Systems Modelling and Design
Systems Modelling and Design Table of Contents 1.
Introduction to Geotechnical Engineering...................................................................................................... 3 Problem Solving to Engineering Design ............................................................................................................. 3
2.
Engineering Design ......................................................................................................................................... 4 Engineering Design Process................................................................................................................................ 4
3.
Run-Off Modelling .......................................................................................................................................... 4 Single-Store Model ............................................................................................................................................. 5 Two-Store Model................................................................................................................................................ 5
4.
Site Investigations ........................................................................................................................................... 6 Geotechnical Site Investigations ........................................................................................................................ 6 Geotechnical Engineering Projects ..................................................................................................................... 6
5.
Water and Stresses in Soil & Rock .................................................................................................................. 7 Introduction to Porous Media ............................................................................................................................ 7 Hydrostatic Porewater and Lithostatic Pressure ................................................................................................ 7 Stress and Strain Measurement ......................................................................................................................... 8 Capillarity ........................................................................................................................................................... 8
6.
Flow in Porous Media and Darcy's Law ........................................................................................................ 10 Stokes Lubrication Equation ............................................................................................................................. 10 Permeability (k) ................................................................................................................................................ 11 Darcy Velocity................................................................................................................................................... 12 Conservation of Mass and Darcy’s Law ............................................................................................................ 12
7.
Measurement of Hydraulic Conductivity ...................................................................................................... 13 Bernoulli’s equation ......................................................................................................................................... 13 Darcy’s Law....................................................................................................................................................... 13 Determination of k by laboratory testing ......................................................................................................... 14 Field permeability testing................................................................................................................................. 14 Permeability Exercise ....................................................................................................................................... 15
8.
Flow Net Fundamentals ................................................................................................................................ 15 Permeability and Pressure Driven Flow ........................................................................................................... 15 Pressure Contours ............................................................................................................................................ 16
9.
Flow Nets – Examples ................................................................................................................................... 17 Construction of Flow Nets ................................................................................................................................ 17 Calculation of Seepage and Pore Water Pressure ............................................................................................ 18 Example Problem ............................................................................................................................................. 19
10.
Water Supply Systems ............................................................................................................................. 20
Open-Channel Flow .......................................................................................................................................... 20 Pipe-Line Design ............................................................................................................................................... 20 Pump Performance Curves............................................................................................................................... 21 11.
Seepage Force and Quicksand ................................................................................................................. 21
Seepage Force .................................................................................................................................................. 21 1
Quicksand ......................................................................................................................................................... 23 Calculations Using Flow Nets ........................................................................................................................... 23 12.
Control of Seepage and Filters ................................................................................................................ 25
Why do we control seepage ............................................................................................................................. 25 Methods to control seepage ............................................................................................................................ 25 Filters ................................................................................................................................................................ 25 13.
Landslides ................................................................................................................................................ 26
Types of Slides .................................................................................................................................................. 26 Rheology and Triggering................................................................................................................................... 26 Numerical simulation ....................................................................................................................................... 28 Triggering of landslides .................................................................................................................................... 28 Landslide overview ........................................................................................................................................... 28 14.
Slope Stability .......................................................................................................................................... 28
Terminology ..................................................................................................................................................... 28 Limit Equilibrium and Factor of Safety (FoS) .................................................................................................... 29 Mohr-Coulomb Failure Criterion ...................................................................................................................... 29 15.
Method of Slices ...................................................................................................................................... 30
Introduction to the Method of Slices ............................................................................................................... 30 Bishop’s Simplified Method ............................................................................................................................. 31 Example – Bishop’s Method ............................................................................................................................. 32 16.
Slope Stabilisation Methods .................................................................................................................... 33
Slope Stabilisation Projects .............................................................................................................................. 33 Stabilisation of Slopes ...................................................................................................................................... 33 17.
Embankment Dams ................................................................................................................................. 34
Types of Embankment Dams ............................................................................................................................ 34 Design Considerations ...................................................................................................................................... 35 Seepage through Embankment Dams .............................................................................................................. 35 18.
Practical Examples of Slope Stability Assessment ................................................................................... 36
Ground Models ................................................................................................................................................ 36 Slope Stability Case Study: Wye River Bushfires .............................................................................................. 37 The Concept of Risk Assessment in Slope Stability .......................................................................................... 38 Qualitative Risk Assessment ............................................................................................................................. 39 Quantitative risk assessment ........................................................................................................................... 39 Risk Mitigation Measures ................................................................................................................................. 40 Hillside Construction Practice .......................................................................................................................... 40 Common Groundwater Issues in Melbourne Basements ................................................................................ 41 19.
Introduction to Numerical Modelling ...................................................................................................... 41
About Numerical Modelling ............................................................................................................................. 41 Model Verification and Validation ................................................................................................................... 42 Numerical Models in Civil Engineering ............................................................................................................. 42 Discretisation.................................................................................................................................................... 42 Basics of the Finite Element Model .................................................................................................................. 43 Summary of Numerical Modelling, Simulation and FEM ................................................................................. 43 2
1.
Introduction to Geotechnical Engineering
Shallow Subsurface · Soil layers O Horizon is the top layer at the surface which consists of surface litter (leaves, sticks), animal waste and dead organisms A Horizon (topsoil) contains organic humus which typically gives it its dark colour B Horizon (subsoil) consists of mostly inorganic rock such as sand, silt and clay C Horizon sits atop bedrock and is made up of mostly weathered rock fragments · Soil and bedrock · Thin layer of poorly indurated materials on a more or less solid base, very different mechanics and fluid flow properties · Soil properties can vary dramatically Risks · ·
Sinkholes: Karst or salt mining and hydrocarbon in salt caverns Landslides: can use computer simulation to model landslides using infiltration, seepage, soil mechanics, non-linear constitutive relationships
Role of Geotechnical Engineers · Site characterisation: stability, durability, side effects · Risk assessment: earthquakes, landslides, sinkholes, liquefaction, debris flows, rock falls, non-intuitive impact of engineering measures · Construction/restoration · Water capture, storage and control (e.g. flood control) · Energy extraction and storage · Sustainability, environmental impact and harmony with the natural environment (aesthetics) · Design and implementation of embankments, tunnels, dikes and levees, channels, reservoirs, landfills, geothermal processes · Monitoring and maintenance of engineered systems · Modelling, simulation and uncertainty analysis (e.g. forecasting and predictions) Soil Mechanics vs. Geomechanics · Consolidated vs. unconsolidated · Drill path and well design · Injection (fracture pressure) and production schemes (compaction) · Pressure management · Hydraulic fracture design: orientation and extent · Assessment of operation induced compaction and thermal strains · Re-activation of faults · Fines production · Evolution of permeability over time and Volumetrics · Directional/tectonic stresses vs. topography and engineering induced stresses Reservoir Geomechanics · Reservoir characterisation · Drilling · Stimulation · Reservoir engineering · Production · Injection
Problem Solving to Engineering Design General Problem Solving – IDEAL Framework · Identify · Define · Explore 3
· ·
Act Learn
Scientific Method · Ask a question · Do background research · Construct a hypothesis and the resulting prediction you will be testing (predictions must be measurable) · Test your hypothesis by doing an experiment · Reproducibility · Analyse the data and interpret the results · Conclusion Induction vs Deduction Induction · Precedence based inferences · Trial and error Deduction · Hypothesis-driven knowledge discovery
2.
Engineering Design
An engineering solution is the optimum solution, the end result, that taking many factors into account, is most desirable.
Engineering Design Process · · · · ·
3.
Identify problem Structure problem Generate proposals Evaluate proposals Communicate solution
Run-Off Modelling
· · ·
Stochastic Rainfall model: Models rainfall over time Catchment Rainfall-Runoff Model: Models inflow to water storage from rainfall over time Reservoir Model: Water storage over time
4
Single-Store Model · · ·
𝑞𝑐 = 𝑒𝑣𝑒𝑛𝑡 𝑟𝑢𝑛𝑜𝑓𝑓 𝑟𝑐 = 𝑟𝑢𝑛𝑜𝑓𝑓 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = 𝑝𝑟𝑜𝑝. 𝑜𝑓 𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 𝑏𝑒𝑐𝑜𝑚𝑚𝑖𝑛𝑔 𝑟𝑢𝑛𝑜𝑓𝑓 𝑝 = 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑡𝑖𝑜𝑛
·
𝜃 = 𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 =
·
𝑛 = 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦 =
𝑉𝑣𝑜𝑖𝑑
· · · · · · · · · ·
𝑖 = 𝑖𝑛𝑓𝑖𝑙𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑚/𝑑) 𝑞 = 𝑡𝑜𝑡𝑎𝑙 𝑟𝑢𝑛𝑜𝑓𝑓 𝑑 = 𝑑𝑟𝑎𝑖𝑛𝑎𝑔𝑒 = 𝑏𝑎𝑠𝑒𝑓𝑙𝑜𝑤 𝑒 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑒𝑣𝑎𝑝𝑜𝑡𝑟𝑎𝑛𝑠𝑝𝑖𝑟𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 (𝑚𝑚/𝑑) 𝐷𝑠𝑜𝑖𝑙 = 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑠𝑜𝑖𝑙 𝑙𝑎𝑦𝑒𝑟 𝑃𝐸𝑇 = 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑣𝑎𝑝𝑜𝑡𝑟𝑎𝑛𝑠𝑝𝑖𝑟𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 (𝑚𝑚/𝑑) 𝜃𝑓𝑐𝑝 = 𝑓𝑖𝑒𝑙𝑑 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝜃𝑤𝑝 = 𝑤𝑖𝑙𝑡𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑠𝑜𝑖𝑙 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑏𝑒𝑙𝑜𝑤 𝑤ℎ𝑖𝑐ℎ 𝑝𝑙𝑎𝑛𝑡𝑠 𝑎𝑟𝑒 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑠𝑡𝑟𝑒𝑠𝑠𝑒𝑑 𝐾𝑑𝑟𝑎𝑖𝑛 = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑠𝑜𝑖𝑙 𝑑𝑟𝑎𝑖𝑛𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 (𝑚𝑚/𝑑)
𝑉𝑤𝑎𝑡𝑒𝑟 𝑉𝑡𝑜𝑡𝑎𝑙
𝑉𝑡𝑜𝑡𝑎𝑙
Field capacity (fcp) is the amount of soil moisture/water content held in the soil after excess water has drained away and the rate of downward movement has decreased. This usually takes 2-3 days after rain/irrigation in pervious soils of uniform structure and texture. Wilting point (wp) is the minimal point of soil moisture the plant requires to not wilt. Event Runoff and Infiltration 𝑞𝑠 = 𝑟𝑐 𝑝 𝑟𝑐 = (
𝜃 − 𝜃𝑓𝑐𝑝 ) 𝑛 − 𝜃𝑓𝑐𝑝
𝑖 = 𝑝 − 𝑞𝑠 Actual Evapotranspiration 𝑃𝐸𝑇, 𝜃 − 𝜃𝑤𝑝 ), 𝑒 = 𝑃𝐸𝑇 ( 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 − 𝜃𝑤𝑝 0, {
𝜃 > 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 𝜃𝑤𝑝 < 𝜃 ≤ 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 𝜃 ≤ 𝜃𝑤𝑝
Drainage & Baseflow
𝑑={
𝑘𝑑𝑟𝑎𝑖𝑛 (
𝜃 − 𝜃𝑓𝑐𝑝 ), 𝑛 − 𝜃𝑓𝑐𝑝
0,
𝜃 > 𝜃𝑓𝑐𝑝 𝜃 ≤ 𝜃𝑓𝑐𝑝
Total Runoff 𝑞 = 𝑞𝑠 + 𝑑 → 𝜃𝑡+1 = 𝜃𝑡 +
𝑖−𝑒−𝑑 Δ𝑡 𝐷𝑠𝑜𝑖𝑙
Two-Store Model The two-store model does not assume that drainage and baseflow occur simultaneously.
5
Introduction to Geotechnical Engineering...................................................................................................... 3 Problem Solving to Engineering Design ............................................................................................................. 3
2.
Engineering Design ......................................................................................................................................... 4 Engineering Design Process................................................................................................................................ 4
3.
Run-Off Modelling .......................................................................................................................................... 4 Single-Store Model ............................................................................................................................................. 5 Two-Store Model................................................................................................................................................ 5
4.
Site Investigations ........................................................................................................................................... 6 Geotechnical Site Investigations ........................................................................................................................ 6 Geotechnical Engineering Projects ..................................................................................................................... 6
5.
Water and Stresses in Soil & Rock .................................................................................................................. 7 Introduction to Porous Media ............................................................................................................................ 7 Hydrostatic Porewater and Lithostatic Pressure ................................................................................................ 7 Stress and Strain Measurement ......................................................................................................................... 8 Capillarity ........................................................................................................................................................... 8
6.
Flow in Porous Media and Darcy's Law ........................................................................................................ 10 Stokes Lubrication Equation ............................................................................................................................. 10 Permeability (k) ................................................................................................................................................ 11 Darcy Velocity................................................................................................................................................... 12 Conservation of Mass and Darcy’s Law ............................................................................................................ 12
7.
Measurement of Hydraulic Conductivity ...................................................................................................... 13 Bernoulli’s equation ......................................................................................................................................... 13 Darcy’s Law....................................................................................................................................................... 13 Determination of k by laboratory testing ......................................................................................................... 14 Field permeability testing................................................................................................................................. 14 Permeability Exercise ....................................................................................................................................... 15
8.
Flow Net Fundamentals ................................................................................................................................ 15 Permeability and Pressure Driven Flow ........................................................................................................... 15 Pressure Contours ............................................................................................................................................ 16
9.
Flow Nets – Examples ................................................................................................................................... 17 Construction of Flow Nets ................................................................................................................................ 17 Calculation of Seepage and Pore Water Pressure ............................................................................................ 18 Example Problem ............................................................................................................................................. 19
10.
Water Supply Systems ............................................................................................................................. 20
Open-Channel Flow .......................................................................................................................................... 20 Pipe-Line Design ............................................................................................................................................... 20 Pump Performance Curves............................................................................................................................... 21 11.
Seepage Force and Quicksand ................................................................................................................. 21
Seepage Force .................................................................................................................................................. 21 1
Quicksand ......................................................................................................................................................... 23 Calculations Using Flow Nets ........................................................................................................................... 23 12.
Control of Seepage and Filters ................................................................................................................ 25
Why do we control seepage ............................................................................................................................. 25 Methods to control seepage ............................................................................................................................ 25 Filters ................................................................................................................................................................ 25 13.
Landslides ................................................................................................................................................ 26
Types of Slides .................................................................................................................................................. 26 Rheology and Triggering................................................................................................................................... 26 Numerical simulation ....................................................................................................................................... 28 Triggering of landslides .................................................................................................................................... 28 Landslide overview ........................................................................................................................................... 28 14.
Slope Stability .......................................................................................................................................... 28
Terminology ..................................................................................................................................................... 28 Limit Equilibrium and Factor of Safety (FoS) .................................................................................................... 29 Mohr-Coulomb Failure Criterion ...................................................................................................................... 29 15.
Method of Slices ...................................................................................................................................... 30
Introduction to the Method of Slices ............................................................................................................... 30 Bishop’s Simplified Method ............................................................................................................................. 31 Example – Bishop’s Method ............................................................................................................................. 32 16.
Slope Stabilisation Methods .................................................................................................................... 33
Slope Stabilisation Projects .............................................................................................................................. 33 Stabilisation of Slopes ...................................................................................................................................... 33 17.
Embankment Dams ................................................................................................................................. 34
Types of Embankment Dams ............................................................................................................................ 34 Design Considerations ...................................................................................................................................... 35 Seepage through Embankment Dams .............................................................................................................. 35 18.
Practical Examples of Slope Stability Assessment ................................................................................... 36
Ground Models ................................................................................................................................................ 36 Slope Stability Case Study: Wye River Bushfires .............................................................................................. 37 The Concept of Risk Assessment in Slope Stability .......................................................................................... 38 Qualitative Risk Assessment ............................................................................................................................. 39 Quantitative risk assessment ........................................................................................................................... 39 Risk Mitigation Measures ................................................................................................................................. 40 Hillside Construction Practice .......................................................................................................................... 40 Common Groundwater Issues in Melbourne Basements ................................................................................ 41 19.
Introduction to Numerical Modelling ...................................................................................................... 41
About Numerical Modelling ............................................................................................................................. 41 Model Verification and Validation ................................................................................................................... 42 Numerical Models in Civil Engineering ............................................................................................................. 42 Discretisation.................................................................................................................................................... 42 Basics of the Finite Element Model .................................................................................................................. 43 Summary of Numerical Modelling, Simulation and FEM ................................................................................. 43 2
1.
Introduction to Geotechnical Engineering
Shallow Subsurface · Soil layers O Horizon is the top layer at the surface which consists of surface litter (leaves, sticks), animal waste and dead organisms A Horizon (topsoil) contains organic humus which typically gives it its dark colour B Horizon (subsoil) consists of mostly inorganic rock such as sand, silt and clay C Horizon sits atop bedrock and is made up of mostly weathered rock fragments · Soil and bedrock · Thin layer of poorly indurated materials on a more or less solid base, very different mechanics and fluid flow properties · Soil properties can vary dramatically Risks · ·
Sinkholes: Karst or salt mining and hydrocarbon in salt caverns Landslides: can use computer simulation to model landslides using infiltration, seepage, soil mechanics, non-linear constitutive relationships
Role of Geotechnical Engineers · Site characterisation: stability, durability, side effects · Risk assessment: earthquakes, landslides, sinkholes, liquefaction, debris flows, rock falls, non-intuitive impact of engineering measures · Construction/restoration · Water capture, storage and control (e.g. flood control) · Energy extraction and storage · Sustainability, environmental impact and harmony with the natural environment (aesthetics) · Design and implementation of embankments, tunnels, dikes and levees, channels, reservoirs, landfills, geothermal processes · Monitoring and maintenance of engineered systems · Modelling, simulation and uncertainty analysis (e.g. forecasting and predictions) Soil Mechanics vs. Geomechanics · Consolidated vs. unconsolidated · Drill path and well design · Injection (fracture pressure) and production schemes (compaction) · Pressure management · Hydraulic fracture design: orientation and extent · Assessment of operation induced compaction and thermal strains · Re-activation of faults · Fines production · Evolution of permeability over time and Volumetrics · Directional/tectonic stresses vs. topography and engineering induced stresses Reservoir Geomechanics · Reservoir characterisation · Drilling · Stimulation · Reservoir engineering · Production · Injection
Problem Solving to Engineering Design General Problem Solving – IDEAL Framework · Identify · Define · Explore 3
· ·
Act Learn
Scientific Method · Ask a question · Do background research · Construct a hypothesis and the resulting prediction you will be testing (predictions must be measurable) · Test your hypothesis by doing an experiment · Reproducibility · Analyse the data and interpret the results · Conclusion Induction vs Deduction Induction · Precedence based inferences · Trial and error Deduction · Hypothesis-driven knowledge discovery
2.
Engineering Design
An engineering solution is the optimum solution, the end result, that taking many factors into account, is most desirable.
Engineering Design Process · · · · ·
3.
Identify problem Structure problem Generate proposals Evaluate proposals Communicate solution
Run-Off Modelling
· · ·
Stochastic Rainfall model: Models rainfall over time Catchment Rainfall-Runoff Model: Models inflow to water storage from rainfall over time Reservoir Model: Water storage over time
4
Single-Store Model · · ·
𝑞𝑐 = 𝑒𝑣𝑒𝑛𝑡 𝑟𝑢𝑛𝑜𝑓𝑓 𝑟𝑐 = 𝑟𝑢𝑛𝑜𝑓𝑓 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = 𝑝𝑟𝑜𝑝. 𝑜𝑓 𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 𝑏𝑒𝑐𝑜𝑚𝑚𝑖𝑛𝑔 𝑟𝑢𝑛𝑜𝑓𝑓 𝑝 = 𝑝𝑟𝑒𝑐𝑖𝑝𝑖𝑡𝑎𝑡𝑖𝑜𝑛
·
𝜃 = 𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 =
·
𝑛 = 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦 =
𝑉𝑣𝑜𝑖𝑑
· · · · · · · · · ·
𝑖 = 𝑖𝑛𝑓𝑖𝑙𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑚/𝑑) 𝑞 = 𝑡𝑜𝑡𝑎𝑙 𝑟𝑢𝑛𝑜𝑓𝑓 𝑑 = 𝑑𝑟𝑎𝑖𝑛𝑎𝑔𝑒 = 𝑏𝑎𝑠𝑒𝑓𝑙𝑜𝑤 𝑒 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑒𝑣𝑎𝑝𝑜𝑡𝑟𝑎𝑛𝑠𝑝𝑖𝑟𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 (𝑚𝑚/𝑑) 𝐷𝑠𝑜𝑖𝑙 = 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑠𝑜𝑖𝑙 𝑙𝑎𝑦𝑒𝑟 𝑃𝐸𝑇 = 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑣𝑎𝑝𝑜𝑡𝑟𝑎𝑛𝑠𝑝𝑖𝑟𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 (𝑚𝑚/𝑑) 𝜃𝑓𝑐𝑝 = 𝑓𝑖𝑒𝑙𝑑 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝜃𝑤𝑝 = 𝑤𝑖𝑙𝑡𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑠𝑜𝑖𝑙 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑏𝑒𝑙𝑜𝑤 𝑤ℎ𝑖𝑐ℎ 𝑝𝑙𝑎𝑛𝑡𝑠 𝑎𝑟𝑒 𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒 𝑠𝑡𝑟𝑒𝑠𝑠𝑒𝑑 𝐾𝑑𝑟𝑎𝑖𝑛 = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑠𝑜𝑖𝑙 𝑑𝑟𝑎𝑖𝑛𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 (𝑚𝑚/𝑑)
𝑉𝑤𝑎𝑡𝑒𝑟 𝑉𝑡𝑜𝑡𝑎𝑙
𝑉𝑡𝑜𝑡𝑎𝑙
Field capacity (fcp) is the amount of soil moisture/water content held in the soil after excess water has drained away and the rate of downward movement has decreased. This usually takes 2-3 days after rain/irrigation in pervious soils of uniform structure and texture. Wilting point (wp) is the minimal point of soil moisture the plant requires to not wilt. Event Runoff and Infiltration 𝑞𝑠 = 𝑟𝑐 𝑝 𝑟𝑐 = (
𝜃 − 𝜃𝑓𝑐𝑝 ) 𝑛 − 𝜃𝑓𝑐𝑝
𝑖 = 𝑝 − 𝑞𝑠 Actual Evapotranspiration 𝑃𝐸𝑇, 𝜃 − 𝜃𝑤𝑝 ), 𝑒 = 𝑃𝐸𝑇 ( 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 − 𝜃𝑤𝑝 0, {
𝜃 > 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 𝜃𝑤𝑝 < 𝜃 ≤ 𝜃𝑠𝑡𝑟𝑒𝑠𝑠 𝜃 ≤ 𝜃𝑤𝑝
Drainage & Baseflow
𝑑={
𝑘𝑑𝑟𝑎𝑖𝑛 (
𝜃 − 𝜃𝑓𝑐𝑝 ), 𝑛 − 𝜃𝑓𝑐𝑝
0,
𝜃 > 𝜃𝑓𝑐𝑝 𝜃 ≤ 𝜃𝑓𝑐𝑝
Total Runoff 𝑞 = 𝑞𝑠 + 𝑑 → 𝜃𝑡+1 = 𝜃𝑡 +
𝑖−𝑒−𝑑 Δ𝑡 𝐷𝑠𝑜𝑖𝑙
Two-Store Model The two-store model does not assume that drainage and baseflow occur simultaneously.
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