Step 1 - Generative Design Framework
Design Decision 1: Cantilever Retaining Wall Geometry Optimization Design Variables
- Toe Length (ft)
- Heel Length (ft)
- Stem Base Thickness (ft)
- Top Stem Thickness (ft) Evaluators
- Total Concrete Volume per linear foot (Minimize)
- Factor of Safety against Overturning (Maximize)
- Factor of Safety against Sliding (Maximize)
- Maximum Soil Bearing Pressure (Minimize / Constrain <= 3000 psf) Most Important Tradeoffs to Consider
- Extending the heel utilizes the weight of the retained soil to prevent overturning without adding extra concrete, but requires significantly more site excavation. Widening the toe prevents sliding and distributes the vertical load to reduce bearing pressure, but adds pure concrete dead weight. Tapering the stem saves massive amounts of concrete volume but changes the center of gravity, which heavily influences the eccentricity and resulting maximum bearing pressure on the soil.
Design Decision 2: Office Building Column Grid & Slab Thickness Design Variables
- Column spacing in the X-direction (ft)
- Column spacing in the Y-direction (ft)
- Concrete slab thickness (in) Evaluators
- Total Concrete Volume (Minimize)
- Maximum Slab Deflection (Minimize)
- Total Number of Columns (Minimize) Most Important Tradeoffs to Consider
- Pushing columns further apart creates highly desirable, open architectural layouts by minimizing the column count. However, to prevent the slab from exceeding deflection limits over these longer spans, the slab thickness must be drastically increased, which heavily drives up the total concrete volume and project cost.
Design Decision 3: High-Rise Massing and Wind Sail Reduction Design Variables
- Building base width (ft)
- Top taper percentage (%)
- Corner chamfer/radius size (ft) Evaluators
- Total Wind Surface Area (Minimize)
- Total Leasable Floor Area (Maximize)
- Structural Center of Mass Height (Minimize) Most Important Tradeoffs to Consider
- Tapering the building as it rises and heavily chamfering the corners drastically reduces the wind surface area, saving a fortune in lateral structural steel. However, every square foot shaved off the building envelope is a square foot of prime, high-altitude real estate that cannot be leased out.
Step 2 - Generative Design Study
For this study, I chose to model the Cantilever Retaining Wall Geometry to fulfill the 4-unit requirement. The goal is to determine the optimal cross-sectional dimensions of a tapered concrete cantilever retaining wall that minimizes material usage while safely maintaining strict structural stability requirements (Factor of Safety >= 1.5) and ensuring the foundation soil is not crushed.
Objective: Minimize the total concrete volume of the retaining wall while maximizing (or constraining > 1.5) the Factor of Safety against sliding and overturning, and keeping the Maximum Soil Bearing Pressure below allowable limits. Model: A parametric 3D Dynamo model that generates a 1-foot unit strip of the tapered retaining wall, alongside the retained soil and toe water blocks. The graph uses a physics engine code block to calculate static equilibrium, calculates the eccentric vertical load to find the maximum toe bearing pressure, and includes conditional logic to automatically deploy a concrete shear key if the initial FOS against sliding drops below 1.5. Design Variables:
- Toe Length (1.0 ft to 5.0 ft)
- Heel Length (2.0 ft to 8.0 ft)
- Stem Base Thickness (1.0 ft to 3.0 ft)
- Top Stem Thickness (0.5 ft to 1.5 ft) Constants:
- Total Height (15 ft)
- Base Thickness (1.5 ft)
- Soil Unit Weight (120 pcf)
- Concrete Unit Weight (150 pcf)
- Active Earth Pressure Coefficient (0.33)
- Base Friction Coefficient (0.5) Evaluators:
- Total Concrete Volume (Minimize)
- FOS Overturning (Maximize)
- FOS Sliding (Maximize)
- Max Bearing Pressure (Minimize)
Step 3 - Generative Design Study Results
Explanation of the Scatterplot and Tradeoff Impact: The scatterplot illustrates the complex, four-dimensional tension between material efficiency (Concrete Volume on the X-axis) and foundation performance (Max Bearing Pressure on the Y-axis, with FOS metrics mapped to color/size). The cluster of points representing highly tapered, ultra-efficient concrete walls often results in dangerous eccentricities that drive the toe bearing pressure far beyond safe soil capacities. By filtering the results to only show options where the sliding and overturning FOS are above 1.5 and the bearing pressure is below 3,000 psf, the optimal design zone reveals itself. This data allows a structural engineer to select the most aggressive stem taper and optimal footing spread that satisfies all safety codes, perfectly balancing the material cost against the geotechnical limits of the site.
