Probabilistic approach to the design of anchored sheet pile walls

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Abstract

Following a brief review of the physico-mechanical properties of soils, this work analyzes and comments upon some of the most frequently used approaches in anchored sheet pile wall design. The analysis highlights the conceptual differences between the various approaches, often leading, inevitably, to markedly diverging results. Although the probabilistic approach cannot be applied extensively, mainly because it is difficult to obtain statistical modelling of the soil mass, it nevertheless enables designers to avoid certain ambiguities that are present in the commonly used approach based on the Safety Factor. In addition, the probabilistic approach also permits handling of the calibrations required for the approaches to partial coefficients to be effective and applicable to different local conditions associated with the diversity of soils, different modes of construction, etc. Numerical results obtained for a simple probabilistic model lead to conclusions which are certainly not exhaustive but may contribute significant elements for reflection.

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):P′ALA+PWALWA=P′PLPF+PWPLWPwhere PA and PP 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 marginSM1=Mp−Mawhere 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 φ2 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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