Overturning stability
Overturning stability analysis is performed using characteristic values! The following applies:
The resultant must remain within the 2nd kernel width under both permanent and changeable loads. Base tilt is permissible.
The resultant must remain within the 1st kernel width under permanent loads.
Bearing capacity safety
The program analyses the bearing capacity safety to DIN 4017.
DIN 4017 instructs that the mean soil properties of the soil above the bearing capacity failure plane, which is composed of the two linear components of a logarithmic spiral, can be determined for stratified ground. The governing parameters are summarised in the figure:
Figure 16 Logarithmic spiral
The mean governing soil properties are determined using the following relationships:
cal tan = tan i · li' / li
cal c= ci · li’ / li
cal 2 = 2i · Ai' / Ai
li = length within individual layer
Ai = area of individual layer
The condition for the permissibility of the mean is that the mean friction angle demonstrates a maximum deviation of 5° to the true friction angles. This condition can be checked by the program. If it is not adhered to, the program reduces the largest friction angle in stages until the condition is met
Sliding safety
Sliding safety is computed to EC 7. In addition, the sliding safety of an equivalent horizontal plane is computed for an inclined base plane.
Figure 17 Horizontal equivalent plane
Sliding safety is calculated as follows in accordance with the partial safety factor concept:
General stability
General stability can be simply verified by exporting the data from GGU-CANTILEVER to GGU-STABILITY (GGU slope stability application).
Settlements
Analysis of settlement is compliant with DIN 4019 using the relationships given in the Geotechnical Engineering Handbook (1990; Fourth Edition) (equations 8 and 14 from Section 1.7 Stress analyses). The program determines the stresses at 0.05 m intervals or at layer boundaries and numerically integrates them.
The limiting depth can be defined in three different ways:
with a fixed, user-defined value
as a multiple of the footing width
as the depth at which the total vertical stress exceeds the overburden stress by x% (generally 20%)
If the base of the lowest layer is exceeded during the settlement analysis, the analysis continues using the constrained modulus of this final layer.
For settlement analyses, any preconsolidation loading in kN/m² can be subtracted from the current soil pressure. Settlement analysis will then be performed with the reduced values. The overburden pressure is also reduced by this amount when calculating the limiting depth.
Hydraulic heave
Hydraulic heave safety using global safety factors
The hydraulic heave safety for each layer below the excavation base is determined via a comparison of the soil weights to the flow forces at the respective layer bases.
N = hydraulic heave safety of the layer N
G'i = buoyant self-weight of layer i
SN = flow force of layer N
layer 1 (i = 1) is the uppermost layer
The minimum value of all N is the hydraulic heave safety of the system.
Utilisation factor (hydraulic heave) using partial safety factors
Using the partial safety factor concept the following must be verified:
S'k = characteristic flow force on the percolated soil mass
γH = partial factor for the flow force in favourable or unfavourable subsoil in the
HYD (EC 7) limit state
G'k = characteristic dead load of the buoyant percolated soil mass
γg,stb = partial factor for stabilising permanent actions in the
HYD (EC 7) limit state
layer 1 (i = 1) is the uppermost layer
The so-called utilisation factor µ can also be calculated from this relationship.
µN = utilisation factor of layer N
Utilisation factors ≤ 1.0 mean that sufficient safety is given.
Buoyancy
Buoyancy safety using global safety factors
The buoyancy safety for each soil layer within the excavation is determined via a comparison of the soil weights to the water pressures at the respective layer bases. The self-weights of site plant and structures, frictional forces etc. are not included.
N = buoyancy safety of layer N
Gi = self-weight of layer i
PN = water pressure at base of layer N
layer 1 (i = 1) is the uppermost layer
The minimum value of all N is the buoyancy safety of the system.
If the same permeability has been defined for the whole system, safety against buoyancy is not determined. In certain cases, for example, when permeability on the passive side is much greater than on the active side, the calculation of safety factors for hydraulic uplift is meaningless. If, in such, or similar cases, the message "Buoyancy safety could not be demonstrated" appears, you can either ignore it or set the "Safety against buoyancy" to 1.0, which suppresses the message.
Utilisation factor (buoyancy) using partial safety factors
Using the partial safety factor concept the following must be verified:
Ak = the characteristic hydrostatic buoyant force acting on the lower surface of the
complete structure, the soil layer in question or the excavation structure
γg,dst = partial factor for destabilising permanent actions in the
UPL (EC 7) limit state
Gk,stb = lower characteristic value of stabilising permanent actions
γg,stb = partial factor for stabilising permanent actions in the
UPL (EC 7) limit state
layer 1 (i = 1) is the uppermost layer
The so-called utilisation factor µ can also be calculated from this relationship.
µN = utilisation factor of layer N
Utilisation factors ≤ 1.0 mean that sufficient safety is given.
Verification of deep-seated stability
Verification of deep-seated stability is required for anchored cantilever walls. This primarily serves to determine the necessary anchor lengths. Verification uses the method described by Ranke/Ostermayer (Bautechnik 1968 (Construction Engineering), Issue 10). When verifying deep-seated stability each anchor is first investigated (including the influence of the remaining anchors on the slip plane). Compound slip planes, which are determined by connecting the end points of the anchors involved, are then analysed.
Figure 18 Compound "deep slip planes"
All possible combinations are analysed. For example, when there are four anchors:
Slip plane passes through anchor end points:
1,2 and 1,3 and 1,4 and 1,2,3 and 1,2,4 and 1,3,4 and 1,2,3,4 and 2,3 and 2,4 and 2,3,4 and 3,4
The only condition is that the next anchor end point is always to the right of and above the preceding one.
Figure 19 Compound "deep slip plane", which is not investigated
These slip planes are not critical. The most unfavourable slip plane associated with each anchor is displayed on the screen with the corresponding safety factor. A safety factor of 1.5 is generally required when adopting global safety factors. If this safety factor cannot be achieved or is exceeded heavily, the program can optimise individual anchor lengths.
Using partial safety factors, the possible anchor force is acquired in complete analogy to global safety factors, but is divided by the passive earth pressure partial safety factor. The deep-seated stability is deemed as verified if:
,
where Aposs,k is determined from the force polygon with permanent loads only, and
,
where Aposs,k is determined from the force polygon with permanent and changeable loads. Where:
Ag,k = characteristic anchor force from permanent loads
Aq,k = characteristic anchor force from changeable loads
Here, too, optimisation regarding a utilisation factor of 1.0 is possible.
Heave of anchor soil
Verification of heave of anchor soil is performed like the method described in Section 7.3.4 of the Piling Handbook 1977 (Spundwand-Handbuch 1977).
Reinforced concrete design
Reinforced concrete is designed to EC 2 or, alternatively, to DIN 1045 (old) depending on the selected safety factor concept. Reinforcement is calculated for all wall element sections (see Section 8.15). The output is the section with the largest reinforcement.
The stem area above the footing is designed using the wall internal forces (see Section 8.1.2).
The internal forces M and Q at the stem base/toe and heel intersections are calculated from the soil pressure and any surcharge present. The model concept is a cantilever. The normal force N results from the passive earth pressure.
The following sign rule applies to the spur and wall moments with reinforcement:
