GGU-TRENCH: Safety against slip surfaces endangering the stability of the trench
The safety against slip surfaces endangering the stability of the trench eta(a) (also known as external stability) is calculated pursuant to the old DIN 4126 from
eta(a) = (S - W) / E
S = support force of the suspension [kN]
W = water pressure exerted by groundwater [kN]
E = earth pressure [kN]
The numerator is obtained from the hydrostatic supporting pressure of the suspension, reduced by the water pressure W from groundwater. Because of the finite length of the trench the current earth pressure problem can no longer be treated as a plane earth pressure case. The default method used in the program is the so-called shoulder theory as shown in Figure 7 of DIN 4126 (old). This employs a finite, triangular earth pressure wedge. The friction forces generated on both flanks of the wedge are utilised for consideration of equilibrium conditions, which gives higher factors of safety as opposed to the plane situation. Friction forces on both flanks ensue from the self-weight of the soil, the distributed load and, if required, any line loads present. A linear increase in the lateral pressure stress consistent with the unit weight of the soil is assumed to a depth equal to the width of the trench. Below this depth the lateral pressure stress is constant. This method is therefore also known as "bilinear". DIN 4126 (old) demands a FOS of 1.1 or 1.3 (if loads from structures act in the critical area). With regard to their influence on the lateral pressure stress, any distributed loads present are assumed to decrease linearly from the ground surface (full distributed load) to 0 at a depth corresponding to the trench width.
Alternatively to the bilinear approach, a so-called "sublinear" approach after Terzaghi is often used for the depth distribution of the lateral pressure stress. The theoretical principles are described in detail in, for example, "KILCHERT/KARSTEDT, Standsicherheitsberechnung von Schlitzwänden nach DIN 4126" (KILCHERT/KARSTEDT, Stability analysis of diaphragm walls to DIN 4126 – no translation published) (Beuth Verlag GmbH). The method after Terzaghi is based on the so-called silo theory. The sublinear approach after Terzaghi can also be selected. According to WALZ and PULSFORT (1983; "Rechnerische Standsicherheit suspensionsgestützter Erdwände"; Teil 1 und 2, Tiefbau, Ingenieurbau, Straßenbau, Heft 1 und 2 - "Computed stability of suspension-supported earth walls"; Parts 1 and 2, Tiefbau, Ingenieurbau, Straßenbau, Issues 1 and 2), the sublinear approach after Terzaghi is acceptable if the bilinear approach after DIN 4126 (old) using the bending point defined by the depth z = trench width is not exceeded. This restriction can also be entered in the program.
In contrast to a distributed load, line loads can only act on a limited area beside the guide wall. If you set the check boxes described later in this manual so that line loads act to increase the lateral pressure stress, the program proceeds as follows:
The proportion of the line load inside the respective slip body is converted to an equivalent distributed load ("smearing") and then treated as a distributed load.
Figure 1 Influence of line loads
If footings substantially smaller than the trench width exist in the area of a trench, the point load must be converted to an equivalent line load. However, you should then consider whether the point load contributes at all to the lateral pressure stress on the wall. The proportion giving rise to a corresponding equivalent load that increases the favourably acting lateral pressure stress can therefore be individually defined in the program for each line loading by means of a factor (>= 0.0 and <= 1.0).
If the pressure gradient fS0
lies below 200 kN/m² the full membrane effect of the suspension is no longer available, requiring a reduction in the support force. The reduction depends on the penetration depth of the suspension into the respective soil. The program calculates the reduction in the support force. Therefore, instead of the expression
(S – W)
in the above equation, the program calculates the effective support force S'. Even for limit gradients > 200.0, penetration depths are > "0.0", leading, in principle, to a reduction in the effective support force. In agreement with the DIN 4126 (old), however, the program assumes a penetration depth of "0.0" for limit gradients > 200.0, giving rise to somewhat higher factors of safety.
When determining the support force S in the region of the guide walls pursuant to old DIN 4126 (9.1.4.2), the earth pressure from soil self-weight and permanent, uniformly distributed surcharge may be adopted up to the value of the at-rest earth pressure, instead of the pressure of the supporting suspension, if the guide walls and their bracing are designed for this. The program has a switch which you can use to select from the options offered in the DIN standard. You can incorporate both distributed loads or line loads into the calculation of the guide wall earth pressure. If line loads contribute to the guide wall earth pressure (can be specified), its component will be taken into consideration completely, independent of the factor described above for the lateral pressure component. In addition, for determination of the at-rest pressure on the guide wall from line loads, the line load, in accordance with Figure 1 is converted to an equivalent line load.
Calculation of the earth pressure to be supported by the slurry fluid is for various user-defined depths, varying the slip surface angle. The variation range of the slip surface angle is user-defined.
In accordance with DIN 4126 (old), a safety factor of 1.5 is to be adopted for any cohesion in the slip surface. The GGU-TRENCH program allows a further reduction of the cohesion components in both flanks and in the slip surface, beside the general reduction.
The new standard stipulates that safety is sufficient if the condition
is shown.
Sk = characteristic value of support force to 6.4.2 of DIN 4126:2013
Wk = characteristic value of groundwater pressure
Eahk = characteristic value of earth pressure to 6.4.3 of DIN 4126:2013
The variables in the equation are calculated according to the old DIN 4126. If calculations are consistently performed according to DIN 4126:2013, a safety definition in the sense of the old standard, which provides a guide for the degree of safety, is not obtained. The only statement that can be made is "Stable" or "Instable".
In order to still arrive at a measure of safety, the utilisation factor µ is defined, obtained from:
