By Sarah Moein, Gary Gibson and Behrooz Ghahreman-Nejad
Seismic design of embankment dams often requires an assessment of the earthquake induced ground and dam movements. There are multiple cases where earthquakes have resulted in sliding and lateral spreading of embankments, crest settlement, and in some instances liquefaction and embankment failure. Therefore, evaluation of the effects of earthquakes on embankment dams is of paramount importance for the design.
A site-specific Seismic Hazard Analysis (SHA) is generally the first step to estimate the potential earthquake loads. The results are often presented in the form of site response spectra (conditional mean or uniform hazard), earthquake time histories, and/or plots of peak ground acceleration (PGA) for "Rock Outcrop" as schematically shown below.
The motions at the base and crest of the soil/tailings deposit or embankment profile are referred to as Bedrock and Surface Motions, respectively. For liquefaction, stability and deformation analyses of embankment dams, the Rock Bedrock Motions are to be further processed to develop those within or at the top of the structure.
Considerations of time history analysis
A Uniform Hazard Response Spectrum (UHRS or UHS) or Conditional Mean Spectrum (CMS) is usually developed from the site-specific SHA. ANCOLD Earthquake Guidelines (2019) consider the use of UHS to be conservative and recommend the use of CMS for design purposes. The CMS is developed around a target frequency (or period) considered to be the natural frequency (or period) of the proposed dam structure which is not necessarily constant for tailings and water retaining embankment dams because:
- The natural frequency of an embankment is a function of its height and shear wave velocity of embankment fill materials
- The height and natural frequency of tailings dams vary over time as they are constructed in stages over the life of mine
- Depth of embankment fill and tailings vary due to elevation differences at the foundation level (i.e. if constructed over valleys or sloping grounds)
- Shear wave velocity of the tailings and embankment fill increases with increase in confining stresses (i.e. depth)
- Softening and reduction in shear wave velocity of tailings and embankment fill materials may occur during earthquake loading
Consequently, the natural frequency/period of an embankment dam and in particular a tailings dam is considered to vary and cannot be adequately calculated for derivation of the CMS. ATC Williams believes that the use of UHS, although considered conservative by ANCOLD, provides a better basis for seismic design of structures like tailings dams as shown below.
Time history analysis is the next step to produce design ground motions based on the site UHS or CMS.
The reliability of local site effects can be checked by comparing local records of surface motion compared with bedrock motion recorded either at a nearby rock outcrop or in a deep borehole. High-frequency site response is usually dominated by attenuation and is investigated using small local earthquakes. Medium frequencies are dominated by site resonance and quantified using regional moderate earthquakes. Low frequency effects can be investigated using the body and surface waves from large distant earthquakes.
Main methods in obtaining time history analysis
Time history records (seismograms) are not generally available for project sites due to the limited spread of seismographs. Time history records from other sites with comparable geology and tectonic characteristics are often matched or scaled to the project site design UHS or CMS in a process referred to as time history analysis.
- Spectral Matching: This method uses a non-uniform scaling of an actual or artificial ground motion to closely fit to a target spectrum.
- Spectral or Amplitude Scaling: In this approach, recorded motion is simply scaled up or down uniformly (i.e. by a single scaling factor) to match the target spectrum within a period range of interest at or around the structure natural period, without changing the frequency content or phase spectrum of the original earthquake.
The principal advantage of spectral matching is that fewer ground motions, compared to amplitude scaling, can be used to arrive at an acceptable estimate of the site mean response. Although by closely matching to the site design response spectrum, some characteristics of the original earthquake motion will be lost.
The main advantage of spectral scaling is that the epistemic variation of the original earthquake motion is considered. Nonetheless, the scaled earthquake only matches the site response spectrum at one or a limited number of frequencies, as illustrated below.
The appropriate method should be selected considering the site conditions and availability of suitable earthquake records. The use of records from other sites should be carefully considered to include amplitudes and spectra characteristic of the project site.
ATC Williams has extensive experience in the design of tailings storage facilities and embankment dams for earthquakes, supported by our team of experts in the fields of seismology and geotechnical earthquake engineering.