envelope at a depth of 13.20 m is a little deeper than the previous one, so the downward flow is justified.
After the steady analysis, transient conditions were examined to take into account seasonal climatic changes and alternation of rainy and dry periods. The hydraulic boundary conditions on both vertical and lower horizontal boundaries were fixed at the same values assumed in the steady case.
So as to define boundary conditions at the groundsurface, subsequent considerations are very useful. When rainfall is abundant, a film of water forms at the ground surface and an amount of rain infiltrates. If the climate is cool, evapotranspiration is negligible and infiltrated water moves downward inside the subsoil. Infiltration depends on soil permeability and head gradient, normal to the ground surface, according to Darcy’s law. If the climate is warm, rain evaporates and the aliquot that infiltrates is small and can return to the atmosphere by evapotranspiration. In southern Italy such phenomena occur during the summer: rainfall is brief and intense, and surface runoff is high. Subsoil temperature is also high and water tends to evaporate rapidly, so there is no quantity to recharge the water table. The ground surface can be considered to be impermeable (Fig. 3.3).
Thus, results (Fig. 3.5) were obtained that represent the pore pressure fluctuations, expressed in a water column, as a difference between maximum values, occurring in spring, and minima, occurring in autumn.
At a shallow depth, fluctuations of 3–4 m are possible; they become smaller with depth. This behaviour is well known from experimental data , . The results of the transient analysis are compared (Fig. 3.6(a)) with measurements at a piezometer far from the drained area, where the groundwater is unaffected by drains. The envelope of measurements prolonged for six years is presented: this agrees with the results of the analysis.
Another solution was investigated, namely fixing at the ground surface a film of water during rainy days and impermeable conditions during non-rainy days. This calculation was very time-consuming compared with the previous one and was applied only to small periods. Formally, the hydraulic condition at the ground surface can be written as:
The results of the latter analysis (Fig. 3.6(b)) are compared with measurements taken at a piezometer far from the drained zone.
Modification of the groundwater regime caused by drain trenches
In this work it was shown that an important role of drains working on unstable slopes lies in their capability to reduce seasonal fluctuations of the pore pressure in the subsoil. Using a well-dimensioned system of drains, in winter and spring pore pressure peaks are avoided, with considerable benefit for slope stability. Conventional design methods for drains cannot take into account this aspect, as they do not consider the change in hydraulic conditions at the ground surface and hence cannot consider transient fluctuation of the water table. This aspect was modelled in this work.
Parametric analysis carried out on a slope drained by trenches showed that efficiency evaluated by taking into account realistic infiltration is greater than that calculated with a permanent film of water at the ground surface. Then, efficiency rapidly tends to become that calculated with a permanent film of water, at a depth of 1.5H (where H is the depth of the trenches).
Source: Groundwater regime in a slope stabilized by drain trenches
Authors: Berardino D’Acunto, Gianfranco Urciuoli