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E2445 Soil mechanics IV CIVL4320 Advanced soil mechanics Assignment – Mohr’s Circle © Dr Robert Day, The University of Queensland, 2018 1 CIVL4230 Advanced soil mechanics Assignment – Mohr’s Circle Purpose: To familiarize students with the use of Mohr’s circle of stress and strain. Due: refer to the course profile. 1. Given the stress state illustrated in figure 1, use a Mohr’s circle to find: (a) The magnitude of the principal stresses (b) The direction of the principal stresses (c) The stresses on the horizontal plane H-H. Repeat (a), (b) and (c) using the equations for stress at a point. Figure 1 Figure 2 2. For a strip load (figure 2) on an elastic solid the stress increments at P are: )2(cossin q x )2(cossin q y )2(sinsin q xy Obtain the expression for the principal stress and their directions of the stress increment. Comment on the direction of the major principal stress. 3. A uniform strip load of 200 kPa and width 10 m is applied to the surface of the ground. The bulk unit weight of the soil is 19 kN/m3 and is uniform with depth. A hydrostatic water table is at depth of 2.0 m below the surface. The initial in situ value of K0 (= ?? ′ ?? ′⁄ ) is uniform with depth and equal to 1.5. Consider a point 5 m beneath the edge of the load. Using the above expressions (Question 2) find: (a) The magnitude and direction of max shear stress for the applied (total) stress increment due to the applied stress. Assume full drainage so that ’ = (b) The magnitude and direction of the final maximum shear stress. (Work in terms of effective stress. Draw the Mohr circle for effective stress). Direction of +ve shear stress 40 kPa 30º 20 kPa H H = 10 kPa q 2a x y P CIVL4320 Advanced soil mechanics Assignment – Mohr’s Circle © Dr Robert Day, The University of Queensland, 2018 2 (c) The angle of maximum stress obliquity (') and the directions of the planes of maximum stress obliquity for the final stress state. 4. A test in a simple shear box is carried out on a sample of sand. The box is 80 mm square and after placing the sample is 30 mm thick. (a) During loading under an effective normal stress ’v the sample compresses by 5 mm. Calculate the magnitude and direction of the principal direct strain increments and maximum shear strain increment during 1 x D compression. (b) Keeping this vertical stress (’v) applied, the sample is now subjected to a horizontal shear stress, , (at constant vertical stress). During this process the top surface of the sample moves horizontally by 4.5 mm and upwards by 2.5 mm. Assuming the strain is homogeneous (the same everywhere) throughout the shear box, calculate the magnitude and directions of: (i) the principal strain increments, 1 and 3 (ii) the maximum shear strain increment, max (iii) the angle of dilation, (iv) the orientation of the lines of zero extension (c) Assuming that the lines of zero extension are planes of maximum stress obliquity (failure), derive a Mohr circle of stress and determine the directions of the principal stress. Assessment criteria Assessment is based on the following criteria. Criteria Unsatisfactory / Poor 0 – 50% Sound 50% - 75% Good / Excellent 75% - 100% Process and Understanding Intention unclear. Difficult to understand. Lack of understanding of problem and theory. Calculation methods generally correct. Poorly demonstrated and difficult to follow. Well presented and correct. Clearly set out. Easy to follow. Demonstrates understanding of problem and theory. Accuracy No solution to some problems Few solutions correct within normal engineering accuracy. Solutions to most or all calculations correct within normal engineering accuracy. +ve shear stress 'v 2.5 mm 4.5 mm