Model simulation, LEM and FEM analysis with DeepEX software
Retaining walls are designed to counteract soil pressures across different elevations, support landscaping and structural foundations near buildings, roads, or other infrastructure, and improve road safety by preventing soil slippage or subsidence. Furthermore, these structures are frequently erected in urban transit zones or on private properties, aiming not only to reduce land consumption but also to enhance its efficiency.
DeepEX is an indispensable tool for deep excavation projects, known for its robust capabilities in handling complex engineering challenges. This software excels in ensuring the stability, safety, and efficiency of excavations by facilitating precise modeling, careful planning, and strict compliance with regulatory standards. DeepEX allows engineers to thoroughly analyze soil conditions, design support systems, and maintain structural integrity throughout the project lifecycle.
One of the key advantages of DeepEX is its ability to seamlessly integrate train embankment load simulations into the design of gravity retaining walls with taking into account AREMA specifications. This feature is particularly beneficial for projects involving transportation infrastructure, where the impact of dynamic loads is critical. By automating the application of these loads, DeepEX not only saves time but also enhances the reliability of the design process. The software's comprehensive analysis tools enable engineers to evaluate potential scenarios, optimize designs, and ensure that all safety margins are met, thereby significantly reducing the risk of errors and increasing the overall efficiency of the project.
A. Project Description
In this example, the support provided by a retaining wall for a railway embankment planned on a slope will be analyzed using DeepEX. To avoid encroachment on adjacent properties, one side of the embankment will maintain a normal gradient, while the other side will be supported by a retaining wall. The railway embankment is designed with a thickness of 4 meters, matching the height of the retaining wall, which is also constructed to be 4 meters tall.
B. Soil Properties
In this study, the parameters and stratigraphy of the soil to be modeled are presented in Table 1 and Table 2, respectively.
Table 1- Soil Properties
Soil Type | Su (kPa) | c' (kPa) | Ф’ (deg) | γ (kN/m3) | Eu (kPa) | Es (kPa) |
Back Fill | - | 5 | 35 | 22 | - | - |
Fill | - | 5 | 42 | 22 | - | - |
Clay 1 | 140 | 12 | 35 | 19 | 20900 | 14600 |
Clay 2 | 165 | 16 | 24 | 19 | 52800 | 36900 |
Table 2- Stratigraphy
Soil Layer | Elevation (m) | OCR |
Back Fill | +4 | 1 |
Fill | -0.85 | 1 |
Clay 1 | -2.5 | 1 |
Clay 2 | -12 | 1 |
C. Modelling with DeepEX
The model will be created using the DeepEX with following steps:
· Define soil types and stratigraphy
When modeling a project, it is crucial to accurately define the types of soil in the area, the parameters of these soils, and the geometry. The soil types and geometry given in Table 1 and Table 2 are defined in the program as shown in Figure 1.
Figure 1- Soil Types and Soil Layers in DeepEX
Tip: For structures to be constructed on soil profiles consisting of cohesive units such as clay and silt, it is recommended to provide a 50 cm layer of rock fill to prevent direct contact with the cohesive units. Therefore, in this example, a rock fill has been defined extending 50 cm below the base of the wall.
· Define wall type and wall section properties
In the model, double-clicking on the default wall section brings up the "Edit Wall Data" window. In this window, selecting the "Use Gravity Wall Section" option and clicking on "Edit Section Data" reveals the tab to be used for defining the retaining wall (see Figure 2).
Figure 2 - Edit Wall Data Window - DeepEX
The "Retaining Wall Data" tab contains types of retaining walls commonly used in projects. Desired retaining wall geometry can be selected and parameters such as height, base, and top width are adjusted in the ensuing window. Additionally, details of the wall's reinforcement can be provided in this section. Material definitions for concrete and steel used in the wall can be made under the "Materials" tab.
In this example, the wall under consideration has a height of 4 meters and a base of 2.75 meters. The geometry of the wall is displayed on the right side of Figure 3.
Figure 3 - Retaining Wall Data - DeepEX
· Defining Stages
Considering the construction methodology for a retaining wall, the process begins with the wall's construction, followed by staged backfilling. Since the fill will endure train loads under service conditions, load definitions are applied subsequent to the backfilling. The stages delineated in the DeepEX model are illustrated in Figures 4, 5, and 6.
Figure 4 - General Model – Stage 0 - At rest conditions
Figure 5 - Generated Model – Stage 1 - Initial backfill
Figure 6 - Generated Model – Stage 2 - Final backfill
· Train Embankment Load
The embankment modeled in this project was subjected to the Load Model 71 (LM71) train load as specified in Eurocode EN 1991-2 (2003). This specification imposes a system load of 250 kN per axle, equivalent to 125 kN per wheel. The configuration of the train load within the system is depicted in Figure 7.
Figure 7- Train-Embankment Load Configuration
Figure 8 - Generated Model – Stage 3 - Train load activation
DeepEX provides its users with a variety of loading analysis methods, including AREMA, Elastic (Boussinesq), and One Way Distribution, as illustrated in Figure 7.
D. Analysis and Results
DeepEX not only supports traditional design methods (Limit Equilibrium analysis) but also incorporates advanced numerical techniques such as Finite Element Method (FEM). FEM allows for detailed simulations of complex interactions between soil and structure by discretizing the model into smaller, manageable elements, which enables precise analysis of stress and deformation under various loading conditions. On the other hand, LEM is employed to assess the stability of slopes and retaining walls, focusing on the balance of forces to determine the safety factor against failure. Together, these methods provide a robust framework within DeepEX, allowing engineers to tackle a wide range of geotechnical problems with high accuracy and confidence.
In this example, the generated retaining wall model was analyzed with the traditional LEM method and the FEM method.
In this example, the modeled retaining wall was analyzed with the traditional LEM method and the FEM method. In the LEM model, the wall friction angle was determined as 66% of the soil friction angle, and in the FEM model, this value was defined as 85%. In addition, in the FEM model, the level of mesh, which is an important point in the calculation, was determined as medium density.
After the analysis is succeeded, the Summary table appears. The table below includes some critical checks and values for each construction stage. The following figures present some graphical results from the results tab of DeepEX.
The most critical analysis results for both the Limit Equilibrium Method (LEM) and Finite Element Method (FEM) models are compared in Figure 9. Figure 10 illustrates the most critical results for each stage defined in the LEM analysis, illustrating the comprehensive assessment capabilities of DeepEX in handling complex geotechnical evaluations.
Figure 9 - Comparison of the Results for LEM and FEM Models - DeepEX
Figure 10 - Analysis and Checking Summary Results - Each Stage
With DeepEX, moments and shear forces occurring in the wall throughout all stages are obtainable. Additionally, it facilitates access to critical design considerations for retaining walls, such as sliding, overturning, and bearing capacity results. The effective horizontal soil pressures, effective vertical soil pressures and surcharge load distribution graphs obtained as a result of LEM analysis are presented in Figures 11 to 13.
Figure 11 - Effective Horizontal Soil Pressure Obtained From FEM Stage 3
Figure 12 - Effective Vertical Soil Pressure Obtained From FEM Stage 3
Figure 13 - Surcharge Load Distribution
The settlements obtained as a result of FEM analysis is shown in Figure 14 and the horizontal displacement is shown in Figure 15.
Figure 14 - Settlements Obtained From FEM Stage 3
Figure 15 - Horizontal Displacements Obtained From FEM Stage 3
To access these engineering evaluations, double-clicking the retaining wall is required to open the "Edit Wall Section" interface, as depicted in Figure 2. From this interface, navigating to the "Retaining Wall Data" window and selecting the "Results" tab reveals detailed computational outputs for structural analyses, encompassing assessments of sliding, overturning, and bearing capacities.
Figure 16 - Result for Sliding, Overturning and Bearing Conditions
E. Conclusion
DeepEX enables users to model retaining walls with various dimensions and reinforcement configurations, and to assess their moment and shear capacities under diverse loading conditions, including evaluations for sliding, overturning, and bearing conditions. In this specific instance, the retaining wall supporting a railway embankment subjected to Load Model 71 (LM71) train load has been analyzed. The Elastic (Boussinesq) method was selected for the train load analysis. The results of the analysis demonstrate that the reinforced concrete retaining wall has sufficient structural and static capacity, fulfilling the required criteria for sliding, overturning, and bearing conditions.
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