For a flow problem in an anisotropic medium with kx = 6 kz, what is the relationship between a flow element in the transformed section and the true section?
Explanation
The transformation for an anisotropic flow net either compresses or stretches one axis to create an equivalent isotropic system. If horizontal conductivity (kx) is greater than vertical (kz), the horizontal axis is compressed in the transformed drawing. Consequently, a 'square' in the transformed drawing corresponds to a rectangle stretched horizontally in the real world.
Other questions
What does Laplace's equation of continuity, (d^2h / dx^2) + (d^2h / dz^2) = 0, represent for two-dimensional flow in an isotropic medium?
What is the definition of a 'flow line' in the context of groundwater seepage?
What is an 'equipotential line' in a permeable soil medium?
A 'flow net' is a combination of which two types of lines?
What are the two primary rules that must be followed when graphically constructing a flow net?
In a flow net, what is the term for the strip between any two adjacent flow lines?
The total head loss (H) across a seepage domain is 15 meters. If the corresponding flow net has 10 potential drops (Nd), what is the head loss across each potential drop?
Using a flow net, the total rate of flow (q) through all channels per unit length is calculated. The soil has a hydraulic conductivity (k) of 0.005 m/s, the total head loss (H) is 20 m, the number of flow channels (Nf) is 5, and the number of potential drops (Nd) is 10. What is the value of q?
How must the procedure for constructing a flow net be modified to account for anisotropic soil conditions where the horizontal hydraulic conductivity (kx) is not equal to the vertical hydraulic conductivity (kz)?
When calculating seepage per unit length in an anisotropic soil using a transformed flow net, which formula is correct?
A dam section has a permeable layer with a vertical hydraulic conductivity (kz) of 3x10^-2 mm/s and a horizontal hydraulic conductivity (kx) of 12x10^-2 mm/s. To draw a flow net, the vertical section is plotted using a vertical scale. What factor must be used to determine the horizontal scale?
A flow net is drawn for seepage under a weir, resulting in 7 equipotential drops (Nd). The difference in water level between the upstream and downstream sides is 14 meters. What is the uplift pressure at the base of the weir at a point corresponding to the 4th equipotential line (after 4 drops of potential)? The unit weight of water (gw) is 9.81 kN/m^3.
What assumption about the free surface slope is made in Dupuit's (1863) theory for seepage through an earth dam, as described in Section 8.8?
According to Schaffernak’s solution, which uses a parabolic free surface, what is the formula for the rate of seepage (q) per unit length through an earth dam?
L. Casagrande's improved solution for seepage through an earth dam is recommended when the downstream slope angle (alpha) is greater than what value?
In L. Casagrande’s solution for seepage through an earth dam, what is the modified formula for the rate of seepage (q)?
What is the primary purpose of a 'filter' in geotechnical engineering, as it relates to seepage?
According to the filter design criteria from Terzaghi and Peck, to prevent the movement of particles from the protected soil (S) into the filter (F), which relationship must be satisfied?
What is the filter design criterion suggested by Terzaghi and Peck to ensure the filter material has a high hydraulic conductivity and prevents the buildup of large seepage forces?
What is the physical meaning of the boundary condition where an impervious layer, such as line fg in Figure 8.3b, is located?
For a flow net under a dam, H1 = 5.6 m and H2 = 2.2 m. The net has Nd = 6 potential drops. What is the piezometric elevation at point 'a', which is located after one potential drop, if the ground surface is the datum?
From Example 8.2, for a flow net around sheet piles, the hydraulic conductivity k = 5 x 10^-5 m/sec, total head loss H = 3.4 m, and Nd = 6. The seepage calculation uses a factor of 2.38. What does this factor represent?
What is the continuity equation for two-dimensional flow in an anisotropic soil where kx is not equal to kz?
In a one-dimensional flow problem through two soil layers, what quantity remains constant through both layers?
What is the relationship between flow lines and equipotential lines when a flow net drawn on a transformed section for anisotropic soil is redrawn in a true section?
In Example 8.3, the rate of seepage under a dam in an anisotropic layer is calculated. Given kx = 11.34 ft/day, kz = 5.67 ft/day, H = 20 ft, Nd = 8, and Nf = 2.5, what is the rate of seepage (q)?
What is the primary reason for the deviations from Dupuit's assumption that L. Casagrande (1932) observed in seepage through earth dams with steep downstream slopes?
According to the U.S. Navy (1971) filter design criteria, what is the required relationship between the D15 size of the filter (F) and the D85 size of the protected soil (S) to avoid particle movement?
The U.S. Navy (1971) filter criteria include a special condition for the D15(F)/D15(S) ratio when the uniformity coefficient (Cu) of the protected soil is greater than 4. What is this condition?
What does Condition 5 of the U.S. Navy filter criteria specify for filters used around perforated pipes?
In the derivation of Laplace's equation of continuity, what fundamental principle is applied to an elemental soil block?
In an earth dam with a downstream slope angle of 60 degrees, a height of 20 ft, and a horizontal distance 'd' of 40 ft, which method is more appropriate for calculating seepage?
An earth dam has a height H = 20 ft and a downstream slope angle of 45 degrees. The horizontal distance d = 64.3 ft. Using the graphical solution from Gilboy for L. Casagrande's method, what is the value of 'm' if d/H = 3.215?
In a flow net with rectangular elements, the rate of flow through a channel is modified from the standard square-element formula. If the width-to-length ratio (n = b/l) is constant for all rectangular elements, how is the total rate of flow (q) calculated?
In a constant-head permeability test on a two-layered soil (Figure 8.2), if the head h1 is maintained at the top and the exit head is zero, what is the formula for the head at the interface, h2?
A soil to be protected has D15(S) = 0.05 mm and D85(S) = 0.3 mm. According to Terzaghi and Peck's criteria, which of the following filter materials (F) would be acceptable?
What does a flow element with a width-to-length ratio of 0.5 in a flow net signify?
The continuity equation for one-dimensional vertical flow in the z-direction simplifies to d^2h/dz^2 = 0. What is the general solution for the head, h, as a function of z?
In the context of the U.S. Navy filter design criteria, what is the maximum allowable grain size for any filter material?
For the flow net shown in Figure 8.7, if the average length of flow between equipotential lines d and e at point c is scaled to be 4.1 m, and the head loss between these lines is 0.567 m, what is the average hydraulic gradient at c?
If a flow net has 4 flow channels (Nf) and 12 potential drops (Nd), what is the shape factor of the flow net?
What is the physical interpretation of the condition where the equipotential lines and flow lines are not orthogonal in a true-scale drawing of a seepage problem?
An uplift pressure calculation for a weir shows there are Nd = 7 drops and total head H = 7 m. The base of the weir extends from the 1st equipotential drop to the 6th. What is the uplift force per unit length on the weir if the base is 14 m long and the unit weight of water is 10 kN/m^3? Assume a linear pressure distribution between the points.
In Condition 1 of the U.S. Navy filter criteria, D15(F) / D85(S) must be less than 5. If the uniformity coefficient (Cu) of the protected soil is less than 1.5, how can this criterion be modified?
For the flow net in Example 8.2, the total seepage rate is calculated as 6.74 x 10^-5 m^3/sec/m. If the hydraulic conductivity (k) of the soil were doubled to 10 x 10^-5 m/sec, what would be the new seepage rate, assuming all other conditions remain the same?
Which boundary condition applies to the upstream and downstream surfaces of a permeable layer (lines ab and de in Figure 8.3b) when constructing a flow net?
As a consequence of the upstream and downstream surfaces being equipotential lines, what must be true about the flow lines that meet them?
What is the derivation of Laplace's equation for two-dimensional flow based on?
A flow net is drawn with 3 full flow channels and one channel that is half the width of the others. The net has 8 potential drops. What is the shape factor (Nf/Nd) for this flow net?