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Question 1
ప్రశ్న 1
Under an idealized settlement analysis for a saturated clay deposit subjected to a foundation load, which sequence correctly identifies immediate compression, primary consolidation and secondary compression?
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Explanation:
Settlement is commonly idealized as immediate, primary consolidation and secondary compression components. Immediate compression is the component occurring promptly after loading without awaiting substantial drainage. Primary consolidation represents time-dependent compression associated with dissipation of excess pore-water pressure. Secondary compression represents additional time-dependent deformation of the soil skeleton and is usually considered after the end of primary consolidation. In real deposits these mechanisms may overlap, but the stated sequence is the conventional classification used for settlement analysis.
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Question 2
ప్రశ్న 2
Which physical mechanism is primarily responsible for the gradual decrease in thickness of a saturated, low-permeability clay layer during primary one-dimensional consolidation?
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Explanation:
A sudden applied load generates excess pore-water pressure when a saturated low-permeability clay cannot drain immediately. As drainage proceeds, the excess pore pressure dissipates. Under approximately constant total stress, effective stress increases as pore pressure falls. This increase causes particle rearrangement and a decrease in void ratio and layer thickness. The resulting time-dependent settlement is identified as primary consolidation.
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Question 3
ప్రశ్న 3
Which set of assumptions is most consistent with classical Terzaghi one-dimensional consolidation theory?
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Explanation:
Classical one-dimensional consolidation considers a saturated soil layer subjected to vertical deformation. The lateral strain is restrained in the idealization, and pore-water flow is taken as vertical. Darcy law describes the seepage process under the prescribed assumptions. Soil compressibility and permeability are commonly treated as constant over the stress increment for the linear theory. Actual deposits may violate these assumptions, so predictions must be interpreted with engineering judgment.
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Question 4
ప్రశ్న 4
At a point in a saturated soil deposit, the total vertical stress is 180 kPa and the pore-water pressure is 65 kPa. What is the vertical effective stress at that point?
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Explanation:
The effective-stress principle gives vertical effective stress as total vertical stress minus pore-water pressure. The total stress is 180 kPa. The pore-water pressure is 65 kPa. Subtraction gives 180 - 65 = 115 kPa. It is the effective stress, rather than total stress alone, that controls compression of the soil skeleton.
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Question 5
ప్రశ్న 5
An ideal fully saturated clay specimen is loaded rapidly under undrained one-dimensional conditions by an additional total vertical stress of 60 kPa. Neglecting the instantaneous compression of water and soil solids, what is the initial increment in excess pore-water pressure?
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Explanation:
Under the stated idealization, no significant drainage occurs at the instant of rapid loading. The specimen is fully saturated and the pore water and solids are taken as incompressible for the initial response. Accordingly the added total stress is initially carried as an equal increase in excess pore-water pressure. The initial excess pore-pressure increment is therefore 60 kPa. With subsequent drainage, this excess pressure decreases while the effective-stress increment increases.
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Question 6
ప్రశ్న 6
After a sustained load increment has been applied to a saturated clay layer, the excess pore-water pressure at a point decreases from 50 kPa to 18 kPa while total vertical stress remains unchanged. By how much does vertical effective stress increase at that point?
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Explanation:
Effective stress equals total stress minus pore-water pressure. The total vertical stress is stated to remain constant. Hence the effective-stress increase equals the decrease in excess pore-water pressure. The pore-pressure reduction is 50 - 18 = 32 kPa. The effective-stress increase is consequently 32 kPa.
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Question 7
ప్రశ్న 7
A homogeneous saturated clay layer has the same thickness and coefficient of consolidation in two otherwise identical cases. Case I permits drainage from one face only, whereas Case II permits drainage from both faces. What is the approximate ratio of times t(II)/t(I) required to reach the same average degree of primary consolidation?
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Explanation:
Time to achieve a specified average degree of consolidation is proportional to the square of the longest drainage path. For single drainage, the drainage path is the full layer thickness H. For double drainage, the longest path becomes H/2. Therefore the time ratio is (H/2)^2/H^2 = 1/4. Double drainage consequently permits the same degree of primary consolidation in approximately one-quarter of the time. This comparison assumes the same soil properties and loading conditions in both cases.
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Question 8
ప్రశ్న 8
Which statement correctly distinguishes normally consolidated (NC) and overconsolidated (OC) soils using their one-dimensional effective-stress histories?
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Explanation:
Normal consolidation means the present vertical effective stress is the maximum that the soil has experienced in its stress history. For a normally consolidated soil, the overconsolidation ratio is approximately one. An overconsolidated soil has experienced a higher past vertical effective stress than the current value. This past maximum is represented by the preconsolidation pressure. Soil stress history affects the compressibility path followed during subsequent loading.
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Question 9
ప్రశ్న 9
A clay layer has a present vertical effective overburden stress of 120 kPa and a preconsolidation pressure of 300 kPa. What is its overconsolidation ratio (OCR)?
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Explanation:
The overconsolidation ratio is the preconsolidation pressure divided by the present vertical effective stress. The preconsolidation pressure is 300 kPa. The present vertical effective stress is 120 kPa. Hence OCR = 300/120 = 2.50. Since OCR exceeds unity, the soil is overconsolidated under this conventional stress-history definition.
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Question 10
ప్రశ్న 10
An overconsolidated clay has initial vertical effective stress 120 kPa and preconsolidation pressure 240 kPa. A new sustained load ultimately increases vertical effective stress to 180 kPa. Which compression path is most appropriate for an idealized settlement estimate?
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Explanation:
The initial effective stress of 120 kPa is below the preconsolidation pressure of 240 kPa. The final effective stress of 180 kPa also remains below 240 kPa. The stress increment therefore lies on the recompression or reloading portion in the idealized e-log stress representation. Its slope is described by the recompression index, commonly smaller than the virgin compression index. Settlement can occur along this recompression branch even though virgin compression has not been reached.
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Question 11
ప్రశ్న 11
In a plot of void ratio e against log10 vertical effective stress obtained from an oedometer test, what does preconsolidation pressure represent?
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Explanation:
The e-log effective-stress curve reflects the loading and stress history of the soil. Overconsolidated material commonly displays a relatively gentle recompression portion before yielding into a steeper virgin compression branch. The transition helps in estimating the preconsolidation pressure. This pressure represents the maximum past vertical effective stress in the idealized stress-history framework. In practice its interpretation can be affected by sample disturbance, soil structure and curve-fitting method.
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Question 12
ప్రశ్న 12
On the virgin compression portion of an oedometer e-log10 effective-stress plot, void ratio decreases from 0.96 at 100 kPa to 0.72 at 1000 kPa. What is the compression index Cc?
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Explanation:
Compression index is the magnitude of the slope of the virgin compression line on an e-log10 effective-stress plot. It is calculated as Cc = (e1 - e2)/log10(sigma2/sigma1). The change in void ratio is 0.96 - 0.72 = 0.24. The stress ratio is 1000/100 = 10, whose base-10 logarithm is one. Therefore Cc = 0.24, which is dimensionless.
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Question 13
ప్రశ్న 13
A normally consolidated clay layer is 4 m thick with initial void ratio 1.00 and compression index Cc = 0.30. Its vertical effective stress increases from 100 to 200 kPa uniformly through the layer. Using log10(2) = 0.3010, what is its approximate primary consolidation settlement?
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Explanation:
For a normally consolidated layer, primary settlement is S = H Cc/(1 + e0) log10(sigmaf/sigma0). The supplied parameters are H = 4 m, Cc = 0.30 and e0 = 1.00. The effective-stress ratio is 200/100 = 2. Hence S = 4 × 0.30/2 × 0.3010 = 0.1806 m. The approximate settlement is 0.181 m under the stated uniform-stress assumption.
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Question 14
ప్రశ్న 14
Which comparison of the recompression or swelling index Cr with the virgin compression index Cc is generally correct for an ordinary overconsolidated clay?
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Explanation:
The virgin compression index Cc describes the reduction in void ratio per log cycle of effective stress on the normally consolidated branch. The recompression or swelling index Cr is associated with unloading or reloading behaviour below the preconsolidation pressure. For many clays the magnitude of this slope is appreciably smaller than Cc. Thus an overconsolidated clay can show relatively modest compression when reloaded below its previous maximum stress. Both indices are dimensionless in the conventional e-log10 effective-stress representation.
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Question 15
ప్రశ్న 15
An overconsolidated clay layer has thickness 5 m, initial void ratio 1.00, recompression index Cr = 0.04 and preconsolidation pressure 250 kPa. Its effective stress increases from 100 to 200 kPa. With log10(2) = 0.3010, what is the approximate primary settlement?
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Explanation:
The final effective stress of 200 kPa is below the preconsolidation pressure of 250 kPa. Therefore the entire stated stress increment is treated as recompression. The primary settlement is S = H Cr/(1 + e0) log10(200/100). Substitution gives S = 5 × 0.04/2 × 0.3010 = 0.0301 m. This is approximately 30.1 mm.
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Question 16
ప్రశ్న 16
An overconsolidated clay layer is 3 m thick with initial void ratio 1.00, Cr = 0.05 and Cc = 0.25. Vertical effective stress rises from 100 to 400 kPa, crossing the preconsolidation pressure of 200 kPa. Take log10(2) = 0.3010 and assume these indices remain applicable. What is the approximate primary settlement?
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Explanation:
The loading increment crosses the preconsolidation pressure and must be split into two branches. Recompression from 100 to 200 kPa uses Cr = 0.05, and virgin compression from 200 to 400 kPa uses Cc = 0.25. The primary settlement is S = H/(1 + e0) [Cr log10(200/100) + Cc log10(400/200)]. Substitution gives S = 3/2 × (0.05 + 0.25) × 0.3010 = 0.13545 m. The approximate settlement is 135 mm when rounded to the nearest millimetre.
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Question 17
ప్రశ్న 17
A laterally restrained clay layer has initial thickness 2.0 m and void ratio 1.00. After a particular loading stage its void ratio is 0.90, and the solids volume and cross-sectional area remain constant. What is the decrease in thickness?
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Explanation:
Void ratio is the void volume divided by the volume of soil solids. Under a constant cross-sectional area and constant solids volume, layer thickness is proportional to 1 + e. The one-dimensional thickness reduction is H0 (e0 - e1)/(1 + e0). Inserting the values gives 2.0 × (1.00 - 0.90)/2.00 = 0.10 m. The layer thickness therefore decreases by 0.10 m.
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Question 18
ప్రశ్న 18
In an incremental consolidation test, void ratio decreases from 0.90 to 0.84 when vertical effective stress increases from 100 to 200 kPa. What is the average coefficient of compressibility av over that increment?
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Explanation:
The average coefficient of compressibility is the decrease in void ratio divided by the increase in vertical effective stress. The void-ratio reduction is 0.90 - 0.84 = 0.06. The effective-stress increase is 200 - 100 = 100 kPa. Thus av = 0.06/100 = 0.0006 kPa^-1. Its units are the reciprocal of the stress units, unlike the dimensionless compression index.
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Question 19
ప్రశ్న 19
For a specified small stress increment, the coefficient of compressibility is av = 0.0008 kPa^-1 and the initial void ratio is e0 = 1.00. What is the approximate coefficient of volume compressibility mv for that increment?
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Explanation:
For a small one-dimensional stress increment, the coefficient of volume compressibility is mv = av/(1 + e0). The coefficient av is given as 0.0008 kPa^-1. The initial void ratio is 1.00, so the denominator is 2.00. Hence mv = 0.0008/2.00 = 0.0004 kPa^-1. This parameter links a small increase in effective stress to the corresponding volumetric strain.
వివరణ:
Question 20
ప్రశ్న 20
A saturated clay layer is 3.0 m thick and its representative coefficient of volume compressibility is 4.0 × 10^-4 kPa^-1. If the effective-stress increment is 50 kPa throughout the layer and linear one-dimensional compression is assumed, what is the approximate primary settlement?
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Explanation:
Under the stated linear approximation, primary consolidation settlement is S = mv DeltaSigma H. The coefficient of volume compressibility is 4.0 × 10^-4 kPa^-1. The effective-stress increment is 50 kPa, giving a one-dimensional strain of 0.020. Multiplication by the 3.0 m thickness yields S = 0.020 × 3.0 = 0.060 m. This equals 60 mm of settlement.
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Question 21
ప్రశ్న 21
Which statement correctly identifies the physical significance of the coefficient of consolidation cv?
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Explanation:
The coefficient of consolidation cv controls how rapidly excess pore-water pressure dissipates in the idealized one-dimensional problem. It is related to vertical permeability and volume compressibility by cv = k/(mv gammaw) when consistent units are used. Its dimensions are L^2/T, usually reported as m^2/s or m^2/year. A larger cv generally signifies a faster consolidation response for the same drainage path. The final settlement magnitude must be evaluated separately using the relevant compressibility and loading parameters.
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Question 22
ప్రశ్న 22
A soil has vertical permeability k = 9.81 × 10^-10 m/s and coefficient of volume compressibility mv = 5.0 × 10^-4 kPa^-1. If the unit weight of water is 9.81 kN/m³, what is cv = k/(mv gammaw)?
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Explanation:
The coefficient of consolidation is obtained from cv = k/(mv gammaw). Here mv gammaw = (5.0 × 10^-4 kPa^-1)(9.81 kN/m³), which equals 0.004905 m^-1 because 1 kPa equals 1 kN/m². Dividing 9.81 × 10^-10 m/s by 0.004905 m^-1 gives 2.0 × 10^-7 m²/s. The pressure and unit-weight units are consistent in this substitution. Thus the correct consolidation coefficient is 2.0 × 10^-7 m²/s.
వివరణ:
Question 23
ప్రశ్న 23
In a conventional laboratory oedometer test used to evaluate one-dimensional consolidation properties, which combination of measurements and boundary conditions is most appropriate?
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Explanation:
The oedometer test confines a soil specimen laterally within a rigid ring. Vertical loading is applied in increments, and deformation is recorded at selected times. Porous drainage boundaries allow the drainage conditions to be defined during the test. The time-deformation data help evaluate the coefficient of consolidation, while the effective-stress and void-ratio results describe compressibility. In Indian soil testing practice, IS 2720 (Part 15) addresses determination of consolidation properties.
వివరణ:
Question 24
ప్రశ్న 24
A saturated clay layer is 2.0 m thick and drains from both faces. Its coefficient of consolidation is 0.020 m²/day, and the time factor for 50% average consolidation is given as Tv = 0.197. Approximately how much time is required for 50% average primary consolidation?
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Explanation:
The time factor is Tv = cv t/Hdr^2. Double drainage in a 2.0 m layer makes the longest drainage path Hdr = 1.0 m. Rearranging the time-factor equation gives t = Tv Hdr^2/cv. Substituting the supplied values yields t = 0.197 × 1.0^2/0.020 = 9.85 days. This is the approximate time for 50% average primary consolidation under the specified assumptions.
వివరణ:
Question 25
ప్రశ్న 25
During the secondary-compression segment of a constant-load oedometer record, void ratio falls from 0.81 at elapsed time 1 day to 0.78 at 10 days, both measured after the end of primary consolidation. What is the coefficient of secondary compression C_alpha based on log10 time?
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Explanation:
The secondary compression index C_alpha is the magnitude of the slope of void ratio against log10 time during the secondary-compression stage. The supplied decrease in void ratio is 0.81 - 0.78 = 0.03. The time ratio is 10/1 = 10, whose base-10 logarithm equals one. Therefore C_alpha = 0.03/1 = 0.030. The result is dimensionless and describes secondary compression under the stated constant-load test conditions.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. Immediate compression, followed by primary consolidation and then secondary compression. సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: A. Dissipation of excess pore-water pressure through drainage, with increasing effective stress in the soil skeleton. సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: C. Only vertical deformation and drainage in a saturated soil layer, with Darcy flow and idealized constant properties. సమాధానం: C.
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Question 4 ప్రశ్న 4Answer: B. 115 kPa. సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: D. 60 kPa because the initially undrained pore water carries the applied stress increment. సమాధానం: D.
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Question 6 ప్రశ్న 6Answer: C. 32 kPa. సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: A. 1/4. సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: C. NC soil has the greatest past vertical effective stress equal to its present value, whereas OC soil has experienced a greater vertical effective stress in the past. సమాధానం: C.
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Question 9 ప్రశ్న 9Answer: D. 2.50. సమాధానం: D.
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Question 10 ప్రశ్న 10Answer: A. Use the recompression portion of the e-log effective-stress curve because the final stress remains below preconsolidation pressure. సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: B. The estimated maximum past vertical effective stress, often indicated by the transition from recompression to virgin compression behaviour. సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: C. 0.24. సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: B. 0.181 m. సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: D. Cr characterizes the gentler unloading or reloading e-log stress branch and is typically smaller than Cc for virgin compression. సమాధానం: D.
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Question 15 ప్రశ్న 15Answer: A. 30.1 mm. సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: C. 135 mm. సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: B. 0.10 m. సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: D. 0.0006 kPa^-1. సమాధానం: D.
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Question 19 ప్రశ్న 19Answer: C. 0.0004 kPa^-1. సమాధానం: C.
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Question 20 ప్రశ్న 20Answer: A. 0.060 m. సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: B. It is a rate parameter linking permeability and volume compressibility, with dimensions of length squared per time. సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: C. 2.0 × 10^-7 m²/s. సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: D. Lateral strain is restrained, vertical load is applied in increments and specimen deformation is observed with time under defined drainage conditions. సమాధానం: D.
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Question 24 ప్రశ్న 24Answer: C. 9.85 days. సమాధానం: C.
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Question 25 ప్రశ్న 25Answer: B. 0.030. సమాధానం: B.