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Geotechnics 3 > 7 - 2D flows in soils > Flashcards

7 - 2D flows in soils Flashcards

1
Q

What are the two main issues in flow problems in soils?

A

Quantity of water flowing
Pore water pressure

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2
Q

What is the purpose of predicting the quantity of flow in soils?

A

To assess leakage through a reservoir embankment or the supply of fresh water to a well.

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3
Q

Why is determining pore water pressure important?

A

To evaluate forces and pore pressures that may cause ground movement.

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4
Q

What is steady downward flow?

A

Steady downward flow occurs when water is pumped from an underground aquifer, where pore pressures are lower than hydrostatic pressures.

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5
Q

What is steady upward flow?

A

Steady upward flow occurs when an artesian well connects the ground surface to a water source, providing pressures higher than hydrostatic pressures. This drives water up and out of the well with little or no pumping.

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6
Q

What is an artesian well?

A

An artesian well is one in which groundwater pressure is sufficient to push water up and out of the well without the need for pumping.

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7
Q

What historical example illustrates artesian pressure?

A

Many old fountains in London were originally driven by artesian pressure in aquifers confined beneath the London Clay.

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8
Q

What has caused the artesian pressure in London’s aquifers to decrease?

A

Pumping from the aquifers over many years has lowered the water pressures below artesian levels.

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9
Q

How can aquifers be recharged?

A

Aquifers may be recharged by supplementing or replacing the natural infiltration process to replace extracted water.

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10
Q

What is transient (or unsteady) flow in soils?

A

Transient flow occurs when water is expelled from pores due to changes in pore size, typically associated with consolidation.

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11
Q

What are flownets used for in soil flow problems?

A

Flownets are used to visualize and solve flow problems, helping determine flow rate, pore pressure, and effective stress in 2D flow situations.

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12
Q

How are flownets formed?

A

Flownets are formed from two orthogonal sets of curves:

Flowlines – indicating the direction of seepage along a hydraulic gradient.
Equipotential lines – connecting points of equal total head.

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13
Q

What does a constant flow rate imply about the hydraulic gradient in 2D flow?

A

If the flow rate is constant, the hydraulic gradient must be constant along the direction of flow, and the hydraulic head will vary linearly in that direction.

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14
Q

What is a flowline in a flownet?

A

A flowline indicates the direction of seepage along a hydraulic gradient, representing the path of constant flow rate.

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15
Q

What is an equipotential line in a flownet?

A

An equipotential line connects points of equal total head (h). Water would rise to the same level in standpipes installed on a single equipotential line.

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16
Q

What happens to the flow velocity along an equipotential line?

A

There is no component of flow velocity along an equipotential line because the hydraulic gradient (iE) is zero along this line.

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17
Q

What is the relationship between flowlines and equipotential lines?

A

Flowlines and equipotential lines must cross at right angles, ensuring no flow velocity along the equipotential lines.

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18
Q

Can adjacent flowlines cross in a flownet?

A

No, adjacent flowlines must never cross because two packets of water cannot share the same volume in space.

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19
Q

What is Darcy’s law for flow through soil?

A
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20
Q

How is the flow rate calculated between two flow lines in a flownet?

A
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21
Q

What happens when the flow elements are curvilinear squares in a flownet ?

A
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22
Q

What is the formula for the total flow rate through multiple channels in a flownet?

A
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23
Q

How is the total head at a given equipotential line calculated in a flownet?

A

and is the number of the downstream boundary

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24
Q

How is the pore pressure calculated using the total head in a flownet?

A
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25
Q

What is an equipotential line in the context of flow in soils?

A

An equipotential line is a surface on which the total head is fixed, indicating no change in head along the line.

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26
Q

What boundary conditions are present where water enters and exits the soil?

A

The surface where water enters the soil has a fixed total head (h1).
The surface where water exits the soil has a fixed total head (h2).

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27
Q

What is a flowline in a flownet?

A

A flowline is a surface across which there is no flow, such as an impermeable soil layer or wall. For example, a sheet pile wall’s outer boundary is a flowline.

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28
Q

What is a common mistake when working with flow problems in soils?

A

A common mistake is converting between unit systems incorrectly. It is best to work in SI units (meters, seconds) with permeability in m/s and convert the final result to other units (e.g., liters/hour, m³/hour) afterward.

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29
Q

What is the first step in constructing a flownet?

A

Draw the geometry of the problem with its boundaries to a convenient scale.

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30
Q

What is the next step after observing the general flow pattern in flownet construction?

A

Locate the boundary flow lines, including the longest and shortest ones, to define the flow direction.

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31
Q

What should you do after drawing the geometry in flownet construction?

A

Observe the general pattern of flow to understand the direction and distribution of the flow.

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32
Q

What is the importance of locating constant head lines in a flownet?

A

Constant head lines (where water enters and exits the soil) are key to establishing fixed total heads (h1 and h2) and determining the flow pattern.

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33
Q

How do you sketch the flowlines in a flownet?

A

Sketch the intermediate flowlines based on the observed flow pattern and the boundary conditions.

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34
Q

How should equipotential lines be sketched in a flownet?

A

Sketch equipotential lines, aiming to create curvilinear squares, ensuring they cross the flowlines at 90 degrees.

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35
Q

What should you do if the flownet does not meet the desired pattern?

A

Adjust and/or add equipotential lines and flowlines as necessary to complete the flownet.

36
Q

What are the main assumptions when analyzing fluid flow through porous media?

A

The fluid has constant density, independent of pore water pressure.
Darcy’s Law describes the interaction between water and the soil.
Continuity of flow is ensured: the flow into the soil equals the flow out.

37
Q

What is the role of the flownet in solving Laplace’s Equation?

A

The flownet is the most commonly used method for solving Laplace’s Equation. It visually represents flowlines and equipotential lines, which help calculate flow rates and pore pressures.

38
Q

What does Laplace’s Equation tell us about the flow of water through soil?

A

Laplace’s Equation describes how the pressure (or hydraulic head) changes in the soil, which directly affects how water flows through it.

39
Q

What does Darcy’s law describe in the x-direction?

A
40
Q

What does Darcy’s law describe in the z-direction?

A
41
Q

What does the conservation of masss and continuity of flow state?

A
42
Q

What is the general form of the equation after combining Darcy’s law and the conservation of mass ?

A
43
Q

What is Laplace’s equation in isotopic soils(where permeability is the same in all directions)?

A
44
Q

What does it mean for a soil to be hydraulically anisotropic?

A

It means the soil has different permeability in different directions. For example, permeability parallel to the planes of stratification (horizontal) is typically greater than the permeability perpendicular to these planes (vertical).

45
Q

What is the significance of transforming the x-direction in anisotropic soils?

A

By transforming the x-direction, we can apply the flownet method to solve 2D flow problems for soils with different horizontal and vertical permeabilities, making it easier to analyze the flow.

46
Q

How does anisotropic permeability affect the flownet construction?

A

Anisotropic permeability requires the horizontal scale of the problem to be adjusted (transformed) according to the ratio of permeabilities, while the vertical scale remains unchanged. This ensures accurate representation of flow behavior in soils with different horizontal and vertical permeabilities.

47
Q

What is the general equation for fluid flow in anisotropic soils?

A
48
Q

How can the anisotropic soil equation be transformed into a standard Laplacian equation?

A
49
Q

How would you adjust the horizontal scale of a flownet for anisotropic soils?

A
50
Q

What is unconfined flow?

A

Unconfined flow occurs when there is no “obvious” upper flowline,

51
Q

What is the phreatic surface?

A

The phreatic surface is the top flowline in an unconfined flownet. It represents the surface where the pore pressure is zero, and it is always perpendicular to the upstream slope of a dam.

52
Q

How is the path of the phreatic surface estimated in unconfined flow?

A

The path of the phreatic surface must be estimated before constructing the flownet. Along the top flowline, there is no water pressure head, so total head changes must match elevation changes (Δh = Δz).

53
Q

Why is a filter constructed on the downstream side of an embankment dam?

A

A filter is constructed on the downstream side to prevent water from seeping out and causing erosion of the dam. The filter keeps the seepage contained within the dam.

54
Q

Can the same calculations used for confined flownets be used for unconfined flownets?

A

Yes, once the flownet for unconfined flow is established, the same calculations (for flow rate and pore pressures) can be performed as with confined flownets.

55
Q

What are numerical solutions used for in seepage problems?

A

Numerical solutions, like Finite Element Method (FEM) or Finite Difference Method (FDM), are used for complex problems that cannot be solved with hand-drawn flownets, such as irregular geometry or varying soil properties.

56
Q

What is the Finite Element Method (FEM)?

A

FEM divides the flow regime into many discrete elements. Each element captures geometric details of the problem, and hydraulic gradients within each element are assumed to be constant. The flow rate through adjacent elements is equal, and the results are an approximate solution that depends on the number of elements.

57
Q

How does the number of elements affect FEM results?

A

Increasing the number of elements improves the resolution of the output and the accuracy of the solution. More elements result in smoother flowlines and a more accurate model of the flow.

58
Q

What types of flow problems can FEM be used for?

A

FEM can be used for complex flow problems such as:

Anisotropic soils (kx ≠ kz)
Stratified or non-homogeneous soil profiles
Saturated and unsaturated flow
Transient flow (consolidation)
Complex boundary conditions and geometry.

59
Q

What are some commercially available FEM software for seepage problems?

A

Commercially available FEM software includes SEEP/W, FLAC, PlaxFlow, and SVFlux. These tools are used for routine seepage analysis and can solve complex seepage problems efficiently.

60
Q

What is the Finite Difference Method (FDM)?

A

The Finite Difference Method involves dividing the flow field into a network of nodes. The variation in total head is assumed to be linear between adjacent nodes, and flow rate into a node is calculated based on head differences, using Laplace’s Equation in a finite difference form.

61
Q

What is the limitation when using FDM with curved boundaries?

A

Curved boundaries in FDM need to be approximated with straight segments because the flow field is discretized using a grid of points, which cannot easily represent curved shapes directly.

62
Q

What are the advantages of FEM over FDM?

A

FEM provides a better description of geometry, is more suitable for complex shapes, is more computationally efficient, and directly provides the required parameters.

63
Q

What are the advantages of FDM over FEM?

A

FDM is simpler to implement, requiring less computational power and is often used with basic software for simpler problems.

64
Q

What is the “quick condition” or “quicksand condition”?

A

The quick condition occurs when upward water pressure is high enough to cause the effective stresses in soil to disappear. This results in the soil behaving like a fluid, leading to instabilities such as piping and liquefaction during earthquakes.

65
Q

How does the upward flow of water affect the soil during the quick condition?

A

The upward flow of water can cause the effective stresses in the soil to disappear. This occurs because the increase in pore pressure due to seepage reduces the effective stress, which is essential for soil strength.

66
Q

What is the relationship between seepage force and quicksand conditions?

A

When the seepage force becomes too large, it leads to the quicksand condition, where the soil behaves as a fluid. The seepage force can cause a loss of frictional strength and soil instability.

67
Q

How do you calculate the seepage force in quicksand conditions ?

A
68
Q

What is the force balance in quicksand conditions ?

A
69
Q

What is the critical hydraulic gradient (ic)?

A

The critical hydraulic gradient is the upward hydraulic gradient at which the seepage force just balances the buoyant weight of a soil element. It is given by the equation: ic = y0 / yw

70
Q

What is the typical value for the critical hydraulic gradient for most soil types?

A

1.0

71
Q

How is the hydraulic gradient calculated from a flow net?

A

To calculate the hydraulic gradient from a flow net, the total head difference is divided by the flow distance. This helps in determining if the critical hydraulic gradient is being reached.

72
Q

What is the Factor of Safety (FoS) against downstream heave?

A

The Factor of Safety against downstream heave is defined as:
FoS = W’ / J

W’ = the buoyant weight of the critical soil zone
J = the seepage force acting on the critical zone

73
Q

How is the buoyant weight of the critical soil zone calculated?

A

W’ = 1/2D^2 * y’

d = depth of embankement
y’ = the weight of the soil.

74
Q

What happens if the Factor of Safety (FoS) is below 1?

A

If the Factor of Safety (FoS) is below 1, downstream heave will occur, and remediation methods must be implemented to prevent instability.

75
Q

What are two possible solutions to prevent downstream heave?

A

To prevent downstream heave, you can:

Increase the embedded length (D): This reduces the hydraulic gradient by making water travel through more soil.
Provide a surcharge above the susceptible element in the form of a filter: This increases the buoyant weight of the soil and requires more seepage force to eliminate effective stress.

76
Q

What is soil piping?

A

Soil piping is a failure mechanism in which a pipe-shaped discharge channel or tunnel forms between soil and the foundation, leading to structural instability. It can be caused by either heave or subsurface erosion.

77
Q

What are the two processes that cause soil piping?

A

Soil piping can be caused by:

Piping due to heave: Sudden rise of soil at the downstream toe of a structure.
Piping due to subsurface erosion: Subsurface erosion starts at springs near the downstream toe and progresses upstream.

78
Q

What type of soil is most prone to piping due to subsurface erosion?

A

Fine-grained cohesionless materials, such as silts and very fine sands, are most prone to piping due to subsurface erosion, as they can easily experience grain-by-grain removal.

79
Q

How can subsurface erosion affect dams?

A

Subsurface erosion can lead to catastrophic failures of dams, as it starts at the downstream toe and works its way back toward the reservoir, forming pipes or channels under the dam. This often occurs without warning, sometimes many years after the reservoir is filled.

80
Q

How are protective filters used to prevent piping in dams?

A

Protective filters are used to prevent the migration of fine-grained materials like silt and sand, which are prone to subsurface erosion and piping. These filters help to maintain the stability of the dam foundation by preventing soil loss.

81
Q

What caused the failure of the Teton Dam on June 5, 1976?

A

The failure was initiated by a large leak near the right (northwest) abutment of the dam, about 35 m below the crest. The leak progressively enlarged, causing erosion into the bedrock, leading to the collapse of the dam.

82
Q

What were the consequences of the Teton Dam failure?

A

The collapse resulted in the deaths of 11 people, extensive property damage, and a federal government payout of over $300 million in claims. Total damage estimates ranged up to $2 billion.

83
Q

What were the potential causes of the Teton Dam failure based on geological, hydrological, and geotechnical studies?

A

The failure might have been caused by:

Discontinuities (fissures) in the rock on one side of the dam,
High permeability and improper compaction of the filling materials (especially windblown silt),
High seepage forces once the leak started.

84
Q

How did engineers prevent failure at Ulley Dam in 2007?

A

Engineers quickly responded by placing impermeable geomembranes on the ‘dry’ side of the dam and adding extra fill material on top of the membrane, preventing a runaway failure from occurring

85
Q

What is a graded soil filter, and why is it used in dam construction?

A

A graded soil filter is a filter made of one or more layers of carefully graded soil placed between potentially migrating soil and a drain. It prevents the migration of fine particles while maintaining adequate permeability for water flow.

Geotechnics 3 (8 decks)

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