Probabilistic approach to the design of anchored sheet pile walls
Introduction
Up to now, the approach to the geotechnical design of retaining structures has always been essentially deterministic, i.e. with single values assigned to the mechanical properties of soils and with a single factor estimating the safety of the design, regardless of both the uncertainties pertaining to the calculation procedures and/or variability of the soil properties.
Eurocode 7 incorporates design procedures implementing partial coefficients to reduce strength parameters and to amplify actions, the same as other European National Codes. In addition, the possibility of defining the intervening properties on a statistical basis accounts for soil variability in the design approach. These so-called, “semiprobabilistic” methods can be calibrated either by referring to the working stress design (WSD) or, more rationally, on the basis of probabilistic methods taking into account the intrinsic variability of soils.
The limitation of these methods lies in the lack of knowledge of the probability density distribution (often assumed to be normal) and the fluctuation scale (generally assumed from information given in the literature), associated with soil variability. Therefore, researchers should concentrate on developing probabilistic methods based upon a statistical characterisation of soil properties.
In the following section, the current knowledge about the variability of soils is outlined. Thereafter, the paper gives a detailed account of classical methods used to calculate retaining structures by the limit state design approach and a probabilistic approach to the evaluation of safety is proposed.
Section snippets
The variability of soils
Geotechnical parameters for direct use in evaluating stability or calculating deformation can be obtained by two major methodological approaches:
- •
by laboratory testing, allowing “direct” measurements of the investigated parameters;
- •
by in situ testing which requires “transformation models” to derive values of the parameters from measurements.
In either case, however, the investigated soil volumes represent only a minor part of the volume subjected to stress variation in situ. The results of
Generalities about sheet pile design
The following objectives should be achieved in a geotechnical study of sheet piles [2]:
a. Analysis of collapse conditions.
b. Estimation of stresses and displacements of structural elements under working conditions.
c. Estimation of soil displacements adjacent to the site of excavation under working conditions.
For the collapse conditions, the study should attempt to test:
- 1.
The stability of walls and any other retaining systems.
- 2.
The stability of excavations with respect to bottom heave.
- 3.
Stability with
Usual methods of limit state design analysis
Some limit state design methods for anchored sheel pile walls are briefly reviewed in the following paragraphs (note that stresses in the tie rod and sheet pile wall, taken as structural elements, are not considered here);
(a) The working stress design (WSD) is widely used in North America [22]. The depth of embedment below the dredge line is determined by considering the equilibrium of moments about the anchor point (Fig. 4a):where P′A and P′P are the resultant
The estimation of safety and probabilistic approaches
As mentioned above, estimating safety from a single coefficient that must be compared with a ratio (of forces, moments or pressures) may introduce a number of different approaches many of which imply a possible intrinsic ambiguity of that same ratio. Li et al. [33] have pointed out that in certain cases (slopes and retaining walls), action (demand) and resistance (capacity) can be defined in different ways resulting in different values of the deterministic ratio (Safety Factor).
On the other
The probabilistic approach
The schematic representations of actions and resistances and the geometrical data describing a sheetpile wall are shown in Fig. 7.
The equilibrium relative to the anchor point that is required for evaluating penetration depth defines the first expression of the safety marginwhere Mp is the moment of passive thrust relative to the anchor point; Ma is the moment of active thrust relative to the anchor point.
A second expression of the safety margin is needed to evaluate stress in the tie
Comment on results
Fig. 8 shows the depth D of penetration obtained for the different mean values of φ and for the two indicated values of C.V., with a fluctuation scale taken to be 0.5 m. As mentioned above, the earth-wall friction angle was assumed to be equal to and φ. A value of β=3 was imposed [53], roughly corresponding to a collapse probability of approximately 10−3. The figure also shows that the higher the value of the earth-wall friction the lower the depth of penetration. The latter is remarkably
Conclusions
Probabilistic methods are currently being applied only within geotechnical engineering research due to a number of reasons: among them, the problems involved in, and the cost of, developing a soil model that will account for soil variability. Add to that the problem of calibrating the calculation model which, at any rate, is also shared by the deterministic approaches.
Still, it is worth insisting on the investigation at the probabilistic approach so that the approaches to partial coefficients
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