Example: Top/Down Excavation - Diaphragm Walls with Concrete Slabs
This example presents the design of a top/down excavation model (reinforced concrete diaphragms with concrete slabs), supporting a 9.5m excavation.
The model is generated and analyzed in DeepEX software, using all the available analysis methods (Limit Equilibrium, Non-Linear and Finite Element Analysis).
A. Introduction - Project Description
In this example we will design a top down excavation of 9.5m between two diaphragm walls (60cm thick walls), connected with concrete slabs. The Figure below presents the project model. Tables 1 and 2 present the soil properties and the stratigraphy respectively. Table 3 presents the external loads. Table 4 presents the support properties. The general ground surface is at El. 0m and the general water table is at El. -3m.
Table 1: Soil properties.
Table 2: Stratigraphy.
Table 3: External loads.
Table 4: Support parameters.
For the bottom slab, we will choose to have no effective moment connection with the wall. In addition, we will choose to include for this slab a user-defined unbraced length of 3 m.
B. Modeling with DeepEX
B.1. Edit Soil Properties and Stratigraphy
In DeepEX we can create an unlimited number of soils and define the soil type and soil properties for each soil. The soil properties can be defined manually for each soil, or be estimated from SPT values and other test results. The following figures present some soil properties and the project stratigraphy as defined in Tables 1 and 2.
B.2. Examined Wall Section
In DeepEX, we need to manually define the wall type and wall section to be examined in a model. The software will calculate all wall stresses and capacities according to the selected design standard and provide extensive results and check ratios for each construction stage. Based on the results, we can easily optimize the wall section, either manually, or with the use of DeepEX automatic optimization tools. In this example, we assume the use of a 60cm thick reinforced concrete diaphragm. Table 5 summarizes the examined wall section properties.
Table 5: Wall parameters.
B.3. External Surcharge
In this model we will apply an external surcharge of 20 kPa, developed for 15m, starting 0.5m behind the wall, as presented in Table 3. DeepEX will calculate the horizontal stresses that are developed on the wall, using the Elasticity Equations.
B.4. Construction Stages
In DeepEX, we can create and analyze all construction stages of a model. The construction stages both allow the more advanced analysis methods (Non-Linear – Finite Element Analysis) to converge, and can assist us with the final model optimization.
B.5. Analysis Methods and Analysis Settings
The generated model will be analyzed with all analysis methods available in DeepEX Software – Limit Equilibrium Analysis, Non-Linear Analysis (Elastoplastic springs) and Finite Element Analysis.
For the Limit Equilibrium Analysis method, we will use Active and Passive soil pressures for the driving and resisting side, in all construction stages with cantilever excavation and 1 support level (Stages 0 to 3). For all Stages with multiple support levels, we will use the Peck 1960 Apparent Pressures for the driving side (Stages 4 to 8).
For the calculation of wall moment and shear diagrams (Beam Analysis) we will use Blum’s method, which considers the support locations are hinges and uses a virtual support below the excavation, at the point of zero net pressures.
We will calculate the water pressures, considering the Simplified Flow method.
In all Stages, we will use as wall friction 50% of the soil friction for the resisting side and zero wall friction for the driving side.
In all cases, we will use the Eurocode 2 Specifications for the calculation of all concrete members structural capacities, with a reduction factor of 1.5.
C. LEM, NL and FEM Analysis Results in DeepEX and Model Optimization
The table below includes the most critical results and checks (displacements, wall moment, wall shear, support reactions, wall embedment FS and more), for each analysis method, among all construction stages. All calculated result graphs can be also presented on the model area for each constructions stage.
Table 6: DeepEX critical results/analysis method
C.1. Wall Results and Optimization Recommendations
The most critical results for the wall analysis (Displacements, Moments and Moment Check Ratios, Shears and Shear Check Ratios, Wall Embedment Safety Factors) are explained below. A good evaluation of these results can direct us to important decisions, for the wall section optimization.
Wall Moments and Moment Ratio: The calculated most critical moment from Limit Equilibrium method is quite smaller than the one from the more advanced methods (Non-Linear and FEM). The moment check ratio produced by all methods (Ratio = Moment Capacity/Developed Moment) is less than one, so the wall thickness and provided longitudinal reinforcement seem to work fine for this case. We could consider decreasing our wall thickness and/or longitudinal reinforcement, but this would also affect the check displacements in the Non-Linear and Finite Element Analysis.
Wall displacements: In cases with multiple support levels, the displacements estimated from the LEM analysis might be unrealistic. For such models, we should always run more advance methods like the Non-Linear or/and Finite Element analysis. These methods calculate the wall displacements using the defined soil model and modulus of elasticity of the soils. FEM considers full soil-structure interaction. In our model, the displacements from FEM seem to be close to 1 cm. If there is a strict limitation for displacements, we might need to consider increasing the wall section.
Wall Shears and Shear Ratios: We see that the wall shear check ratio is significantly smaller than 1, with all analysis methods. Based on this result, we can consider decreasing the shear reinforcement size and/or increasing the distance between the shear rebars.
Wall Embedment Safety Factor: Wall Embedment Safety Factors are calculated when we perform the Limit Equilibrium Analysis (or the combined LEM + Non-Linear Analysis). The most critical FS in this model is the Rotational F, which is 4.8. Targeting for a minimum FS = 1.5 since we perform a service design, we can be safe to decrease the wall depth. We can run a couple of tests and optimize the wall depth, to achieve a factor closer to 1.5.
The following Figures illustrate some of the calculated wall result graphs.
C.2. Support Results and Optimization Recommendations
From Table 6, we can see that the most critical support reactions and support structural checks are similar for all analysis methods. The following figure presents the calculated support structural ratios in Limit Equilibrium Analysis method, for each slab. We can see that the base slab is less stressed than the others. Based on these results, we could check thinner slab sections and try reducing the provided reinforcement.
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