Question

The vertical stress at the toe was found to be 3.44 MPa at the base of the gravity dam section. If the downstream face of the dam has a slope of 0.617 horizontal: 1 vertical, the maximum principal stress at the toe of the dam when there is no tailwater is _______________

(a) 1.7 MPa

(b) 2.4 MPa

(c) 3.6 MPa

(d) 4.8 MPa

I got this question during an internship interview.

The above asked question is from Design of Gravity Dams topic in portion Gravity Dam Design and Construction of Irrigation Engineering

Answer 1

The correct option is (d) 4.8 MPa

The explanation: The principal stress at the toe is given by Pat toe = Pv. secΦ^2 (without considering the tailwater) where Pv = 3.44 MPa and tan Φ = 0.617/1 i.e.Φ  = 31.67°

Pat toe = 3.44 x sec(31.67°)^2 = 4.74 MPa.