Attention: ● The exam consists of four questions. ● ● Use of non-programmable calculators are permitted. However, programmable calculators and calculator functions of mobile phones are prohibited. Wherever necessary, specify the units in your answers. [In-class participants] ● Four answer sheets are provided. Write down your name and ID number on every answer sheet. Use one answer sheet per question and answer them in sequence, starting from [Question 1]. If the front page of an answer sheet is insufficient to complete your answer, use the back page of the same answer sheet after clearly indicating your intent. [Online participants] ● ● You must keep your camera ON throughout Zoom connection during the exam. You must finish writing at 15:15 and complete submitting the answer sheets via PandA by 15:30. Your submission will not be accepted after the deadline regardless of any reason. Give yourself ample time to get through PandA for submitting the answer sheets. . ● You may answer a major question over multiple answer sheets but do not answer multiple major questions on the same answer sheet. You must indicate your name and student ID on all the sheets. Any suspicious behavior through camera will result in failed credit of the course and serious penalties. [Question 1] (1) Provide concise explanations of the following terms. Graphics and equations may be used if necessary. 2) Degree of saturation 4) Maximum dry density l) Liquidity index 3) Soil particle density (2) Answer the following questions regarding soil compaction. 1) Compaction energy, Ec, is defined as:
E c : Compaction energy (kJ/m³), W R : Weight of rammer (hammer) (kN), N L : Number of layers, V : Volume of mold (m 3 ), H : Drop height of rammer (hammer) (m), N B : Number of blows per layer When the compaction tests are performed by the following three methods using a single well-graded soil sample, draw the positional relationships of the compaction curves generally obtained by each of the methods A to C. In addition, draw the zero-air-void curve in the same figure. Showing the outline and positional relationship of each curve is enough.
2) Soil with a maximum dry density of ρdmax (Mg/m³) was adjusted to its optimum water content w opt (%), and then compacted with a compaction degree D t (%) to build an embankment. Express the dry density ρ a and the wet density ρ t of the embankment using mathematical symbols. 3) Define the effective stress, σ ′ , at t the bottom of the sand layer using mathematical symbols for the ground conditions given in Figure 1. In addition, find the effective stress, σ2', at the bottom of the sand layer when the groundwater level rises to the ground surface due to rainfall. Then, derive the magnitude relationship of the effective stress σ ' and σ 2 '. Here, the wet unit weight γ (kN/m 3 ) and the saturated unit weight γ sa (kN/m 3 ) of each layer are shown in the figure, and the unit weight of water is γ , (kN/m³). Assume that the structure of the ground does not change due to fluctuations in the groundwater level.
[Question 2]
The constant head permeability test of a sand column as s hown in the Figure 2 was carried out. The measurement was performed 3 times for 10 seconds, and the average discharge was 2.30 [cm³]. Answer the following questions regarding the water flow in a saturated sand column. The cross-sectional area of the sand column is 1.00×10 [cm²], the specific gravity of soil particle, G s , is 2.70, the void ratio, e , is 0.60, the density of the fluid (water), ρ w , is 1.00 × 10 3 [kg/m 3], respectively. Assume that the sand column is s saturated, the water flow is governed by Darcy’s law, and the steady-state condition is established for all cases below. Friction loss and shape los in pipes can be ignored, the reference plane is shown in the figure, and the gravitational acceleration is 9.81 [m/s 2 ]. (1) Draw the potential head (elevation head) above the reference plane, the pressure head and the hydraulic head (total head or piezometric head) of the sand layer, respectively. In addition, write the values of each head at both top and bottom surfaces of the sand layer. (2) Determine both hydraulic gradient and hydraulic conductivity (coefficient of permeability) of the sand layer. (3) Determine the unit weight of the saturated sand and the vertical effective stress at the bottom surface of the sand layer. (4) The drainage port of the upstream tank located 10 cm above the reference plane is closed and the water level is gradually raised. Determine the water level above the reference plane when the sand layer becomes quicksand.
[Question 3]
An incremental loading one-dimensional consolidation test is conducted on the saturated clay sample obtained at the center (depth of 10m from the ground surface) of a half-space ground shown in Figure 3. The test is also known as "oedometer test" with a specimen of 6 cm in diameter and 2 cm thick. The loading starts from 10 kN/m² and is then carried out on a 24 hour cycle with the incremental ratio Δρ n+1/p n = 1 (Δρ n+1 : stress increment at the n+1 loading step, p n : stress at the n loading step). Answer the following questions. (1) Assuming that the clay is normally consolidated, find the consolidation yield stress p c. (2)   When the consolidation is completed with the stress at the 5th loading step ps = 160 kN/m² (10 → 20 → 40 → 80 → 160), the height of the specimen is found to be H 5 = 1.821 cm. Then, after the next (6th) loading step of Δρ 6 = 160 kN/m², the settlement ΔH 6 = 0.161 cm is observed for the 6th loading p 6 = 320 kN/m². Calculate the average height of the specimen  H 6  (the arithmetic mean of the heights before and after the 6th loading step) by using H s and H 6 and find the volumetric (vertical) strain, εν generated by the 6th loading step of Δρ 6 = 160 kN/m² with the reference of the average height of the specimen H 6 . When the void ratio, es = 2.50 is obtained at t the end of consolidation after the 5th stage loading stress of ps = (3) 160 kN/m², find the void ratio, e 6 at t the end of consolidation after the 6th stage loading stress of p 6 = 320 kN/m². Find the coefficient of volume change, m v for the 6th stage loading stress of ρ 6 = 320 kN/m² ( Δρ = 160 kN/m²). (4) Assuming the assumption noted in (1) is held, calculated the compression index, Cc. (5) From the state shown in the figure, the groundwater level was lowered by 2 m to the upper surface of the clay (6) layer. Calculate the final settlement that occurs in the clay layer due to groundwater lowering. The consolidation of the clay layer shall occur one-dimensionally, and the representative stress of the clay layer shall be the one at the central depth (sampling point). (Hint: It is necessary to find the void ratio e 0 in the center of the clay in the initial state. From question (1), the clay layer is assumed to be normally consolidated, and Cc is found in (5). By using e s at p s = 160 kN/m 2 indicated in (3), the initial void ratio e 0 can be obtained.) Y, = 19.0 kN/m³,
Yw = 9.8 kN/m³ Ysat = 16.8 kN/m³
[Question 4]
(1) Answer the appropriate words in the blanks provided below. In the direct shear test tests, Coulomb's failure criterion can be obtained from the relationship between the various normal stresses and the stress at failure under those normal stresses. (D The uniaxial compression test is mainly used for clays to obtain the unconfined compressive strength of the clay. The ratio of the compressive strength of a naturally deposited sample to that of a remolded sample is ③ called theのつ気It is known that the higher the index of the clay, the greater the (4) The triaxial compression test is carried out in the stress is zero. The stress state where the O stress states at failure in tests carried out under various confining pressures are illustrated by Mohr's circles,ののand Mohr's failure criterion is obtained from the of these circles. The Mohr-Coulomb failure criterion is (6) of Mohr's failure criterion.のThe change in volume due to shear is called . In general, dense sands and overconsolidated clays (9 pore pressures in consolidation undrained triaxial in volume due to shear and produce (8) compression tests. (2) Stress state at a certain point in soil is as shown in Figure 4. 1) Find the values of the maximum and minimum principal stress, and their directions of the principal plane. 2)   Find the stress acting on the A-A plane. Figure 4 (3) Consolidated-undrained ( CU ) triaxial compression test of a normally consolidated clay in saturated condition under the confining pressure σ3 = 300 kN/m² was undertaken. Answer the following questions if the axial stress σ ৷ and pore water pressure uw measured at failure were σ ৷ = 500 kN/m² and uw = 180 kN/m². 1) Draw the Mohr's stress circles for total stress and effective stress at failure. 2) By assuming that the Mohr-Coulomb failure criterion is s satisfied, determine the internal friction angle φ ' based on the effective stress of this clay. Note that cohesion c' = 0 kN/m² can be regarded for normally consolidated clays. 3) Find the orientation of the failure plane. 4) If consolidated-drained (CD) triaxial compression test was carried out using the same clay, find the value of the axial stress σ1 at failure.