Seismic Design of Foundations: The 2015 Canadian Building Code Provisions
Bibliographic record
Abstract
The concept of allowing foundations to rock as a way of limiting the seismic forces that are induced into an existing structure is well known. Currently, designers of new buildings in Canada are permitted to allow their foundations to rock at force levels as low as 50% of the elastic demand without having to consider the increased displacements in the structure, which is a concern. Also, the current rocking foundation provisions are often misused by designers of high-rise buildings having numerous floor levels below grade with shear walls interconnected by numerous stiff diaphragms connected to large foundation walls supported on separate foundations. The results of a study on rocking footings has been used to develop new design provisions for the Canadian building codes - both the loading code and the code for design of concrete foundations. Nonlinear analyses of rocking footings were done using OpenSees. Nonlinear fibre elements were used to model concrete shear walls and the QzSimple1 model was used for the nonlinear cyclic behaviour of the soil. The initial stiffness of the soil springs were calibrated to give an initial rotational stiffness of the foundation consistent with Gazetas’ well-known equation. Clay, three different sands (loose, medium and dense) and rock were studied. Three different building heights (5, 10 and 20 story) and two different mass ratios, which is equal to axial load on the footings as a ratio of the seismic mass, (0.4 and 0.6) were examined. A large variety of each type of building with very different strength shear walls and very different size footings were studied. Ten ground motions scaled to the 2500-year UHS for Vancouver BC, which has similar seismicity to Seattle, were used for each of the buildings. The new Canadian design provisions require designers of all foundations that are not restrained from rotating freely to consider how the movements of foundation will influence the seismic-force-resisting-system (SFRS) and most importantly, the gravity-load resisting structure surrounding the SFRS. The requirement to consider foundation movements is for foundations that are both not capacity-protected by the SFRS, i.e., “rocking foundations,” as well as for foundations that are capacity-protected. Significant movements may occur in the latter case because of the assumed uniform bearing stress in soil or rock that is used to calculate the overturning resistance of the foundation. Simplified procedures were developed to determine the rotation of a foundation in static equilibrium using the concept of an equivalent rectangular bearing stress block as commonly used for bending of nonlinear concrete sections. This simplified hand-calculation approach gives very accurate estimates of foundation rotations when compared with the nonlinear analysis. In addition, procedures were developed for estimating the effective stiffness of a rotational spring that can be used in a linear dynamic analysis to determine the increased displacements of a structure with rocking foundations. The effective linear stiffness accounts for the reduction in stiffness due to footing uplift and nonlinear soil compression, and reduces with increased rocking as a function of the ratio of footing overturning resistance to elastic demand on a fixed-base structure.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".