Problem 1. Consider a drainage system that consists of horizontal drains located at an elevation ho above the base of an unconfined aquifer of thickness b = 10 m (see Figure 1). The recharge rate is r= 100 mm/yr, and the hydraulic conductivity of the aquifer is K = 1 m/d. The design condition of the drainage system is to avoid ponding at the ground surface. You can ignore the vadose zone for this problem. 1. Obtain the relation between the half-distance between drains, L, and the elevation of the drains, ho. Plot this function over the range of feasible lengths. 2. The cost of each individual drain can be split as the cost of the material (fixed) and the cost of installation (which is assumed to be proportional to the depth b-ho). If the fixed cost is $500 and the installation cost is $100 per meter of aquifer length per meter of depth, can you build a drainage system for less than $1 per meter of aquifer length? If so, what depth ho and spacing 2L would you choose? K= 1 m/day 2L r = 100 mm/yr Figure 1: Schematic of the drainage system. b

Problem 1. Consider a drainage system that consists of horizontal drains located at an elevation ho above the base of an unconfined aquifer of thickness b = 10 m (see Figure 1). The recharge rate is r= 100 mm/yr, and the hydraulic conductivity of the aquifer is K = 1 m/d. The design condition of the drainage system is to avoid ponding at the ground surface. You can ignore the vadose zone for this problem. 1. Obtain the relation between the half-distance between drains, L, and the elevation of the drains, ho. Plot this function over the range of feasible lengths. 2. The cost of each individual drain can be split as the cost of the material (fixed) and the cost of installation (which is assumed to be proportional to the depth b-ho). If the fixed cost is $500 and the installation cost is $100 per meter of aquifer length per meter of depth, can you build a drainage system for less than $1 per meter of aquifer length? If so, what depth ho and spacing 2L would you choose? K= 1 m/day 2L r = 100 mm/yr Figure 1: Schematic of the drainage system. b

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Field applications of hydraulic conductivity

Hydraulic conductivity is one of the hydraulic properties of soil defined as a measurement of the ability of a porous medium to permit water movement or fluid flow through it. It is denoted by the letter K. It is influenced by the density and viscosity of the fluid. It is also called permeability. Hydraulic conductivity is defined as the ratio of velocity to the hydraulic gradient. The different methods used to determine the hydraulic conductivity are laboratory methods (constant head permeability tests and falling head tests), in-situ field methods (pumping in and pumping out tests), small scale field tests (infiltration tests and slug tests), and indirect methods such as estimation from grain size, consolidation test data, and horizontal capillary test. The pedotransfer function (PTF) method is a specific empirical estimating approach employed in the soil sciences is also used to determine the hydraulic conductivity of the soil.

Question

Problem 1. Consider a drainage system that consists of horizontal drains located at an
elevation ho above the base of an unconfined aquifer of thickness b 10 m (see Figure
1). The recharge rate is r = 100 mm/yr, and the hydraulic conductivity of the aquifer is
K = 1 m/d. The design condition of the drainage system is to avoid ponding at the ground
surface. You can ignore the vadose zone for this problem.
1. Obtain the relation between the half-distance between drains, L, and the elevation of
the drains, ho. Plot this function over the range of feasible lengths.
2. The cost of each individual drain can be split as the cost of the material (fixed) and
the cost of installation (which is assumed to be proportional to the depth b – ho). If
the fixed cost is $500 and the installation cost is $100 per meter of aquifer length per
meter of depth, can you build a drainage system for less than $1 per meter of aquifer
length? If so, what depth ho and spacing 2L would you choose?
K= 1 m/day
2L
=
r = 100 mm/yr
Figure 1: Schematic of the drainage system.
b

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