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Question 1
ప్రశ్న 1
What fundamental seepage concept distinguishes Khosla's theory from Bligh's creep theory?
Explanation:
Khosla rejected the assumption that seepage water simply creeps along the contact between the floor and foundation. He treated seepage through a permeable foundation as a potential-flow problem involving a family of streamlines and equipotential lines. Each seepage particle follows a flow path through the soil rather than the bottom contour of the structure. The resulting pressure distribution depends on the complete geometry of the floor, cutoffs and foundation boundaries. Therefore Option B is correct.
వివరణ:
Question 2
ప్రశ్న 2
For steady two-dimensional seepage through a homogeneous isotropic foundation, which equation forms the mathematical basis of Khosla's theory?
Explanation:
Steady seepage through a homogeneous isotropic porous medium can be represented by a potential function. For incompressible flow satisfying continuity, that potential satisfies Laplace's equation. In two dimensions the equation is ∂²φ/∂x² + ∂²φ/∂y² = 0. Solutions of this equation define the streamline and equipotential pattern beneath the hydraulic structure. Khosla's method is therefore fundamentally different from Bligh's empirical creep-length approach.
వివరణ:
Question 3
ప్రశ్న 3
What did Khosla's analysis show about the loss of seepage head beneath an impervious floor?
Explanation:
Bligh assumed a uniform loss of head proportional to creep length. Khosla's potential-flow analysis showed that the actual pressure and head-loss distribution is nonlinear. The distribution changes when floor length, cutoff depth, cutoff position or foundation boundaries change. A straight hydraulic-gradient line therefore does not accurately represent the actual uplift beneath the floor. Hence Option C is correct.
వివరణ:
Question 4
ప్రశ్న 4
What is the central idea of Khosla's method of independent variables?
Explanation:
A complete barrage foundation containing several piles and floor levels is mathematically complicated. Khosla therefore decomposed the complex profile into a number of simpler standard profiles. Analytical or graphical solutions for these individual profiles provide pressure percentages at selected key points. The effects are then used for the corresponding points of the actual profile with the required corrections. This procedure is the basis of the method of independent variables, so Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which of the following is one of the standard simple profiles used in Khosla's independent-variable method?
Explanation:
Khosla developed standard solutions for simplified floor and cutoff arrangements. One important standard profile consists of a horizontal impervious floor of negligible thickness with a sheet pile at the upstream or downstream end. Other useful profiles include an intermediate sheet pile and a depressed horizontal floor without a cutoff. These standard profiles permit the complicated barrage section to be handled through independent-variable concepts. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
In Khosla's method, pressure percentages are principally determined at which locations?
Explanation:
Khosla's standard profiles identify specific key points at which residual pressure is evaluated. These include points at the junctions of the floor and sheet piles and the bottom or tip of a pile. For a depressed floor, relevant bottom corners also become key points. Pressure percentages obtained at such points are then used in the analysis of the complete profile after appropriate corrections. Therefore Option B is correct.
వివరణ:
Question 7
ప్రశ్న 7
At a particular key point, Khosla analysis gives a residual pressure of 65 percent of the total seepage head. If H = 6.0 m, what are the residual pressure head and corresponding uplift pressure intensity for γw = 9.81 kN/m³?
Explanation:
A pressure percentage of 65 means that the residual pressure head is 0.65 times the total seepage head. Thus the residual head is 0.65 × 6.0 = 3.90 m. The corresponding uplift pressure is γw h = 9.81 × 3.90. This gives approximately 38.26 kPa. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
For a simple horizontal impervious floor without an effective downstream cutoff, what important conclusion follows from Khosla's potential-flow solution near the downstream exit?
Explanation:
Khosla's solution for a simple horizontal floor shows a severe concentration of hydraulic gradient at the downstream exit. In the idealized absence of a downstream cutoff, the theoretical exit gradient becomes infinite. This demonstrates why a downstream pile or cutoff is fundamentally important for piping safety. Simply extending a flat floor does not remove this singular exit condition in the idealized solution. Therefore Option B is correct.
వివరణ:
Question 9
ప్రశ్న 9
Why is the downstream cutoff especially important according to Khosla's theory?
Explanation:
Piping failure is strongly influenced by the local hydraulic gradient where seepage emerges downstream. Khosla's analysis showed that this exit condition cannot be assessed adequately through an average creep gradient alone. A deeper downstream cutoff forces the flow pattern downward and reduces the exit-gradient concentration. Its depth must also remain compatible with the expected scour level around the structure. Therefore Option B is correct.
వివరణ:
Question 10
ప్రశ్న 10
For a simple profile consisting of a floor of length b and a downstream cutoff of depth d, which expression represents Khosla's exit gradient?
Explanation:
Khosla's potential-flow solution provides a specific expression for the exit gradient at a downstream cutoff. It is GE = (H/d) multiplied by 1/(π√λ). The parameter λ depends on α = b/d through λ = [1 + √(1 + α²)]/2. The expression explicitly includes the total seepage head, floor length and downstream cutoff depth. Therefore Option A is correct.
వివరణ:
Question 11
ప్రశ్న 11
A hydraulic structure has H = 6 m, floor length b = 40 m and downstream cutoff depth d = 5 m. Using α = b/d, λ = [1 + √(1 + α²)]/2 and GE = (H/d)/(π√λ), what is the approximate exit gradient?
Explanation:
The ratio α is 40/5 = 8. The corresponding λ is [1 + √65]/2, which is approximately 4.531. Substitution gives GE = (6/5)/[π√4.531]. The resulting value is approximately 0.1794, equivalent to about 1 in 5.57. Therefore Option A is correct.
వివరణ:
Question 12
ప్రశ్న 12
For the structure in the previous numerical example, if the specified permissible exit gradient for the foundation soil is 0.20, what does the Khosla check indicate?
Explanation:
The calculated exit gradient is approximately 0.179. The stipulated permissible value is 0.20. Since 0.179 is smaller than 0.20, the calculated gradient satisfies the stated criterion. This conclusion applies only to the exit-gradient check under the supplied assumptions. Other requirements such as scour depth, structural stability and uplift must still be checked separately.
వివరణ:
Question 13
ప్రశ్న 13
For fixed seepage head and floor length, what is the general effect of increasing the depth of the downstream cutoff in Khosla's formulation?
Explanation:
Cutoff depth appears directly in the Khosla exit-gradient relationship and also alters the parameter b/d. Increasing the downstream pile depth generally forces seepage to travel deeper before emerging. The concentration of hydraulic gradient at the exit is consequently reduced. A downstream cutoff therefore plays a major role in piping safety. Its final depth must nevertheless satisfy both seepage and scour requirements.
వివరణ:
Question 14
ప్రశ్న 14
For a fixed seepage head and downstream cutoff depth, what is the general effect of increasing the impervious floor length in the simple Khosla exit-gradient relation?
Explanation:
Increasing floor length raises the ratio α = b/d when cutoff depth remains fixed. This increases λ in the exit-gradient expression. Because √λ appears in the denominator, the calculated exit gradient tends to decrease. Nevertheless, floor length alone is not a substitute for an effective downstream cutoff because the cutoff controls the local exit condition strongly. Therefore Option A is correct.
వివరణ:
Question 15
ప్రశ్న 15
Which statement most appropriately compares the hydraulic roles of upstream and downstream cutoffs?
Explanation:
Every cutoff alters the potential-flow field and consequently changes pressure distribution beneath the structure. An upstream cutoff therefore has a meaningful effect on uplift and seepage conditions. The downstream cutoff has additional importance because the critical exit-gradient region lies near the downstream end. Khosla's work emphasized that inadequate downstream cutoff depth can lead to undermining or piping. Therefore Option B is correct.
వివరణ:
Question 16
ప్రశ్న 16
Which three corrections are conventionally applied when Khosla's standard-profile pressure percentages are used for an actual barrage or weir profile?
Explanation:
The ideal standard profiles used by Khosla are deliberately simplified. When they are applied to a real structure, neighboring piles can influence one another and require an interference correction. Actual floors also possess finite thickness rather than the negligible thickness assumed in the standard solution. Sloping portions of the floor introduce another geometric correction. Thus pile interference, floor thickness and floor slope are the three standard corrections, making Option B correct.
వివరణ:
Question 17
ప్రశ్న 17
Why is a correction for mutual interference of piles required in Khosla's method?
Explanation:
The independent-variable method initially considers simple profiles separately. In an actual barrage, however, upstream, intermediate and downstream piles coexist within the same seepage field. The pressure effect at one pile is therefore influenced to some degree by neighboring piles. A mutual-interference correction accounts for this departure from perfect independence. The correction improves the application of standard-profile results to the complete foundation geometry.
వివరణ:
Question 18
ప్రశ్న 18
Why is a floor-thickness correction required in Khosla's method?
Explanation:
Khosla's standard profiles idealize the impervious floor as having negligible thickness. The percentage pressures read from the standard solution therefore correspond to idealized junction levels. In a real structure the pile-floor junction occurs at the bottom of a floor having finite thickness. The pressure at the actual junction must consequently be adjusted from the idealized value. This requirement is the basis of the floor-thickness correction.
వివరణ:
Question 19
ప్రశ్న 19
For the conventional Khosla slope correction, what sign is applied to a floor slope when considered in the direction of seepage flow?
Explanation:
Khosla's conventional correction procedure distinguishes between downward and upward slopes along the direction of flow. A downward slope receives a positive correction. An upward or rising slope receives a negative correction. The magnitude depends on the floor slope and the relevant horizontal length relative to the pile spacing. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
A standard-profile calculation gives a pressure of 58 percent at a key point. If the already-evaluated corrections applicable at that point are +3 percent for pile interference, -2 percent for floor thickness and +1 percent for floor slope, what corrected pressure percentage results?
Explanation:
The question supplies the corrections algebraically, so they can be added directly to the basic pressure percentage. The net correction is +3 - 2 + 1 = +2 percentage points. The corrected percentage is therefore 58 + 2 = 60 percent. No additional sign interpretation is required because the signs have already been supplied. Therefore Option C is correct.
వివరణ:
Question 21
ప్రశ్న 21
What important foundation assumption underlies the usual Khosla standard solutions?
Explanation:
The standard Khosla potential-flow solutions are derived assuming a permeable foundation of effectively infinite depth. Real alluvial deposits can instead be underlain by an impervious stratum at a finite depth. If that boundary is sufficiently deep, the infinite-depth approximation can remain satisfactory. If it is shallow, the pressure and flow pattern may differ significantly from the standard solution. A finite-depth seepage model may then be required, so Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
According to Central Water Commission guidance, the infinite-depth approximation used in Khosla theory gives practically comparable results when the depth of the pervious stratum is at least approximately which value?
Explanation:
Khosla's analytical theory assumes an infinitely deep permeable foundation. Central Water Commission training material notes that electrical-analogy studies found practically comparable results when the pervious-stratum depth is about five times the cutoff depth or two and one-half times the length of the barrage, whichever is larger. If this condition is not satisfied, the infinite-depth Khosla solution may give erroneous pressure and seepage results. In such cases, the seepage field should be investigated by an appropriate mathematical or physical model. Therefore Option B is correct.
వివరణ:
Question 23
ప్రశ్న 23
How are Khosla pressure percentages used in assessing the structural requirement of an impervious floor?
Explanation:
The percentage pressure at a point represents the residual seepage pressure head as a fraction of the total head causing flow. That head can be converted into an uplift pressure acting beneath the floor. The floor thickness or reinforced-floor system must be adequate to resist the resulting net uplift under the governing load condition. Corrections for pile interference, floor thickness and slope are therefore important because they affect the estimated uplift. Thus Option A is correct.
వివరణ:
Question 24
ప్రశ్న 24
Which comparison between Bligh's and Khosla's approaches is most accurate?
Explanation:
Bligh treats seepage as creeping along the bottom contour and assumes linear loss of head with creep length. His piping criterion is consequently based primarily on an average gradient and an empirical creep coefficient. Khosla instead represents seepage as potential flow and evaluates pressure at key points using mathematically derived standard profiles. Khosla also explicitly evaluates the local downstream exit gradient and the effect of sheet-pile geometry. Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Which sequence best represents the engineering use of Khosla's method for a complex weir or barrage foundation?
Explanation:
The independent-variable method begins by representing the actual foundation profile through simpler standard forms. Pressure percentages at relevant key points are then obtained from the appropriate Khosla solutions or curves. Corrections are applied for pile interference, finite floor thickness and slopes where applicable. The corrected pressures are used for uplift design, while the downstream geometry is checked for a safe exit gradient. If the checks are unsatisfactory, the floor or cutoff arrangement is revised, so Option B is correct.
వివరణ:
Question 26
ప్రశ్న 26
Consider the following statements about Khosla's theory: I. Seepage beneath a hydraulic structure is treated as potential flow through the foundation. II. Head loss beneath the floor is generally nonlinear. III. A downstream cutoff is important for controlling the exit gradient. IV. Standard-profile pressures may require corrections for pile interference, floor thickness and floor slope. Which option is correct?
Explanation:
Statement I is correct because Khosla's theory is based on a potential-flow representation of seepage. Statement II is correct because the pressure distribution is not the linear distribution assumed by Bligh. Statement III is correct because the downstream exit gradient is a critical piping consideration and is strongly influenced by cutoff depth. Statement IV is correct because these three corrections are required when idealized standard-profile solutions are applied to real structures. Therefore all four statements are correct and Option D is the valid answer.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. Seepage water is treated as potential flow following a system of streamlines through the permeable foundation సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: A. ∂²φ/∂x² + ∂²φ/∂y² = 0 సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: C. It is generally nonlinear and depends on the geometry of the floor, cutoffs and foundation సమాధానం: C.
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Question 4 ప్రశ్న 4Answer: B. Dividing a complex foundation profile into simpler standard profiles whose individual effects can be evaluated and appropriately combined సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: A. A horizontal floor of negligible thickness with a sheet pile at an end సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: B. At key points such as floor-pile junctions, pile tips and relevant corners of depressed floors సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: A. 3.90 m and approximately 38.26 kPa సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: B. The exit gradient is theoretically infinite, demonstrating the need for a downstream cutoff సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: B. It reduces the critical concentration of seepage gradient near the downstream exit and helps prevent piping or undermining సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: A. GE = (H/d)[1/(π√λ)], where λ = [1 + √(1 + α²)]/2 and α = b/d సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: A. 0.179, approximately 1 in 5.57 సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: B. Safe with respect to the stated criterion because 0.179 is less than 0.20 సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: A. It generally reduces the exit gradient and improves piping safety సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: A. It tends to reduce the exit gradient by increasing the geometric parameter λ సమాధానం: A.
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Question 15 ప్రశ్న 15Answer: B. Both influence uplift and the seepage field, but the downstream cutoff is particularly important for controlling the exit gradient and piping సమాధానం: B.
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Question 16 ప్రశ్న 16Answer: B. Corrections for mutual interference of piles, floor thickness and floor slope సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: A. Because each sheet pile in a real profile can modify the seepage field and pressure effect associated with neighboring piles సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: A. Because standard-profile solutions normally assume negligible floor thickness, while the actual pile-floor junction may lie at a different elevation సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: A. Positive for a downward slope and negative for an upward slope సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: C. 60 percent సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: A. The permeable foundation is idealized as extending to effectively infinite depth సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: B. Five times the cutoff depth or 2.5 times the length of the barrage, whichever is larger సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: A. They help determine residual uplift pressures that the floor must safely resist సమాధానం: A.
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Question 24 ప్రశ్న 24Answer: A. Bligh uses a bottom-contour creep concept and average gradient, whereas Khosla uses potential-flow solutions, pressure distribution and local exit-gradient considerations సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: B. Idealize the complex profile into standard components, determine key-point pressure percentages, apply applicable corrections, check uplift and exit gradient, and revise floor or cutoff geometry if necessary సమాధానం: B.
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Question 26 ప్రశ్న 26Answer: D. I, II, III and IV సమాధానం: D.
