Interactive Cantilever Retaining Wall Design Simulator

Cantilever Retaining Wall Design Simulator

Created By : Ir. MD Nursyazwi

A comprehensive academic tool for analyzing the stability of cantilever retaining walls.

Instructions on How To Use

This interactive tool provides a comprehensive analysis of the stability of a cantilever retaining wall. Cantilever walls are rigid structures, relying on their stem and footing to resist lateral earth pressure. The simulator operates on fundamental principles of soil mechanics, assuming a homogenous soil profile and level backfill. The simulation process involves the following steps:

• Step 1: In the "Data Input" section, specify the geometric and material properties of the wall and surrounding soil.
• Step 2: Execute the simulation by clicking the "Calculate Design" button to compute the relevant stability factors.
• Step 3: Review the results presented in the "Data Output" section, which provides a quantitative assessment of the design's stability.
• Step 4: Observe the "Graphical Simulation" to gain a visual understanding of the forces acting on the wall and the resulting pressure distribution.
• Step 5: For an in-depth understanding of the underlying theoretical framework, consult the "Science Explanations" section.

Data Input

The Data Input section allows for the specification of critical design variables that govern the wall's structural and geotechnical behavior. The parameters, including wall geometry and soil properties, can be calibrated to different international design standards, which apply specific partial safety factors to ensure a conservative and reliable design.

Design Standard Simplified Analysis Malaysian Standard (MS) British Standard (BS 8002) Eurocode 7 (EC7) American Standard (AASHTO)

Partial Safety Factor for Soil Unit Weight (Gamma_G)

Wall Height (H) (m)

Stem Width (W_stem) (m)

Footing Height (H_footing) (m)

Toe Width (B_toe) (m)

Heel Width (B_heel) (m)

Soil Unit Weight (Gamma_s) (kN/cubic meter)

Concrete Unit Weight (Gamma_c) (kN/cubic meter)

Soil Friction Angle (phi) (degrees)

Wall-Soil Friction Angle (delta) (degrees)

Ultimate Bearing Capacity (q_ult) (kN/sq. meter)

Optimal Design Finder

This tool will help you find a combination of footing dimensions and angles that provides the best overall stability. It iterates through a range of options and recommends the design that results in the highest factor of safety for overturning, sliding, and bearing capacity.

Recommended Optimal Design Parameters:

Optimal Heel Width: -

Optimal Toe Width: -

Overall Factor of Safety: -

Graphical Simulation

The Graphical Simulation illustrates the principal forces acting on the cantilever wall. This visual representation aids in understanding the force vectors and their points of application, which are critical for moment and shear calculations. The diagram includes the active earth pressure (P_a) acting horizontally and the total vertical resisting forces (W_v) representing the self-weights of the wall and the soil on the heel.

Data Output

The Data Output section presents the quantitative results of the stability analysis. It provides calculated factors of safety against overturning and sliding, as well as the maximum bearing pressure at the foundation base. These values are essential for determining the wall's compliance with established safety criteria.

Design Verdict: -

Factor of Safety Against Overturning: -

Factor of Safety Against Sliding: -

Factor of Safety Against Bearing Capacity: -

Maximum Bearing Pressure: -

Graphs and Charts

The Graphs and Charts section provides a visual interpretation of the calculated bearing pressure distribution along the foundation base. The shape of the pressure diagram—whether trapezoidal or triangular—is indicative of the resultant force's eccentricity relative to the middle third of the base, a fundamental principle for preventing tensile stresses in the soil.

Science Explanations

Key Design Principles

The stability of a cantilever retaining wall, a type of gravity wall, is evaluated based on three primary conditions: stability against overturning, stability against sliding, and bearing capacity. The simulator calculates the factors of safety for each condition. This image shows the key components: the vertical stem, the horizontal footing, and the backfill soil resting on the heel.

Active and Passive Earth Pressure

To accurately account for the wall's geometry, the simulator now uses Rankine's Theory for active earth pressure. The driving force is the active earth pressure (P_a), which is resisted by the wall's self-weight and the weight of the soil on the heel. For sliding stability, the passive earth pressure (P_p) acting on the toe of the footing provides additional resistance against the lateral movement.

Overturning Stability

Overturning stability is assessed by comparing the restoring moments to the overturning moments about the toe. The overturning moment (M_o) is generated by the active earth pressure (P_a) acting on the stem. The restoring moments (M_r) are generated by the combined weights of the wall components (stem, footing) and the soil resting on the heel of the footing. The factor of safety against overturning is the ratio of M_r to M_o.

Sliding Stability

Sliding stability is evaluated by comparing the total horizontal resisting force to the horizontal driving force. The driving force is the active earth pressure (P_a). The resisting force is the sum of the friction force at the base (a function of the total vertical weight and the soil's friction angle) and the passive earth pressure (P_p) acting on the toe. The factor of safety against sliding is the ratio of the total resisting force to the driving force.

Bearing Capacity

The bearing capacity of a foundation soil refers to its ability to support the loads applied by the structure without undergoing a shear failure. It is a critical check to ensure the soil itself is strong enough to carry the weight of the wall and the additional vertical loads from the earth pressure. The Factor of Safety for Bearing Capacity is calculated as the ratio of the ultimate bearing capacity of the soil (q_ult) to the maximum pressure applied by the wall (q_max). The design is considered safe if this ratio is greater than a specified value (typically 2.0 to 3.0).

Bearing Pressure

The bearing pressure analysis verifies that the stress applied to the foundation soil does not exceed its ultimate bearing capacity. This is determined by the magnitude and eccentricity of the resultant vertical force. An eccentric load can lead to a non-uniform pressure distribution, with the maximum pressure occurring at the edge of the base, which is a critical design consideration.

The formulas for maximum and minimum bearing pressure are given by: q_max/min = (V / B) * (1 ± (6e / B)), where e is the eccentricity of the resultant force, V is the total vertical force, and B is the total base width.

International Design Standards

Different countries and regions employ specific design standards. These codes often introduce partial safety factors to account for uncertainties in material properties, loads, and design assumptions. While the fundamental principles remain the same, the application of these factors changes the final required dimensions for a stable and safe design. This simulator provides a simplified comparison by adjusting key input values according to typical code-based factors, but it is not a substitute for a detailed professional analysis.

References

The methodologies and principles employed in this simulator are founded on established geotechnical engineering textbooks and design codes. The following references provide a deeper understanding of the theoretical background:

• Structural Engineering Reference Manual

  A comprehensive reference for structural engineering principles and design.

• Principles of Geotechnical Engineering

  A classic textbook covering fundamental concepts in soil mechanics and geotechnical engineering.

• Foundation Analysis and Design

  A detailed guide on the analysis and design of foundations for various structures.

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