DReW Seismic: Displacement of Retaining Walls due to Earthquakes

Stability analysis of embedded cantilever retaining walls in seismic area is generally carried out by calculating a factor of safety against a possible mechanism of collapse. However, a more rational approach consists in assessing the performance of the structure in terms of accumulated permanent displacement (Fig. 1). Indeed, this approach is required by many national standards as well as Eurocode 8 Part 5 (§7.1(1)P; §7.1(2)). However, the effectiveness of a performance-based approach is strongly related to the ability of the employed method to assess the earthquake-induced displacements of the structure. In this context, the Newmark’s method, which is commonly employed for the assessment of the permanent displacement of gravity retaining walls due to earthquake, generally leads to inadequate results when it is applied to embedded retaining structures, as both numerical and experimental studies have shown. Advanced numerical methods, such as FEM and FDM, can definitely provide a satisfactory comprehension of the performance of embedded retaining walls under seismic conditions. However, the employment of such methods for routine applications is still impracticable for the difficulty of handling complex constitutive models, which require a large number of parameters of difficult determination.

In this context, DReW Seismic is a software which allows readily evaluating the permanent displacement of embedded cantilever retaining walls, such as diaphragm or sheet-pile walls, after an earthquake. It is based on a method, of simple application, that performs the prediction of the permanent displacement of the top of the wall owing to a given seismic event. DReW Seismic is simple to use and requires a limited number of input parameters. In addition, a database of acceleration time-histories is provided. These aspects make the software quite attractive for practical applications. DReW Seismic is developed on the basis of the method recently published by Conte, Pugliese and Troncone (2022) in the journal Géotechnique.

To calculate the wall displacement due to the earthquake, DReW Seismic compares the ground acceleration time-history with the critical threshold, which is updated during the earthquake to account for the progressive development of the passive resistance of the soil. When the ground acceleration exceeds the critical threshold, the motion equation is solved to calculate the angular acceleration of the wall. Once this latter is known, angular velocity and rotation (θ) of the wall are calculated by successive integration. Finally, the displacement of the top of the wall (u) is calculated under the assumption that the wall rotates rigidly around a point located close to its base (Fig. 1). A schematic representation of the above described integration procedure is shown in Fig. 2.

GENERAL FEATURES IN DReW SEISMIC

DReW Seismic performs a seismic analysis of embedded cantilever retaining walls in cohesionless soils, calculating the evolution with time of the permanent displacement of these structures owing to earthquakes. The seismic analysis refers to the solution developed by Conte, Pugliese and Troncone (2022). The main features of the software are listed below:

• The redistribution of the soil pressure on the wall as a function of the wall displacement is accounted for, as required by Eurocode 7 Part 1 at §9.7.1(5)
• Different typology of structures: diaphragm and sheet-pile walls
• Layered soil
• Cohesionless soil
• Presence of surcharge

For the sake of completeness, a pseudostatic analysis can be performed as well. This latter refers to the procedure developed by Conte, Troncone and Vena (2017).

REQUIRED INPUT

DReW Seismic is very easy to be used and requires a limited number of input parameters (Fig. 3). In particular, the following data is required:

• Excavation height, H;
• Embedment depth, D;
• Soil unit weights, γ₁ and γ₂;
• Angle of shearing resistance of the involved soils, φ₁ and φ₂;
• Friction angle at the soil-wall interfaces, δ₁ and δ₂;
• Unit weight of the wall, γ_wall;
• Wall thickness, B (in case of diaphragm wall);
• Pile diameter, d, and spacing between piles, s (in case of sheet-pile wall) ;
• Surcharge intensity, q.

Moreover, since a seismic analysis is performed, an acceleration time-history representative of the considered site is required. To this purpose, it is possible to refer to an acceleration time-history that has been previously recorded at the site. A database of earthquakes to refer to is available on this website.

If a pseudostatic analysis is performed, the horizontal and vertical seismic coefficients, respectively k_h and k_v, are required.

OUTPUT

DReW Seismic provides the outputs listed below when a seismic analysis is performed:

• displacement time-history owing to a given earthquake. The displacement is calculated for the top of the wall (Fig. 1);
• comparison between the ground acceleration time-history and the corresponding critical threshold, which is also updated during the earthquake;
• evolution with time of the angular acceleration of the wall;
• evolution with time of the angular velocity of the wall;
• evolution with time of the rotation of the wall;
• evolution with time of the net pressure at the wall end and comparison of this latter with the corresponding limit value;
• evolution with time of the depth in which the passive resistance is completely mobilized;
• evolution with time of the center of rotation of the wall;
• evolution with time and depth of the net pressure acting on the wall.

When a pseudostatic analysis is performed, the following outcomes are provided:

• net pressure acting on the wall;
• shear force;
• bending moment.

Displacement of Retaining Walls due to Earthquakes – DReW Seismic

DReW Seismic is a software which allows a readily prediction of the permanent displacement of embedded cantilever retaining walls (diaphragms and sheet-pile walls) after an earthquake. DReW Seismic is very simple to use and requires a limited number of input parameters.