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Yhd-12.3105 Subsurface Hydrology Unsaturated Flow Teemu KokkonenEmail: firstname.surname@aalto.fi Tel. 09-470 23838 Room:272 (Tietotie 1 E) Water Engineering Department of Civil and Environmental Engineering Aalto University School of Engineering

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Yhd-12.3105 Subsurface Hydrology Transient flow Soil Moisture Profile – From Groundwater level to soil surface Recall some definitions –Groundwater level is defined to be that level where soil water pressure is atmospheric –Below the groundwater level the soil is saturated with water and above the groundwater level the soil is unsaturated –Immediately above the groundwater level there is a capillary fringe that is (amost) fully saturated

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Yhd-12.3105 Subsurface Hydrology Transient flow Unsaturated Zone Water originating from precipitation or irrigation infiltrates through the soil surface and percolates through the unsaturated zone –This forms recharge to an aquifer –Harmful substances move with water In unsaturated zone the water pressure is negative –Water is retained in soil by capillary forces, which are a combination of cohesive and adhesive forces Does the percolating water in the figure above enter the subsurface drain? Why / why not?

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Yhd-12.3105 Subsurface Hydrology Transient flow Tensiometer Soil sample hchc Porous plate Water 1. How can you read the pressure head in the soil sample using the tensiometer shown in the figure? 2. The porous plate needs to be airtight. Why? 3. Why does the water entering the soil sample does not significantly affect the measurement? Negative water pressure in soil is measured using a tensiometer

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Yhd-12.3105 Subsurface Hydrology Transient flow Water Retention Curve A graph that shows the relationship between soil water pressure head and moisture content of soil is called the water retention curve In the water retention curve the soil water pressure head is typically expressed as a pF value –pF value is the 10-based logarithm of the absolute value of the pressure head expressed in centimeters of water column height Pressure head is – 100 cm. What is the corresponding pF value? Pressure head is – 100 cm => pF value is 2 As pressure head values range across a large scale taking a logarithm lead s to a garph that is easier to interpret

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Yhd-12.3105 Subsurface Hydrology Transient flow Water Retention Curve II III I I:Porosity II:Air-entry pressure head h a haha III:Residual moisture content res res

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Yhd-12.3105 Subsurface Hydrology Transient flow Water Retention Curve It will not be a great surprise that different soils have water retention curves of different shape Clay Sand Which one of the shown water retention curves is for a clay soil and which one for a sand soil? Why?

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Yhd-12.3105 Subsurface Hydrology Transient flow Water Flow in Unsaturated Zone What are the differences to saturated (groundwater) flow? –Hydraulic conductivity is a function of the moisture content of soil When moisture content decreases large soil pores are emptied first, which leads both in reduced cross-sectional area of flow and increased tortuosity of the flow paths => hydraulic conductivity drops –The air-filled pore space is a function of the moisture content of soil Recall the large difference (several orders of magnitude) in the storativity of confined and unconfined aquifers Recall that moisture content and pressure head are related via the water retention curve –Hydraulic conductivity and the air-filled pore space can also be expressed as a function of pressure head

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Yhd-12.3105 Subsurface Hydrology Transient flow Darcys Law in Unsaturated Zone As presented earlier the hydraulic head H is the sum of pressure head h and gravity head z In the unsaturated flow the interest often is to study percolation to groundwater, so let us first write Darcys law in one dimension and in vertical direction Here the direction of the z-axis is points downward – hence the negative sign.

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Yhd-12.3105 Subsurface Hydrology Transient flow Darcys Law in Unsaturated Zone: 3D Why is the -1 present in the equation of q z missing from the equations for q x and q y ?

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Yhd-12.3105 Subsurface Hydrology Transient flow Unsaturated Hydraulic Conductivity Pressure head Hydraulic conductivity Coarse gravel Fine sand Clay Peat Relationship between the pressure head and the hydraulic conductivity for different soil types

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Yhd-12.3105 Subsurface Hydrology Transient flow Unsaturated Hydraulic Conductivity The water retention curve (pF curve) and the unsaturated hydraulic conductivity can be described with the following equations originally proposed by M.Th. van Genuchten and Y. Mualem Where is the soil moisture (cm 3 /cm 3 ), R is the residual water content of soil (cm 3 /cm 3 ), S is the saturated water content of soil (cm 3 /cm 3 ), S is the saturation of soil (cm 3 /cm 3 ), h is the pressure head (cm), and h a is the air entry pressure head. Symbols,, and refer to the parameters of the van Genuchten model, and = 1 – 1/. K is the unsaturated hydraulic conductivity, K S is the saturated hydraulic conductivity (cm/h), and K R is the relative conductivity of unsaturated soil (K R = K / K S ).

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Yhd-12.3105 Subsurface Hydrology Transient flow Reminder: Transient Groundwater Flow in 3D Specific storativity S 0 volume of water added to storage, per unit volume and per unit rise in hydraulic head

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Yhd-12.3105 Subsurface Hydrology Transient flow Flow in Unsaturated Zone: Richards Equation Specific moisture capacity: Differential water capacity: Volume of water released from (or added to) storage per unit decrease (or increase) of pressure head C [1/m]

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Yhd-12.3105 Subsurface Hydrology Transient flow Differential Water Capacity The definition was: Differential water capacity: C [1/m] Volume of water released from (or added to) storage per unit decrease (or increase) of pressure head From the definition above it follows:,where is the volumetric moisture content So:

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Yhd-12.3105 Subsurface Hydrology Transient flow Differential Water Capacity Moisture content Pressure head h h

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Yhd-12.3105 Subsurface Hydrology Transient flow Numerical Solution – Richards Equation Let us discretize the Richards equation in 2D for a longitudial section: z (j) x (i) Sink / source

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Yhd-12.3105 Subsurface Hydrology Transient flow Numerical Solution – Richards Equation z (j) x (i) x z

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Yhd-12.3105 Subsurface Hydrology Transient flow Numerical Solution – Richards Equation

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Yhd-12.3105 Subsurface Hydrology Transient flow Numerical Solution – Richards Equation Approximating the differential water capacity C 1.Estimate using the Van Genuchten equation the moisture content that corresponds to the pressure head at the desired time and location 2.Perturbate the pressure head with a small displacement of h 3.Compute the moisture content at h + h Recall that. How would you approximate C? 4.Now you can estimate C using the difference method as

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