When spread footings are used for bridges, they are to bear on bedrock a minimum of 1 foot below the recommended rock scour depth. Footings are to be initially sized so that the breadth (and length if applicable) is equal to or greater than the eccentricity divided by 0.45. Consequently, the eccentricity needs to be known during the Log, Tip, and Type meeting, when spread footings are indicated by site conditions. Once the footing has been initially sized, bedrock strength parameters and bearing resistance should be calculated based on the Rock Mass Rating (RMR) system as follows:
- The RMR should be in accordance with LRFD Bridge Design Specifications, 2012, and not later editions.
- If the RMR is less than 50, the general bearing resistance equation (LRFD Equation 10.6.3.1.2a-1) should be used.
- If the RMR is greater than or equal to 50, the bearing resistance should be calculated using the lower bound equation specified in the LRFD Specifications (LRFD Equation 10.8.3.5.4c-2).
- The geotechnical engineer has the latitude to use either equation for a site when the RMR values are varying by as much as 3 RMR points above or below 50.
When using the general equation, the rock strength parameters should be estimated using the Bieniawski, 1989, correlations as follows:
- c = 0.104 x RMR (ksf)
- φ = 5 + RMR/2
When using the general equation, the correction factors for groundwater are to be taken as 1 since the bedrock RMR is discounted for water, and the buoyant weight of rock should be used for footings that can be submerged. The unit weight of the soil is usually neglected since it can be scoured away. No discount to the RMR for joint orientation should be made from Table 10.4.6.4-2 of LRFD. When bedrock is dipping between 20° and 80°, the resistance factor should be reduced by 0.50 (Φ = 0.225) to account for loss of bearing on inclined bedding.
The “m” and “s” parameters used in the lower bound equation should be determined from LRFD Table 10.4.6.4-4 of the 2012 edition, by interpolation.
A resistance factor of 0.45 should be used to determine the factored bearing resistance when using either of the above equations.
Once the factored bearing resistance is estimated, the engineer must compare it to the factored bearing pressure. As required in LRFD, the stress distribution on rock is triangular or trapezoidal for eccentrically loaded footings. Consequently, the maximum bearing pressure at the toe of the footing needs to be estimated using the following equation:
- σvmax = ΣV/B(1+6e/B) (LRFD Equation 184.108.40.206-2 on a 1-foot strip basis)
Bearing resistance calculations should be included in the geotechnical report.
Base sliding is not normally considered since our footings are recessed a minimum of 1 foot into bedrock and the concrete is poured against the rock. However, should the bedrock dip greater than 20°, the geotechnical engineer must consider whether the bedding orientation is favorable or unfavorable relative to the outside slope; if the orientation is unfavorable, then a base sliding check must be performed in the strength limit state using the friction angle of the bedding plane.
Settlement of bedrock due to elastic compression is usually negligible for the typical loadings and moduli encountered for our bridges, except for large bridges supported on weak rock. Where tall piers can be eccentrically loaded, tilt can be significant even for a small amount of differential elastic settlement in the bedrock. The max/min bearing stress and bedrock settlement procedures presented in LRFD are to be used in the service limit state when calculating tilt. The geotechnical engineer should note in his report whether a bedrock settlement check is required or is negligible.