Slope Stability Analysis using Tekla Tedds | Solved Example

Slope stability analysis can be carried out manually by a number of METHODS. Manual analysis of slope stability is usually a very tedious and time-consuming process. Presently, there are a number of software that can be used to model and analyse a slope. Softwares such as Geoslope, Plaxis, etc. can effectively and efficiently model and analyse a slope.

The primary essence of slope stability analysis is to determine the factor of safety against failure. It is possible to analyse a slope manually within a shorter period of time using the iterative processes available in Tekla Tedds software. The software has the capacity to analyse slopes to determine and satisfy suitable factors of safety against failure using either of the two most popular methods of slope stability analysis: the Fellenuis (Swedish circle) method and the Bishop’s simplified method. The software determines the suitable method to use based on the input variables.

The software is subject to the following assumptions and limitations:

1. The slope may feature two layers, each with distinct soil properties. It assumes that the boundary between soil types is horizontal and above the toe of the slope.
2. The toe of the slope may be submerged as in the case of a water retaining embankment such as an earth dam or canal bank. In this case, it assumes that the soil up to the water surface is saturated.
3. Where the toe of the slope is submerged only a single soil type may specified.
4. A hard layer may be specified beneath the toe of the slope, this is assumed to constrain the depth of any slip circle.
5. In the case of undrained slopes, tension cracks, and hydrostatic force may be applied.
6. The auto analysis allows a number of trial circles to be analysed in a single process. If a large number of trial circles is specified this calculation can take several minutes to complete, particularly in the case of drained slopes where the method of slices is used.
7. An option in the calculation includes a check of the factor of safety for an undrained homogenous slope using Taylor’s stability number method.
8. The radius of any trial circle must encompass the entire slope, the minimum radius stated in the calculation is the shortest radius that achieves this.
9. Where the minimum radius extends below a hard layer the area of the slip circle is still calculated as it was without the hard layer, ignoring the loss of material below it. This situation will likely occur where the hard layer is located immediately beneath the slope.
10. An optional factor of safety check ensures that a specified factor of safety is achieved and displays an appropriate message in the output.

Example (Question 9.11, Chapter 9, Pg 351: Geotechnical Engineering by Venkatramaiah):

An earth dam of height 20 m is constructed of soil which the properties are:

Bulk unit weight of soil, γ = 20 kN/m³

Cohesion, c = 45 kN/m²

The angle of internal friction, ϕ = 20^o

The side slopes are inclined at 30^o to the horizontal. Find the factor of safety immediately after the drawdown.

Solution (as obtained from Tekla Tedds software)

Slope Geometry

Angle of slope;                                                                 b = 30 deg

Height of slope;                                                                H = 20000 mm

Horizontal length of slope;                                             L = H / Tan(b) = 34641 m

Soil Properties

Bulk unit weight;                                                               g = 20 kN/m³

Drained shear strength;                                                  c’ = 45 kN/m²

Shear resistance;                                                             f’ = 20 deg

Pore pressure ratio;                                                         r_u = 0.3

Origin co-ordinates;                                                         x = 5000 mm; y = 20000 mm

Radius of circle;                                                                R = 29825 mm

Sector angle;                                                                    θ = 137.888^o

Number of slices;                                                             N = 20

Width of each slice;                                                         b = (AB + L + EF) / N = 2598 mm

For each slice, angle;                                                      α_N = asin(x_N / R)

Weight of slice;                                                                 W_N = b x h_N x g

Effective normal reaction force at the base of slice; N’_N = max(W_N x (cos(a_N) – r_u ´ sec(a_N)), 0 kN/m)

Shearing force induced along base;                            T_N = W_N x sin(a_N)

Sum of effective normal reaction forces;                    SN’ = 5999.011 kN/m

Sum of shearing forces induced along the base;            ST = 3263.375 kN/m

Factor of safety using Fellenius’ method;                   F = (R x c’ x θ x π / 180^o + tan(f’) x ΣN’) / ΣT = 1.659

Required factor of safety;                                               F_req = 1.5

PASS – Actual factor of safety exceeds required factor of safety

From the Results of the analysis, it can be seen that the required factor of safety is 1.5. This value corresponds with the value obtained from the Text from which this question was extracted. The software went ahead to determine the actual factor of safety and was able to show that the slope would be stable at the specified parameters after drawdown because the required factor of safety is less than the actual factor of safety.