Presentation on theme: "Yhd Subsurface Hydrology"— Presentation transcript:
1Yhd-12.3105 Subsurface Hydrology Unsaturated FlowTeemu KokkonenTelRoom: 272 (Tietotie 1 E)Water EngineeringDepartment of Civil and Environmental EngineeringAalto University School of Engineering
2Soil Moisture Profile – From Groundwater level to soil surface Recall some definitionsGroundwater level is defined to be that level where soil water pressure is atmosphericBelow the groundwater level the soil is saturated with water and above the groundwater level the soil is unsaturatedImmediately above the groundwater level there is a capillary fringe that is (amost) fully saturated
3Unsaturated ZoneDoes the percolating water in the figure above enter the subsurface drain? Why / why not?Water originating from precipitation or irrigation infiltrates through the soil surface and percolates through the unsaturated zoneThis forms recharge to an aquiferHarmful substances move with waterIn unsaturated zone the water pressure is negativeWater is retained in soil by capillary forces, which are a combination of cohesive and adhesive forces
4TensiometerNegative water pressure in soil is measured using a tensiometerSoil samplePorous plateWaterhc1. 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?
5Water Retention CurveA graph that shows the relationship between soil water pressure head and moisture content of soil is called the water retention curveIn the water retention curve the soil water pressure head is typically expressed as a pF valuepF value is the 10-based logarithm of the absolute value of the pressure head expressed in centimeters of water column heightAs pressure head values range across a large scale taking a logarithm lead s to a garph that is easier to interpretPressure head is – 100 cm. What is the corresponding pF value?Pressure head is – 100 cm => pF value is 2
6Water Retention Curve III III: Residual moisture content qres qres II: Air-entry pressure head hahaIIII: Porosity
7Water Retention CurveIt will not be a great surprise that different soils have water retention curves of different shapeClaySandWhich one of the shown water retention curves is for a clay soil and which one for a sand soil? Why?
8Water Flow in Unsaturated Zone What are the differences to saturated (groundwater) flow?Hydraulic conductivity is a function of the moisture content of soilWhen 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 dropsThe air-filled pore space is a function of the moisture content of soilRecall the large difference (several orders of magnitude) in the storativity of confined and unconfined aquifersRecall that moisture content and pressure head are related via the water retention curveHydraulic conductivity and the air-filled pore space can also be expressed as a function of pressure head
9Darcy’s Law in Unsaturated Zone As presented earlier the hydraulic head H is the sum of pressure head h and gravity head zIn the unsaturated flow the interest often is to study percolation to groundwater, so let us first write Darcy’s law in one dimension and in vertical directionHere the direction of the z-axis is points downward – hence the negative sign.
10Darcy’s Law in Unsaturated Zone: 3D Why is the -1 present in the equation of qz missing from the equations for qx and qy?
11Unsaturated Hydraulic Conductivity Coarse gravelRelationship between the pressure head and the hydraulic conductivity for different soil typesFine sandPeatClayHydraulic conductivityPressure head
12Unsaturated 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. MualemWhere is the soil moisture (cm3/cm3), R is the residual water content of soil (cm3/cm3), S is the saturated water content of soil (cm3/cm3), S is the saturation of soil (cm3/cm3), h is the pressure head (cm), and ha 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, KS is the saturated hydraulic conductivity (cm/h), and KR is the relative conductivity of unsaturated soil (KR = K / KS).
13Reminder: Transient Groundwater Flow in 3D Specific storativity S0volume of water added to storage, per unit volume and per unit rise in hydraulic head
14Flow 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 headC [1/m]
15Differential 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 headFrom the definition above it follows:,where q is the volumetric moisture contentSo:
16Differential Water Capacity Moisture content qPressure head hDqDh
17Numerical Solution – Richards Equation Let us discretize the Richards equation in 2D for a longitudial section:x (i)Sink / sourcez (j)
18Numerical Solution – Richards Equation z (j)x (i)DxDz
20Numerical Solution – Richards Equation Approximating the differential water capacity CEstimate using the Van Genuchten equation the moisture content that corresponds to the pressure head at the desired time and locationPerturbate the pressure head with a small displacement of DhCompute the moisture content at h + DhNow you can estimate C using the difference method asRecall thatHow would you approximate C?