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[交流] SOME COMMENTS ON MODELLING DEEP EXCAVATION PROBLEMS WITH PLAXIS

SOME COMMENTS ON MODELLING DEEP EXCAVATION PROBLEMS WITH PLAXIS
Description of problem
The specification of the problem follows from figure 1. The construction steps, prop levels and a simplified soil profile are also indicated. It follows from this figure that the excavation is 30 m wide and 12 m deep.

figure 1 Cross section of excavation.
figure 2 shows the mesh which consists of 200 15-noded triangle elements. The wall is assumed to be in place i.e. the construction of the wall has not been modelled. The diaphragm wall was considered as linear elastic material and the relevant parameters are given in Table 1. The diaphragm wall is supported by two props modelled by using fixed-end anchor elements (figure 2).

figure 2. Finite element mesh.
Table 1. Stiffness parameters for diaphragm wall.
diaphragm wall E [MPa] [-]
concrete 21000 15
The strength and stiffness parameters for the soil layers used in the drained, elastic perfectly plastic analysis using a Mohr-Coulomb failure criterion, which serves as reference calculation, are given in Table 2.
Table 2. Soil properties.
soil layer friction angle [ o]
cohesion [kPa] E [MPa] [-]
layer 1 35.0 2.0 20 0.40
layer 2 26.0 10.0 12 0.40
layer 3 26.0 10.0 80 0.30
The following computational steps have been performed:
step 1: initial conditions (layer 1: ko = 0.5, layer 2+3: ko = 0.65) and self weight of diaphragm wall
step 2: excavation to a depth of 4.0 m
step 3: excavation to a depth of 8.0 m, prop in -3.0 m in place
step 4: excavation to a depth of 12.0 m, props in -3.0 and -7.0 m in place.
A comparison of the results obtained from various analyses from different codes and users according to these specifications is given in [1]. In the following some results from additional investigations which have been made in order to clarify some discrepancies are presented.
Influence of interface elements on the deformation behaviour
A parametric study was carried out to investigate the influence of interface properties on the deformation behaviour varying the reduction factor R from 0.45 to 1.0. R=1.0 serves as reference solution, i.e. no interface behaviour is considered (strictly speaking a minor influence remains compared to a mesh without interface elements because of some prefixed interface properties). It is well known that for these types of problems finite element calculations usually exhibit somewhat unrealistic vertical displacements of the wall when simple elastic-perfectly plastic constitutive laws are employed. This behaviour is usually not observed in practice.It follows from figure 3 however that the use of interface elements improves the numerical predictions significantly. The first two excavation steps still lead to a heave of the wall but as expected the lower the value of the factor R is, the less heave is calculated. In the last excavation step (both props built-in) the wall settles, especially in the case of low wall friction, corresponding to the movement of the surrounding soil as indicated in figure 4, which compares qualitatively well which observations in the field.

figure 3 Vertical displacement at top of diaphragm wall.

figure 4 Incremental displacement field for excavation step 3.

The horizontal displacements of the top of the wall increase with decreasing R. The influence of the factor R on the horizontal displacements of the toe of the wall is not as pronounced. As expected the lateral earth pressure distribution is only slightly influenced by R (figure 5). The effect on the bending moments is pointed out in figure 6. If wall friction is reduced bending moments increase, the maximum difference being less than 30% for the final excavation step for R ranging from 0.5 to 1.0.

figure 5 Lateral earth pressure distribution.

figure 6 Bending moments after excavation step 3.

Beam-elements vs continuum elements for modelling of the diaphragm wall:
When comparing PLAXIS results for the problem given by the AK 1.6 as described in section 2 some differences which could not be easily explained became apparent. It was suggested that these differences are caused by the element type used for modelling the wall (beam or continuum).figure 7 shows that this is indeed correct. Beam elements lead to less (unrealistic) upwards movements of the wall. This may be partly due to the stresses acting on the bottom cross section of the wall pushing the wall upwards, which is not the case for beam elements where stress transfer is possible only via interface friction. It is also interesting to see that the interface properties have a more pronounced effect in combination with beam elements.In addition horizontal displacements of the top of the wall (+ve denotes displacement towards the excavation) are also very much influenced whether beam or continuum elements are used. The influence of the interface properties is also obvious (figure 8).

figure 7 Heave of diaphragm wall.

figure 8 Horizontal displacement of top of wall.

Influence of prop stiffness
Finally the influence of the prop stiffness is briefly addressed. figures 9 and 10 show the expected behaviour as far as maximum bending moments and prop forces are concerned. The irregularities in figure 9 are due th the change of sign of the maximum value for very soft props. Considering prop stiffnesses of 1e+4 to 1e+5 as common in practical applications it follows that it is worthwile optimizing prop levels and stiffnesses according to the designed excavation sequence. It is important to note that the overal deformation behaviour is not very much influenced by the prop stiffness which follows e.g. from figure 11 where the horizontal displacement of the top of the wall is seen to increase significantly only in the case of soft props.

figure 9 Maximum bending moments vs prop stiffness.

figure 10 Prop forces vs prop stiffness.

figure 11 Horizontal displacement of the top of the diaphragm wall.

Conclusion
The influence of some parameters important in the analysis of deep excavation problems using PLAXIS has been addressed. It can be concluded that the use of interface elements in connection with beam elements for modelling the retaining wall is to be preferred over continuum elements. The stiffness of the props has significant influence on bending moments and prop forces (as expected) but relatively little influence on the overall deformation behaviour, at least for prop stiffnesses in the range commonly used in practice. Further studies in particular with respect to constitutive modelling are presently under progress.
Literature
[1] H.F.Schweiger (1997). Berechnungsbeispiele des AK 1.6 der DGGT - Vergleich der Ergebnisse für Beispiel 1 (Tunnel) und 2 (Baugrube). Tagungsband Workshop "Numerik in der Geotechnik", DGGT/AK 1.6, 1-29.
H.F.Schweiger & M.Freiseder, Institute for Soil Mechanics and Foundation Engineering, Technical University Graz, Austria

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