# 7.3 Design of slopes

### 7.3.1 Methods of design of soil slopes

The designer may use some or all of the following design methods:

- a) limit-equilibrium methods (see BS EN 1997-1:2004, 11.5.1, which requires horizontal interslice forces to be assumed unless horizontal equilibrium is checked; this excludes Janbu's original method and the Swedish circle [aka Fellenius] method, but allows, for example, Bishop's, Janbu's simplified and modified and Sarma's methods);
- b) numerical methods (see BS EN 1997-1:2004, 2.4.1(12));
- c) physical modelling (see BS EN 1997-1:2004, 2.6);
- d) prescriptive measures (see BS EN 1997-1:2004, 2.5);
- e) observational method (see BS EN 1997-1:2004, 2.7 and CIRIA R185 [16]);
- f) stability charts;
- g) infinite slope method.

### 7.3.2 Methods of design of rock slopes

Unlike soil slopes, the design of rock slopes is dominated by discontinuities, and recognized references such as Hoek and Bray (in Wyllie and Mah [26]) and TRL [27] should be consulted.

The design should consider:

- a) the stability of the rock mass, which in most cases is governed by conditions in the joint system of the mass rather than by the strength of the intact rock; an assessment is required of the discontinuities within the rock mass, including any infilling;
- b) drainage requirements to manage groundwater, particularly where preferential groundwater flow is most likely (e.g. along soil/rock interface, discontinuities, permeable zones);
- c) local experience or exposures in similar strata;
- d) standard details required to deal with all the adverse conditions that can be reasonably anticipated (e.g. rock bolting, dentition work, drainage); and
- e) potential deterioration of the rock mass or discontinuities due to weathering effects during the design life of the excavated face.

In rock slope design it is particularly important that the designer should assess the ground conditions anticipated within an excavation (including potential unfavourable conditions), the proposed works best suited to deal with those conditions, and the form of inspection and design check as part of the works. For new rock cuttings, a trial excavation should usually be made to enable a check to be made of the design assumptions prior to cutting the face to the required finished position.

Weak, heavily weathered rocks can exhibit engineering characteristics intermediate between those of a soil and those of a rock; in cases of doubt, separate analyses of slope stability should be made assuming that the material behaves either as a soil or as a rock.

### 7.3.3 Factors of safety and partial factors

The verification of the overall stability of slopes should be carried out in accordance with BS EN 1997-1:2004.

The overall stability of slopes should be checked against DA1 Combination 2. For completeness, DA1 Combination 1 should also be checked if the designer considers that the loading applied to the slope (other than the mass of the ground in the slope) might control the failure mechanism rather than the ground strength parameters [see BS EN 1997-1:2004, 2.4.7.3.4.2(3)].

COMMENTARY ON 7.3.3

BS EN 1997-1:2004, 11.5.1 details the requirements for determining the overall stability of slopes and BS EN 1997-1:2004, 2.4.7.3.4 sets out the Design Approaches which are to be applied. The National Annex adopts Design Approach 1 (DA1), which requires verification that the limit state of rupture or excessive deformation will not occur with either of the following combinations of sets of partial factors.

Combination 1: A1 "+" M1 "+" R1 Combination 2: A2 "+" M2 "+" R1 Where "+" implies "to be combined with".

In Combination 1, partial factors in excess of unity are applied to unfavourable actions or the effects of actions whereas in Combination 2, the inverse of partial factors exceeding unity are applied to the soil parameters. This has the effect of increasing the effect of actions in Combination 1 and reducing the ground strength in Combination 2. The basic equations that govern are:

where

- F
_{d}is the design value of an action; - γ
_{F}is the partial factor for that action; - F
_{rep}is the representative value for that action; - X
_{dis}the design value for a material property; - X
_{k}is the characteristic value for that material property; and - γ
_{M}is the partial factor for that material property.

The partial factors that should be applied to actions and to ground strength parameters are set by NA to BS EN 1997-1:2004, which are given in Table 4, Table 5 and Table 6. However,

NA to BS EN 1997-1:2004 does not provide partial factors for actions for the specific situation of earthworks. In the absence of these, the values in Table 4 are recommended [based on the values for buildings given in NA to BS EN 1990:2002+A1, Table NA.A1.2 (A)]. Reference should be made to the current version of NA to BS EN 1997-1 to ensure the correct partial factors are used for design.

Action | Symbol | Set | ||

A1 | A2 | |||

Permanent | Unfavourable | γ_{G} |
1,35 | 1,0 |

Favourable | 1,0 | 1,0 | ||

Variable | Unfavourable | γ_{Q} |
1,5 | 1,3 |

Favourable | 0 | 0 |

Soil parameter | Symbol | Set | |

M1 | M2 | ||

Angle of shearing resistance ^{A)} |
γ_{ϕ'} |
1,0 | 1,25 |

Effective cohesion | γ_{c'} |
1,0 | 1,25 |

Undrained shear strength | γ_{cu} |
1,0 | 1,4 |

Unconfined strength | γ_{qu} |
1,0 | 1,4 |

Weight density | γ_{g} |
1,0 | 1,0 |

^{A)} Factor applied to tan ϕ' (see text of this clause for partial factor applied to residual angle of shearing resistance). |

Resistance | Symbol | Set |

R1 | ||

Earth resistance | γ_{R;e} |
1,0 |

COMMENTARY ON 7.3.3 (continued)

Combination 1 involves applying partial factors to actions or the effects of actions whilst using unfactored values for the soil parameters and earth resistance. This approach is not usually relevant for checking the overall stability of a slope where earth is the main element providing resistance, since structural strengths do not provide resistance against overall stability failure and failure is controlled by uncertainty in the ground strength rather than uncertainty in the actions.

In addition the treatment of actions due to gravity, loads and water is difficult since these loads might be unfavourable in part of the sliding mass but favourable in another part. In a traditional analysis of a circular failure surface, part of the slope mass is producing a positive driving moment (i.e. it is unfavourable) and part of the slope mass is producing a negative driving moment (i.e. it is favourable) and the moments produced by the two parts depend on the position of the point about which moment equilibrium is checked. The application of different partial factors to each part of the slope introduces scope for confusion and requires a degree of complexity of analysis that is not readily available and not justified given the nature of the problem.

For this reason, a note to 2.4.2 of BS EN 1997-1:2004 states "Unfavourable (or destabilizing) and favourable (or stabilizing) permanent actions may in some situations be considered as coming from a single source. If they are considered so, a single partial factor may be applied to the sum of these actions or to the sum of their effects." This note, commonly referred to as the "single-source principle", allows the same partial factor to be applied to stabilizing and destabilizing actions. When using Combination 1, it is recommended that the partial factor for the unfavourable action of the soil is applied to the weight density of the soil and the effect of this application can be summarized as follows.

- • In an effective stress analysis, the effect of the partial factor is to increase the destabilizing action and to increase simultaneously the shearing resistance of the soil, which cancels the effect of the partial factor.
- • In a total stress analysis, the increase in weight density increases the destabilizing action without increasing the shearing resistance of the soil. However, a higher partial factor is applied to the undrained strength in Combination 2 than to the permanent destabilizing action in Combination 1.

In both cases, Combination 1tends to be less critical than Combination 2 in almost all design situations. (Exceptions might occur when extremely large variable actions apply or the soil strength is extremely low.) Bond and Harris [28] discuss the way in which the single-source principle should be applied to slopes and embankments and show that Combination 2 results in an equivalent global factor of safety of about 1.25 for typical situations where an effective stress analysis is used.

If the single-source principle is not applied, then a special procedure has to be followed, if using commercially available software, in order to apply different factors to stabilizing and destabilizing actions. Frank et al [5] describe one such procedure, but by ignoring the single-source principle, Combination 1 becomes more critical than Combination 2 in most design situations using an effective stress analysis and results in an equivalent global factor of safety of about 1.35. However, Frank et al [5] recommend that Combination 2 normally be used for checking the overall stability of earthworks since the stability is governed by the shear strength of the soil rather than the application of the load of the earthworks.

Subclause 2.4.7.3.4.2(3) of BS EN 1997-1:2004 states that, in circumstances where it is obvious that one of the two combinations governs the design, calculations for the other combination need not be carried out, but the designer needs to be sure that this is the case (e.g. based on past experience of similar designs). Therefore it is acceptable to base designs on Combination 2 alone (invoking the single-source principle) for many typical situations.

Where there is significant uncertainty about the density of the ground a sensitivity analysis should be undertaken [see BS EN 1997-1:2004, 11.5.1(12)].

Guidance on the use of advanced numerical methods in conjunction with the partial factors given in BS EN 1997-1:2004 is provided by Frank et al [5]; however, the designer should consider the relevance of such methods to the problem under consideration before embarking on advanced design since the overall stability of most routine slopes can be verified using limit-equilibrium methods.

The partial factors normally used for overall stability analyses may not be appropriate for slopes with pre-existing failure surfaces [BS EN 1997-1:2004, 11.5.1(8)], in which case the following approaches are relevant.

- Where the soil parameters for pre-existing failure surfaces are determined by back analysis partial factors of unity should be used for actions and the effects of actions, soil parameters and earth resistance since the objective in this case is to determine the value of the mobilized shear strength along the pre-existing failure surface.
- In the case where the residual strength of the soil is used for design purposes (whether determined from back analysis, laboratory or in-situ testing or from published data) Design Approach 1, Combination 2 is likely to govern the overall stability of the slope. BS EN 1997-1:2004, 11.5.1(8) states that partial factors normally used for overall stability need not be appropriate for the analysis of existing failed slopes therefore lower values of the partial factors for ground strength parameters than those given in NA to BS EN 1997-1:2004 for Set M2 (i.e. the factors used in Design Approach 1 Combination 2) may be applied to residual strength. The partial factor used with the residual angle of shearing resistance should be chosen with due consideration to the confidence level of the data and the consequences of subsequent failure of the slope. Usually it should not be necessary for the partial factor applied to the residual angle of shearing resistance to exceed 1.1 provided the effective cohesion used in conjunction with that angle is set to zero.

For any slope where the consequences of slope failure are abnormally high the selection of characteristic values for the soil parameters should reflect the increased risk (see 7.4) in addition to other considerations listed in BS EN 1997-1:2004, 2.4.5.2(4) and a very cautious value might have to be chosen for the characteristic value. Alternatively, consideration should be given to increasing the partial factors on actions or the effects of actions and/or those for soil parameters.

NOTE The designer is referred to Frank et al [5], Bond and Harris [28] and CIRIA C641 [7] for examples of calculations and further guidance on design to EC7 principles. These references give worked examples of analysis by rotational, wedge and infinite slope methods, consider analysis by computer software or stability charts, and also identify some areas where differences can be expected relative to conventional global factor of safety methods of analysis.

### 7.3.4 Seismic effects

The designer should assess the potential seismicity of the region and, where appropriate, the requirements of BS EN 1998-5.

NOTE It is not normal to consider seismic effects for Category 1 and Category 2 structures in the UK.