Uncertainty and Randomness in Seismic Design

Randomness in Demand and Capacity

Randomness exists in both the demands on a structure and in its capacity to resist them. Earthquake motions are inherently random. Even with increased knowledge, there will be large randomness in both the excitation and response. Structural behavior is affected by random variations in material properties, deterioration, and construction quality. Capacity is also affected by loading history and duration which are both influenced by the randomness of the excitation.

Uncertainty in Demand

There are numerous sources of uncertainty in the expected demands on a structure. These sources of uncertainty include:

  • Seismology
    - what earthquake intensity is expected during a given interval of time?
    - various methods available to improve estimates of intensity, return period, etc.
  • Ground motion characteristics
    - what response spectrum corresponds to an earthquake motion corresponding to a given intensity and soil conditions?
    - what is the expected duration?
  • Structural characteristics
    - what is the structure's actual mass, stiffness, strength, damping, foundation condition, etc ?
  • Modeling
    - have we accurately modeled the structure?
  • Structural Analysis Method
    - which methods do we use - elastic or inelastic, dynamic or static?
    - can our chosen methods capture the important behaviors?

Uncertainty in Capacity

In the past, capacity was generally thought of in terms of strength, and the focus was on determining the strength capacity. Now, for seismic-resistant design, the focus is on deformation and energy dissipation capacity. Strength capacity is still widely used, though, because generally, we are able to predict the strength capacity of elements reasonably well, especially those controlled by flexure. Even for flexural strength capacity, however, there are difficulties:

  • Slab contributions due to composite action
  • Connections - panel zone deformations, welds, bar pull-out, etc.
  • Shear - in members, connections, and structural walls
  • Non-compliant or marginally ductile elements such as those in existing structures
  • Nonstructural components - cladding and other architectural features may actually behave like structural elements, or alter the behavior of structural elements

Also, code and similar design equations are often lower bounds on capacity. The lack of consistency in developing theses equations makes it hard to determine the failure mode of a system. Even when more rational relations for determining capacity are used, system behavior is still uncertain because most capacity estimates focus on elements rather than systems. It is often unknown whether the "failure" of one or two elements will lead to the failure of the system.

The way capacity testing is conducted is another source of uncertainty. Tests are often terminated at some arbitrary level. For example, elements may only be proof tested to a preselected drift or ductility. Many elements have not been tested to failure. Also, many intermediate limit states such as spalling, local buckling, or lateral buckling, have not been documented, making limit states design or evaluations difficult.

Another source of uncertainty in capacity is the fact that both strength and deformation capacity are sensitive to loading history (low-cycle fatigue) and rate-of-loading effects on material strength and deformability.

All of these sources of uncertainty in both demand and capacity show that there is a strong need to make structural system response relatively insensitive to the uncertainty in ground motion and structural characteristics.