Civil Engineering Gate 2013 Questions with Answer

Ques 27 GATE 2013

The soil profile above the rock surface for a 25° infinite slope is shown in the figure, where \(s_u\) is the undrained shear strength and \(\gamma_t\) is total unit weight. The slip will occur at a depth of

Ques 28 GATE 2013

Two different soil types (Soil 1 and Soil 2) are used as backfill behind a retaining wall as shown in the figure, where \(\gamma_t\) is total unit weight, and c' and φ' are effective cohesion and effective angle of shearing resistance. The resultant active earth force per unit length (in kN/m) acting on the wall is:

Ques 29 GATE 2013

A multistory building with a basement is to be constructed. The top 4 m consists of loose silt, below which a dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in the figure. For dense sand, saturated unit weight = 20 kN/m³, and bearing capacity factors \(N_q\) = 40 and \(N_{\gamma}\) = 45. For loose silt, saturated unit weight = 18 kN/m³, \(N_q\) = 15 and \(N_{\gamma}\) = 20. Effective cohesion c' is zero for both soils. Unit weight of water is 10 kN/m³. Neglect shape factor and depth factor. Using a factor of safety = 3, the net safe bearing capacity (in kN/m²) of the foundation is:

Ques 30 GATE 2013

A multistory building with a basement is to be constructed. The top 4 m consists of loose silt, below which a dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of 6 m width which will rest on the top of a dense sand as shown in the figure. For dense sand, saturated unit weight = 20 kN/m³, and bearing capacity factors \(N_q\) = 40 and \(N_{\gamma}\) = 45. For loose silt, saturated unit weight = 18 kN/m³, \(N_q\) = 15 and \(N_{\gamma}\) = 20. Effective cohesion c' is zero for both soils. Unit weight of water is 10 kN/m³. Neglect shape factor and depth factor. The foundation slab is subjected to vertical downward stresses equal to net safe bearing capacity derived in the above question. Using influence factor \(I_f\) = 2.0 and neglecting embedment depth and rigidity corrections, the immediate settlement of the dense sand layer will be:

Ques 31 GATE 2013

A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:

Ques 32 GATE 2013

An isohyet is a line joining points of

Ques 33 GATE 2013

Laplace equation for water flow in soils is given below. \(\frac{\partial^{2}H}{\partial x^{2}}+\frac{\partial^{2}H}{\partial y^{2}}+\frac{\partial^{2}H}{\partial z^{2}}=0\) Head H does not vary in y and z directions. Boundary conditions are: at x = 0, H = 5; and \(\frac{dH}{dx}\) = -1. What is the value of H at x = 1.2?

Ques 34 GATE 2013

At a station, Storm I of 5-hour duration with intensity 2 cm/h resulted in a runoff of 4 cm and Storm II of 8-hour duration resulted in a runoff of 8.4 cm. Assume that the φ-index is the same for both the storms. The φ-index (in cm/h) is:

Ques 35 GATE 2013

At a station, Storm I of 5-hour duration with intensity 2 cm/h resulted in a runoff of 4 cm and Storm II of 8-hour duration resulted in a runoff of 8.4 cm. Assume that the φ-index is the same for both the storms. The intensity of storm II (in cm/h) is:

Ques 36 GATE 2013

The transplantation of rice requires 10 days and total depth of water required during transplantation is 48 cm. During transplantation, there is an effective rainfall (useful for irrigation) of 8 cm. The duty of irrigation water (in hectares/cumec) is:

Ques 37 GATE 2013

There is no value of x that can simultaneously satisfy both the given equations. Therefore, find the least squares error solution to the two equations, i.e., find the value of x that minimizes the sum of squares of the errors in the two equations. 2x=3 4x=1

Ques 38 GATE 2013

What is the minimum number of multiplications involved in computing the matrix product PQR? Matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and 1 column.

Ques 39 GATE 2013

Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson's 1/3 Rule. Take the step length as 1.  \(\int_{0}^{4}(x^{4}+10)dx\)