Engineering Applications — Worked Examples

A one-dimensional horizontal confined strip has length 40.0 m, thickness 20.0 m and unit width into the page. Hydraulic conductivity is $5.00\times10^{-5}\text{ m/s}$ throughout. At the horizontal base datum, left and right pressure heads are 15.0 m and zero. Find gradient and discharge per unit width.

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Use the same strip and exact discharge $3.75\times10^{-4}\text{ m}^3/\text{s per m}$. If identical conditions apply along a represented 200 m width, find daily volume per metre and along the entire represented width.

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Split the 40 m strip into two 20.0 m zones at the same thickness 20.0 m. Set $K_1=5.00\times10^{-6}\text{ m/s}$ on the left and $K_2=5.00\times10^{-5}\text{ m/s}$ on the right, with heads 15.0/0 m. Find discharge, interface head and the head loss in each zone.

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Compare the preceding low-conductivity-left case with the two conductivities swapped. Lengths, thickness and boundary heads remain unchanged. Find the new interface head and compare integrated uplift per unit width. Use the two zone-order panels below.

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Return to uniform $K=5.00\times10^{-5}\text{ m/s}$ along the 40.0 m base, with heads 15.0/0 m. Find pressure halfway along the base and integrated uplift per metre. Use the uniform panel in the profile comparison.

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Set both heads of the same 40.0 m confined strip to 15.0 m. Find net discharge and uplift. Use the equal-head panel in the comparison.

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For the uniform strip, change the left/right heads to 0/15.0 m. Find signed discharge and uplift, and compare with the original 15.0/0 m case.

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A preliminary sketch gives a 40 m dam base and a 10 m deep cutoff. A reviewer proposes replacing a seepage model by a 60 m path, then claims this proves reduced exit gradient and adequate piping resistance. Is the conclusion determined by those dimensions?

An isolated 5.00 m interval takes 45.0 L in 10.0 min at a supplied corrected effective pressure of 0.500 MPa. Flow is stabilized and pressure normalization is appropriate for this teaching stage. Calculate its Lu index.

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In the same 5.00 m interval, stabilized water take is 45.0 L over 10.0 min at 0.500 MPa effective pressure and 135 L over 10.0 min at 1.00 MPa. Compare normalized indices; can the first stage be treated as a constant proportional predictor?

A synthetic monitoring baseline gives diameter 6.000 m. Current accumulated diametric closure is 18.0 mm. Find the current diameter, closure percentage and radial motion if both sides move equally.

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Verified synthetic readings increase from 12.0 to 24.0 mm over 2.00 days. The supplied exercise plan reaches a response trigger at accumulated closure of 25.0 mm or average closure rate of 5.00 mm/day. Determine the comparison.

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A record contains previous/current closure of 18.0/18.0 mm, elapsed time zero and unapproved trigger values. The instrument has retained both readings. Should the software report zero rate and accept the reach?

At a synthetic corridor cutting, mapped joints permit a possible sliding block. A proposed horizontal drain has no demonstrated connection to its water-bearing fractures, and a proposed mesh covers only surface ravelling. Which review is needed before crediting either measure against the deep block?