Step 1: Generative Design Framework
Pile Foundations
The purpose of a pile foundation is to support a structure and to minimize the settlement of the structure. There are several potential tradeoff’s that will be discussed briefly below. This assignment was completed for 3 Units.
- Design Variables
- Radius of Piles — Simply the radius of the piles installed.
- Distance Between Piles — This is the lateral distance between piles.
- Depth of Piles — This is how deep the piles are driven.
- Evaluators
- Cost — The cost of the foundational system is calculated by the volume of concrete required (for piles + pile caps) and the cost to drill the pile holes.
- Settlement of Foundation — The settlement of the foundation is calculated by the surface area of all the piles (assuming skin friction and not point bearing).
- Foundation System Stability — Since skin friction is assumed, the stability of the foundational system depends on the distance between the piles and the radius of the piles themselves.
- Carbon Footprint — Concrete is a very bad material in terms of CO2 emissions and the carbon footprint depends on the volume of concrete used.
- Most Important Tradeoffs to Consider
- Cost vs. Settlement — You want to minimize cost by using the least amount and smallest piles, but want the least amount of settlement which requires the most surface area of piles.
- Cost vs. Stability — You want to minimize cost by using the least amount and smallest piles, but you also want the most stability which comes from the closest spacing and largest piles.
- Carbon Footprint vs. Stability — You want the smallest volume of concrete to reduce carbon footprint, but you want more stability from closer spaced and larger piles.
- Carbon Footprint vs. Settlement — You want You want the smallest volume of concrete to reduce carbon footprint, but you want the least amount of settlement which requires the most surface area of piles.
Seawalls
The purpose of a seawall is two-fold: they can help prevent wave overtopping and storm surges, but also more generally prevent flooding from rising water levels. There are several key tradeoffs to consider when analyzing seawalls.
- Design Variables
- Height of Seawall — How high above the ground the seawall extends.
- Type of Seawall — Different types of seawalls require different heights and characteristics (for example a steel wall versus an armor stone revetment).
- Evaluators
- Wave Dissipation/Flood Protection (and protection from overtopping the wall) — This is a common measure of success for a seawall and could be a function of the type of wall, foreshore characteristics (what’s in front of the wall to break waves), and the height of the wall. This would be calculated by using design equations for each type of wall to estimate wave overtopping based on the height of the structure for a standard coastal situation.
- View Quality from the House to the Water — The view quality of the house is a result of the type of structure and the height of the structure. This could be calculated in Dynamo by placing a long object beyond the wall with a fixed height and seeing how much is visible from a point at the house (changes with the height of the wall).
- Cost — The cost depends greatly on the type and height of the structure installed. This is calculated using material prices for the type of selected wall.
- Environmental Disruption — How much of the natural environment is required to be disrupted. Once again this could be calculated based on the surface area of the structure that is to be installed.
- Most Important Tradeoffs to Consider
- Cost vs. Wave Dissipation — It is a tradeoff between minimizing cost and maximizing the wave dissipation.
- Wave Dissipation vs. View Quality — The goal is to maximize wave dissipation, but maximize view quality. This is a trade off because typically the best performing structures are the tallest and disrupt more view quality.
- Cost vs. View Quality — Cost is to be minimized, but view quality wants to be maximized. This is an interesting tradeoff because it is also reliant on the wave dissipation which is to be maximized.
- Wave Dissipation vs. Environmental Disruption — The goal is to maximize wave dissipation, but minimize environmental disruption. However, the structures that best dissipate waves are large stone revetments that have low slope. This means that it takes up a large surface area, disrupting more of the natural environment and taking up valuable space in your backyard.
Roof Overhang
The purpose of a roof overhang is to protect the building facade from the elements, but can also help reduce energy use. There are several tradeoffs between the cost, energy savings, facade protection, and a sustainability tradeoff as well.
- Design Variables
- Width of Overhang — This represents how much the roof overhangs the facade.
- Material of Overhang — The materials used for the roof/structure.
- Evaluators
- Cost of Materials — How much additional cost is required per foot of overhang. For very large overhangs additional structural elements are required. For example, a standard wooden rafter overhang cannot extend beyond 24” without additional structural reinforcements (as per the Ontario Building Code). This is a non-linear relationship as for overhangs beyond 24” additional cost is required.
- Daylighting/Shading Savings — Clearly, the larger the overhang the more shading that is required. However, if natural daylight is being incorporated into the design, it may be that you actually do not want as much of an overhang. Conversely, in some areas the sun is very intense and more daylight may want to be blocked. This may be a more case-by-case assessment.
- Energy Use Savings — Once again, depending on the climate, the heat gain into the building may want to be maximized (for additional heating) or minimized (for enhanced cooling).
- Carbon Footprint of Materials — Considering whether the embedded carbon (from a life cycle perspective) of the additional materials used will be more or less than the energy saving equivalent is an important metric.
- Facade Protection from the Elements — Larger overhangs typically result in better protection of the facade elements. This could be particularly important for wooden/panelled exteriors.
- Most Important Tradeoffs to Consider
- Cost vs. Energy Savings — An important tradeoff is whether the additional cost will result in energy savings that outweigh the additional costs. Cost is to be minimized but energy savings are attempted to be maximized.
- Cost vs. Daylighting Savings — Once again, the additional costs versus the daylighting savings (through fewer fixtures or energy use). Typically, cost is minimized but daylighting savings is trying to me maximized.
- Energy Use Savings vs. Carbon Footprint of Materials — There is a tradeoff between trying to maximize energy use savings and minimizing the carbon footprint of materials.
- Cost vs. Facade Protection — There is a tradeoff between trying to minimize cost (the shortest hangover) but maximizing the facade protection.
Step 2: Generative Design Framework
I decided to focus on the pile foundation design scenario as I found the tradeoffs interesting and the situation more simple to model than the others. First, the model will be described then it will be put into the context of the generative design framework. The entire dynamo nodal structure can be seen below in Figure 1.
Since not everyone is familiar with foundation elements, I will begin by giving the output of the model and a brief description of the components. A sample output can be seen in Figure 2 below. The cylinders are piles, and the rectangular elements above are the pile caps. This may help make sense of the terminology I use below.
The design consisted of several inputs, in this case the inputs were the size of the structure of interest, the radius of the piles, the depth of the piles, and the spacing between the piles. In order to keep the inputs/constants more straight forward, a “rectangle” was created rather than four lines from point inputs. While this complicated the analysis slightly, I think it created a cleaner input structure. See the inputs in Figure 3 below:
From here, the rectangles were created using the ‘rectangle length’ and ‘rectangle width’ inputs. The individual curves were taken from each side of the rectangle from the poly-curve function. See Figure 3 below:
The first step was creating the pile caps (the rectangular beams that connect above the piles and support the foundation of the structure). This was done through multiple steps. First the list was flattened, then each line was taken from the rectangle individually. Then, for each line, the center point was taken by getting the curve length, cutting it in half, then placing a point at the midpoint of the segment length. This served as the input for origin for the cuboid creation function. The length was simply the length of the line and the height was calculated from an alternate function. For a typical concrete beam, the height is usually between L/8 and L/16, in this case I conservatively assumed the height of the beams was the unsupported length (L) divided by 12. This process was repeated for all four lines and can be seen in Figure 5 below. it
From here, the piles were created. This took the list of curves for the rectangle that represented the perimeter of the structure. From here, the distance between piles (input) was used to split each side into a set of points that would eventually represent piles. The points were translated downwards based on the user-inputted height of pile parameter, then the cylinders were created to replicate the piles (See Figure 6 below).
Nodes were then created to calculate each of the outputs (cost, stability, settlement, and carbon footprint). First, the cost node was created (See Figure 7 below). The cost consisted of two components, the price of the concrete and the price to drill the pile holes. This was achieved by taking the volumes of the pile caps and adding the volume of all the piles, this was then multiplied by the unit cost of concrete per cubic foot ($15 per cubic foot). Then, the depth of the piles was multiplied by the cost to drill each foot. This was taken as a result of $50 per foot depth * 2 * radius * Height of Pile. This function was extracted from average costs of drilling ($100 per foot for a 2’ diameter pile and $25 per foot for a 6” diameter pile). The total cost was then calculated.
Next, the approximate settlement was calculated (See Figure 8 below). This was calculated by using the surface area of all the piles. For a better understanding of the equation and how skin friction and shaft resistance work see Figure 9 below. Only side/skin friction is assumed for this case (the pile is not sitting on a rock for example). Higher shaft resistance typically results in lower settlement. In other words, settlement depends on Qs, which depends on As — therefore settlement can be calculated from 1/sum of pile surface areas. This is an approximation and there are other factors to consider regarding the type of soil but this was simplified to complete the analysis.
Then, the stability of the groups of piles was calculated. The stability of groups is important when dealing with a skin friction scenario as the piles must act as a cohesive unit. For this reason, stability was approximated by the radius of the pile and the spacing between piles. As per the equatiom below in Figure 10, the spacing should be smaller and the radius should be larger to increase stability.
Lastly, with the high environmental impact of concrete, especially in the form of CO2, the carbon footprint was calculated. As seen below in Figure 11, the carbon footprint was calculated using the volume of concrete and 15lbs of CO2 per cubic foot of concrete.
These were all presented in the form of outputs for the study that is to be completed (See Figure 12).
Now that the model has been well-documented and is better understood, it will be discussed in the framework of the Generative Design Framework.
- Objective: The objective of this study is to determine the “ideal” pile sizing and placement to maximize stability, while minimizing cost, structure settlement and carbon footprint.
- Model: As seen above, the model takes inputs for the structure size, pile radius, pile depth, and pile spacing. From here it creates points along the perimeter at the inputted spacing, offsets the points from the height input, then places piles and pile caps. From here it uses volume and other empirical equations to calculate cost, stability, settlement and carbon footprint.
- Design Variables:
- Radius of Piles — Simply the radius of the piles installed.
- Distance Between Piles — This is the lateral distance between piles.
- Depth of Piles — This is how deep the piles are driven.
- Constants:
- Structure Width — the width of the structure of interest.
- Structure Length — the length of the structure of interest.
- CO2 Emissions per Ft3 Concrete — This is set at 15lb/ft3 concrete.
- Cost of Concrete per Ft3 — This is set at $15/ft3 concrete.
- Cost per Foot Depth per Foot Radius for Pile Drilling — Set at $50 per foot diameter per foot depth
- Evaluators
- Cost — The cost of the foundational system is calculated by the volume of concrete required (for piles + pile caps) and the cost to drill the pile holes. It is ideal that this is minimized.
- Settlement of Foundation — The settlement of the foundation is calculated by the surface area of all the piles (assuming skin friction and not point bearing). It is ideal that this is minimized for the least amount of movement in the structure.
- Foundation System Stability — Since skin friction is assumed, the stability of the foundational system depends on the distance between the piles and the radius of the piles themselves. This should be maximized and can help prevent settlement/shifting.
- Carbon Footprint — Concrete is a very bad material in terms of CO2 emissions and the carbon footprint depends on the volume of concrete used. Ideally, this would be minimized.
- Interpretation
Will be discussed in the study section.
Part 3: Study Graph and Results
Tradeoffs can be easily explored through a generative design study. The scenario described above was taken and several design outputs were created. I chose to use the “optimize” method, with a population size of 20 and 10 generations. With this, the rectangle width and length were set constant at 30 and 40, respectively. The variables included the distance between piles, the pile height, and the radius of the piles (See Figure 13 below). There are many interdependencies between these variables in determining the outputs of cost, settlement, stability, and carbon footprint. The tradeoffs between these variables will be discussed below.
The results of the study for each output were in line with what was expected. As seen below in Figure 14, in order for the cost to be minimized, piles of the smallest radius, a small height, and large spacing were selected. Intuitively, one would think that the smallest radius, shortest pile height, and largest spacing would result in the cheapest option. However, because of the dependency of the height of the pile caps, having large spacing may actually hurt the cost due to the additional concrete required. Nonetheless, it is clear that although this is a cheap option, the tradeoff between outputs is clear. As seen in the grey below, while this is the cheapest option, it creates the most settlement, very poor stability, but actually has a very low carbon footprint. Looking at the problem through this lens certainly opens your eyes to the tradeoffs present. Likewise, as a way to verify the model, see Figure 15 below, which has the highest cost option. This makes sense as the highest cost option, and likely the most stable and lowest settlement consist of the smallest spacing between piles, the largest depth, and the thickest possible piles. Similar trends are true for the other outputs and will be briefly discussed below.
Similar to cost, the maximum and minimums for each situation were as expected, which serves to verify the model. In Figure 16 and 17 below, the smallest settlement results are the result of large radius and small distance between piles (to maximize contact surface area). Conversely, the highest settlement comes from a large spacing, small depth, and small radius. For stability (in Figure 18 and 19), the highest comes from the largest radius and smallest spacing (in most cases). In this case, it is clear the generations did not cover all the alternatives as the smallest spacing and largest radius would hypothetically give you the largest stability. Lastly, in Figure 20 and 21 the smallest and highest carbon footprint make sense in terms of spacing and radius.
More important that the individual trends are the ability to compare tradeoffs directly through the study interface. Most of these relationships are non-linear which prove the worthiness of this topic and the usefulness of the study. First, cost and settlement can be seen below in Figure 22. This relationship is useful because it shows that spending more money in favour of less settlement is not always necessary as the decreases in settlement with cost are marginal after about $20,000.
Likewise, adding stability into the mix can help further narrow down design options and get a better idea of the tradeoffs. Cost versus stability alone follows the trend in Figure 23. This is not a clear linear trend and is somewhat scattered. Therefore, adding it to the cost settlement relationship in Figure 24 clarifies the tradeoffs. It is clear that the optimal solution in terms of cost, settlement, and stability is the large dot that falls around $40,000 and 0.005 for settlement. The purpose of this exercise is not to be able to find that ONE solution is the cheapest, most stable, creates the least settlement, and the lowest carbon footprint. This is not possible. But, by creating this study it allows you to balance variables and see how you can make the best of each while taking into account individual priorities.
As a concluding thought, here is carbon footprint added to Figure 24 in Figure 25 below. As expected, the carbon footprint gets larger as you move higher on the x-axis. Therefore, you want to (generally) be lower on the y-axis for settlement, further left on the x-axis for cost, further right on the x-axis for stability, but further left on the x-axis for carbon footprint. Overall, this creates an optimal area near the large light orange dot around $40,000 and 0.0005 settlement (See Figure 26). Based on a plot like this, and the priorities of the project (tight budget, high environmental awareness, poor soil conditions, high earthquake zone), certain variables can be prioritized while still accounting for other important project variables. Using generative design studies like this allows for a large range of alternatives to be tested at once, while emphasizing the variables that matter most to the project.
