SLOPE STABILITY


ate constitutive law) and the reaction forces (provided by the mine plan) the resulting reaction must be calculated.


Sand slopes, behavior in practice


As follows from the discussion above, in engineering practice for sand operations a constitutive model needs to be selected, properties need to be determined in the field and on samples in the lab for all relevant sand (and overburden) layers. In the process of determining the stability of slopes in sand it is important to exclude that the material (here sand) is susceptible to liquefaction by checking based on the criteria discussed by e.g. Bray and Sancio (2006). The following steps described in the text below are applicable only if the sand is not susceptible to liquefaction.


In practice the Mohr-Coulomb constitutive model is still accepted as the constitutive model to describe the behavior of sand close to surface and under normal loading conditions , as are found in civil engineering excavation or sand extrac- tion. The basic parameters for the Mohr-Coulomb model that determine the shear strength of the sand are the friction angle and the cohesion. The friction originates from the interlocking and sliding of the grains when subjected to shear and normal stress (which is a function of normal stress applied to the sand) and cohesion. Cohesion in sands can originate from cementa- tion if the sand is cemented or if there is a clayey component (or from “suction” as is described below). For the same friction angle stable slopes in sand with a cohesion set to 0 (i.e. not taking the cohesion into account for slope design) have much shallower angles at which they are stable than slopes with a small cohesion even if this cohesion only amounts to a few kPa. The authors have analyzed many (steep) slopes in sand without clay or cementation. So why were these slopes stable?


In case of pure (only sand with no significant amount of


clay) non-cemented sands, cohesion is produced by “suction” (“capillary effects”) due to the moisture content of the sand. This effect of moisture content has been observed by nearly


30 - 35 degrees, and under water stable slopes in sand can be as low as 10 - 5 degrees (all of these values represent ranges observed in the field, and are different for cut slopes in virgin terrain and built slopes).


This effect on the shear strength of the sand can be quanti- fied by doing shear strength tests on sand in the lab and the measured cohesion is then called “apparent cohesion”. The theoretic field of study is called unsaturated soil mechanics. The apparent cohesion is zero when the soil is dry or totally water saturated. It can reach important values (up to tens of kPa or even more) at intermediate water contents. The relationship is established by laboratory tests and results in a “retention curve” that describes the dependency of the suction (and the apparent cohesion) on the moisture content.


Although the general effect of moisture content on sand has


been well known (in a qualitative sense) for a long time and the effect is significant for the stability of slopes “the imple- mentation of unsaturated soil mechanics into engineering practice has proven to be a challenge: new technologies and engineering protocols such as those proposed for unsaturated soil mechanics are sometimes difficult to incorporate into engineering practice” (Fredlund et al. 2012).


So why is this still a challenge? Most probably this is related to the fact that the moisture content has a significant effect on the apparent cohesion and that the moisture content is being regarded as a not stable parameter (it is called “apparent”). A parameter such as the apparent cohesion can easily change when changes in e.g. seasons occur (dry summer, wet winter). This is of course true. However for one particular sand extrac- tion (quarry) site, in the same sand deposit (or sand layer), in the same climatic region (with quantifiable seasonal changes) and when considering that face slopes or working slopes (the temporary slopes where extraction occurs) are continuously created and “fresh”, the moisture content and apparent cohe- sion are variable but at the same time finite. In addition the use of design standards such as the Eurocode 7 allows the inclusion of monitoring as part of the design process. In this case monitoring, being thus part of the design process, should be focused on monitoring changes in water content, thus in apparent cohe- sion (whether directly by measuring suc- tion or indirectly by measuring changes in moisture content).


Figure 2. This is a cross section through a slope in silty sand for which a limit equilibrium analyses was performed with various values of apparent cohesion and internal friction angle. Laboratory tests provided a friction angle (φ’) of 35° (at a unit weight of 18 kN/m³).


everyone, as a child when building sand-castles on a beach, or in professional life. The behavior of sand is different when it is completely dry, saturated or at a low water content such as in sands found in their natural state in sand pits and other excavations. At low water contents sand slopes can be stable at very steep angles (e.g. up to 55 degrees or even more). Completely dry, sand slopes have a maximum slope angle of


www.aipg.org


Figure 2 and Table 2 on the following page provide the results of parametric analyses with various values of appar- ent cohesion for different values of the internal friction angle. At a friction angle of 35 degrees the overall factor of safety of the slope is larger than 1 (stable) if the apparent cohesion is 10 kPa or higher, whereas the overall fac- tor of safety is lower than 1 (unstable) if the apparent cohesion is smaller than 10 kPa. In soil mechanics values of tens of 10 kPa are very small and used not to be considered relevant and were therefore not always considered in design.


Sand slopes, design in practice


With all of this in mind how does the actual “doing” take place in practice. This is described below for an existing sand operation:


Oct.Nov.Dec 2020 • TPG 31


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