Abstract：It is focused on the anti-sliding stability problem for multi-slide surfaces of dam foundation. Firstly，a new method called equal safety factor is presented for multi-slide surfaces or double-slide surfaces mode， which is obtained by modifying the wedge method. Subsequently，the reliability research is conducted by using the limited equation composed of safety factor；and the effects of the cross-correlation among strength parameters frictional coefficient f，cohesion c on the stability index are analyzed through calculations of several typical sections of gravity dam foundation. Finally，the safety check formula of ，its permitted index and the corresponding partial coefficients are proposed. The results indicate that the cross-correlation of strength parameters f and c affect the reliability index remarkably. The reliability index b increases nonlinearly with correlation coefficient when the two parameters change from independent to negative correlated ones；and the largest increment is 48.7%. The parameters f，c are usually treated as independent ones for traditional method，which results in reliable calculation result. A suit of corresponding partial coefficients is also proposed for the design check formula of . The recommended values of structure coefficient are classified to three grades with 1.2，1.1 and 1.0 for concrete dams of grade-I，grade-II and grade-III，respectively. Compared with the traditional wedge method，the new method is stricter for bad foundation and high dams，but looser for good foundation and low dams. Using the approach of equal safety factor for design of dam foundation，the safety degree is equivalent or even more reliable to the traditional method；moreover，the distribution of reliability is more reasonable.
