This document discusses modulus of elasticity and hydraulic conductivity. It defines elastic modulus as a material's resistance to deformation from stress, measured by the slope of its stress-strain curve. Hydraulic conductivity is the ease with which water moves through saturated or unsaturated soil pores, driven by gravitational or matric forces. There are empirical and experimental methods to estimate hydraulic conductivity from grain size, pedotransfer functions, or laboratory tests like constant-head or falling-head methods. Field techniques to measure saturated conductivity include ring infiltrometers and pressure infiltrometers, while tension infiltrometers measure unsaturated conductivity.

2. Lec. # 7:
Modulus of Elasticity coefficient; Hydraulic
conductivity
BOT-609 (Plant nutrient water relationships)
Credit hrs: 3 (2-1)
Dr. Noreen Zahra
Assistant Professor, Department of Botany
GCWUF

3. An elastic modulus (also known as modulus of elasticity)
• Is a quantity that measures an object or substance's resistance to being deformed
elastically (i.e., non-permanently) when a stress is applied to it.
• The elastic modulus of an object is defined as the slope of its stress–strain curve in
the elastic deformation region:A stiffer material will have a higher elastic modulus.

4. An elastic modulus has the form:
where
• stress is the force causing the deformation divided by the area to
which the force is applied and
• strain is the ratio of the change in some parameter caused by the
deformation to the original value of the parameter.
• If stress is measured in pascals, then since strain is a
dimensionless quantity, the units of λ will be pascals as well.

9.  Saturated hydraulic conductivity is a quantitative measure of
a saturated soil's ability to transmit water when subjected to
a hydraulic gradient. It can be thought of as the ease with which pores of
a saturated soil permit water movement.
• All pores are contributing to fluxes
• Primarily driven by gravitational forces
• Less common state of flow in soil
Applications:
• Runoff modeling
• Groundwater flow
• Green Infrastructure Assessment

10.  Unsaturated hydraulic conductivity
refers to a measure of soil's water-retaining ability when soil pore space is
not saturated with water.
• Varies depending on pore sizes, which are able to contribute
to water fluxes
• Primarily driven by matric forces
• Most common state of flow in soil
Applications:
• Vadose zone hydrology
• Hyporheic exchange

11. Hydraulic conductivity curves for three different soils. Values to the right of the vertical axis
indicate saturated conductivity values. Values to the left indicate unsaturated values. Note
that the vertical axis is a logarithmic axis. Thus differences are order of magnitude
differences (0=water potantail)

14. There are two methods of estimation of hydraulic
conductivity
1:Estimation by empirical approach
2:Determination by experimental approach
1:Estimation by empirical approach
There are two types of empirical approach
a) Estimation from grain size
b) Pedotransfer function

15. b) Pedotransfer function
In soil science, pedotransfer functions (PTF) are predictive functions of certain soil
properties using data from soil surveys.
Allen Hazen derived an empirical formula for approximating hydraulic conductivity from grain size analyses
a) Estimation from grain size

16. 2. Determination by experimental approach
There are relatively simple and inexpensive laboratory tests that
may be run to determine the hydraulic conductivity of a soil:
constant-head method
falling-head method.

19. FIELD TECHNIQUES: SATURATED HYDRAULIC CONDUCTIVITY
1.Ring infiltrometers (Kfs)
• Single ring infiltrometer (Kfs)
• Double ring infiltrometer (Kfs)
2. SATURO (Kfs)
3. Pressure infiltrometer (Kfs)
4. Borehole permeameters (Kfs)

20. FIELD TECHNIQUES:
UNSATURATED HYDRAULIC
CONDUCTIVITY
1. Tension infiltrometers (K(Ψ))

23. References:
1.Wösten, J.H.M., Pachepsky, Y.A., and Rawls, W.J. (2001). "Pedotransfer functions: bridging the gap between
available basic soil data and missing soil hydraulic characteristics". Journal of Hydrology. 251 (3–4): 123–
150. Bibcode:2001JHyd..251..123W. doi:10.1016/S0022-1694(01)00464-4.
2. Controlling capillary flow an application of Darcy's law
3. Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey: Prentice Hall, 2001ISBN 0-13-025517-3
4.S.B.Hooghoudt, 1934, in Dutch. Bijdrage tot de kennis van enige natuurkundige grootheden van de grond.
Verslagen Landbouwkundig Onderzoek No. 40 B, p. 215-345.
Soil hydraulic conductivity—What it is. How to measure it | METER Environment