2.The average of total head (H) on a weekly basis at two depths, z1 = -100 cm and z2 = -200 cm below ground surface (z = 0 cm), are presented as follows.Week 1H1 at z1 (cm) -150H2 at z2 (cm) -210-170 -160 -145 -120 -150 -170 -185 -220 -250-220 -235 -235 -230 -260 -265 -270 -275 -280The relationship between K and ψ is given as K (cm/d) = 200*|ψ|-2 where ψ is the average matric suction between two depths. Perform the following tasks.(1)Compute matric suction (cm), hydraulic conductivity (cm/d), head difference (H2-H1, cm), darcy flux (cm/d), and flow rate (cm3/d) per unit surface area (1 m2) between two depths for 10 weeks. Use the template worksheet posted in BlackBoard for your convenience.(2)Compute the total volume (cm3) of water passing between z1 and z2 vertically through a unit area (1 m2) during 10 weeks (if a flow rate is negative, moisture flows toward a negative direction).
1. Matric suction was measured in a field site as follows. Assuming that the soil parameters are same as Question 1, perform the following tasks. Depth, cm 0 Suction, cm -240 -220 -150 -133 -115 -90 -81 -73 -60 -51 -43 -35 -30 -12 -5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 (1) Plot a profile for water content in x-axis vs. depth (cm) in y-axis. Use the Brooks-Corey model with a fitting parameter (λ) = 2.5 and air-entry pressure head = -10 cm for the depth-water content profile. (2) Plot a profile for water content in x-axis vs. depth (cm) in y-axis. Use the van Genuchten model with the parameters provided in Question 1. (3) Compare the total water volume (cm3) held in this soil profile per unit surface area (1 m2) using two models (Hint: Compute average water content between two depths and repeat for all depth intervals. Then the sum of [average water content × depth interval] is the available water volume per unit area. 2. The average of total head (H) on a weekly basis at two depths, z1 = -100 cm and z2 = -200 cm below ground surface (z = 0 cm), are presented as follows. Week 1 H1 at z1 (cm) -150 H2 at z2 (cm) -210 -170 -160 -145 -120 -150 -170 -185 -220 -250 2 3 4 5 6 7 8 9 10 -220 -235 -235 -230 -260 -265 -270 -275 -280 The relationship between K and ψ is given as K (cm/d) = 200*|ψ|-2 where ψ is the average matric suction between two depths. Perform the following tasks. (1) Compute matric suction (cm), hydraulic conductivity (cm/d), head difference (H2-H1, cm), darcy flux (cm/d), and flow rate (cm3/d) per unit surface area (1 m2) between two depths for 10 weeks. Use the template worksheet posted in BlackBoard for your convenience. (2) Compute the total volume (cm3) of water passing between z1 and z2 vertically through a unit area (1 m2) during 10 weeks (if a flow rate is negative, moisture flows toward a negative direction). 1 CVE 464/564 Groundwater Hydrology – HW2 (100) Due: 6 pm, Sep 22 (W), 2021 3. The soil characteristics of two soils were determined from a lab test as follows. Saturated hydraulic Residual Air-entry Soil Porosity conductivity soil water content pressure λ Sand 0.43 7.01 m/d 0.05 -30 cm 2.0 Clay 0.38 0.05 m/d 0.07 -125 cm 0.1 Assume two soils are vertically layered (sand is in the upper layer) and the water table is located at z = 0 cm (datum in this problem). Two soils are unsaturated and have the thickness of 70 and 80 cm under a hydrostatic equilibrium, respectively. Perform the following tasks while showing your calculation steps in your answer sheet (or upload worksheet in BlackBoard HW2). Use the BC model to compute water content. Students can plot directly in the provided graph below. (1) Plot a depth vs. suction profile. (2) Plot a depth vs. water content profile 5. The soil with a 230 cm depth has the saturated water content of 0.42, the residual water content of 0.15, and the saturated hydraulic conductivity of 12 cm/d. The VG model parameters are n = 3.1 and α = 0.05 cm-1, respectively. For two different steady state q0 = 1 cm/d and q0 = 10 cm/d, compute matric suction in the ground surface and draw approximate suction profiles (suction in x-axis and depth in y-axis). Assume the ground water table is at the bottom of a soil layer. Hint: page 23 of Module 2 slides. 6. Parameters of sandy clay are given as follows. Air-entry Saturated hydraulic Porosity Effective porosity pressure head conductivity 0.430 0.321 0.239 m 0.014 m/day For the following tasks, use the Green-Ampt method assuming an initial effective saturation (Se) was 30%. (1) Compute and plot F(t) and f(t) from 0 to 12 hours for every 2 hours. Assume there is negligible ponding. (2) Compute the ponding time and the total depth (Fp) of water infiltrated at the time of ponding under different rainfall intensities, 1, 3, and 5 cm/h. #3template GivenCompute WeekH1H2ψ1ψ2mean(ψ)KH2-H1Z2-Z1q=-KiQ=qAQ_7day cmcmcmcmcmcm/dcmcmcm/dcm3/dcm3 1-150-210 2-170-220 3-160-235 4-145-235 5-120-230 6-150-260 7-170-265 8-185-270 9-220-275 10-250-280 Modeling experties U N G TA E K I M C V E , C L E V E L A N D S TAT E U N I V E R S I T Y 2. Unsaturated Zone CVE 564 GROUNDWATER HYDROLOGY Module 2 covers Chapter 6 of Fetter’s textbook Unsaturated zone (Vadose zone) 2 * * Capillary fringe: 0< s="">< 1="" saturated="" zone="" s="1" ks="K" saturated="" unsaturated="" zone="" 0="" ≤="" s="">< 1="" k(ψ)="K" unsaturated="function" of="" matric="" suction="" ψ="" 02_unsaturated="" flow="" in="" soil.wmv="" ▪unsaturated="" zone="" o="" water="" held="" between="" soil="" grains="" by="" capillary="" force.="" o="" when="" further="" drying="" or="" draining="" (higher="" matric="" suction),="" capillary="" water="" disappears="" o="" thin="" film="" of="" water="" remains="" at="" last="" (field="" capacity,="" residual="" water)="" tutorvista.com="" drying="" 3="" characteristics="" of="" unsaturated="" zone="" ▪unsaturated="" zone="" o="" water="" content="" is="" less="" than="" saturated="" water="" content.="" o="" precipitation="" flows="" through="" this="" zone="" and="" recharges="" aquifers.="" o="" water="" content="" and="" movement="" in="" this="" zone="" is="" controlled="" by="" capillary="" forces.="" note)="" matric="" suction="capillary" force="capillary" pressure="tension" head="suction" o="" water="" rise="" due="" to="" surface="" tension="" of="" water-air="" interface="" (capillarity)="" o="" smaller="" space="" between="" soil="" particles="stronger" capillary="" force!="" example:="" clay="" vs.="" sand="" 4="" characteristics="" of="" unsaturated="" zone="" 02_capillary="" rise.wmv="" ▪capillary="" force="" o="" water="" rise="" determined="" by="" the="" radius="" of="" tube="" σ:="" surface="" tension="" of="" fluid="" [mt-2]="" r:="" radius="" of="" the="" tube="" [l]="" o="" compare="" water="" rises="" using="" different="" radii="" of="" tubes="" o="" for="" a="" fluid,="" capillary="" force="" is="" a="" function="" of="" a="" tube="" radius="" analogous="" to="" pore="" size!!="" o="" therefore,="" soil="" moisture="" function="" in="" this="" zone="" is="" subject="" to="" soil="" medium!!="" 2="" cos="" ch="" gr="" ="" ="" ="water" surface="" with="" contact="" angle="" θ="" hc="" r="" 5="" characteristics="" of="" unsaturated="" zone="" ▪pressure="" head="" (matric="" suction)="" o="" negative="" pressure="" (matric="" suction,="" ψ="" [psi]),="" less="" than="" atmospheric="" pressure="" o="" more="" saturated="" soil="" has="" less="" matric="" suction="" o="" soil="" moisture="" profile,="" therefore,="" can="" be="" expressed="" as="" a="" function="" of="" ψ,="" θ(ψ)="" o="" saturated="" hydraulic="" conductivity="" (ks)="" is="" no="" longer="" effective,="" but="" k(θ)="" or="" k(ψ)="" characteristics="" of="" unsaturated="" zone="" porous="" membrane="" to="" initiate="" capillary="" suction="" pressure="" gauge="" 6="" tensiometer="" ψ="" is="" called="" as="" capillary="" pressure,="" air-entry="" pressure,="" matric="" suction,="" capillary="" suction,="" suction="" pressure,="" suction="" head,="" soil="" moisture="" tension,="" tension="" head,="" etc.="" ▪distribution="" of="" soil="" moisture="" o="" soil="" profile="" undergoing="" dry="" and="" wet="" cycles="" o="" minimum="" soil="" moisture="" present="" at="" residual="" water="" content="" (or="" irreducible="" water="" content):="" θr="" o="" note="" that="" clay="" has="" higher="" residual="" water="" content="" due="" to="" its="" unique="" properties="" (e.g.,="" large="" surface="" area,="" texture,="" soil="" structure,="" longer="" water="" residence,="" …)="" 7="" characteristics="" of="" unsaturated="" zone="" when="" wetting="" ▪water="" holding="" properties="" for="" various="" soils="" o="" wilting="" point:="" first="" time="" appearance="" of="" water="" content="" available="" for="" plants="" below="" which="" plants="" wilt="" and="" die="">< θr),="" if="" plants="" no="" longer="" recover="" in="" 12="" hours="" (fig="" 6.5)="" o="" field="" capacity:="" water="" content="" at="" which="" the="" gravity="" force="" of="" water="" is="" equal="" to="" water="" surface="" tension="" (i.e.,="" water="" does="" not="" drained="" by="" gravity="" any="" more),="" called="" specific="" retention.="" o="" field="" capacity="" varies="" by="" time="" due="" to="" different="" recharging="" conditions="" (dry="" or="" wet="" seasons)="" o="" plants="" may="" prefer="" …="" 8="" characteristics="" of="" unsaturated="" zone="" ▪hysteresis="" o="" a="" unique="" pattern="" of="" saturation="" history="" of="" the="" soil="" o="" wetting="" and="" drying="" (drainage)="" branches="" due="" to="" air-entrapment="" in="" the="" soil="" and="" variable="" pore="" radii="" of="" soils="" o="" hysteresis="" depends="" on="" soil="" types="" and="" is="" hard="" to="" incorporate="" in="" hydrologic="" modeling="" o="" for="" a="" given="" water="" content,="" capillary="" pressures="" are="" different="" subject="" to="" hysteresis="" o="" highly="" nonlinear="" relationship="" between="" (matric="" suction)="" &="" (water="" content)="" &="" (hydraulic="" conductivity)="" 9="" characteristics="" of="" unsaturated="" zone="" ▪soil="" water="" characteristic="" curve="" o="" represents="" relationship="" between="" matric="" suction="" and="" water="" content;="" water="" content="" and="" hydraulic="" conductivity;="" or="" ψ="" and="" k="" o="" after="" capillary="" fringe,="" air="" begins="" to="" enter="" the="" soil="" pores,="" called="" air-entry="" tension="" (or="" pressure)="" o="" air-entry="" pressure="" varies="" for="" soil="" types.="" o="" note="" the="" water="" table="" has="" a="" atmospheric="" pressure,="" i.e.,="" matric="" suction="0" 10="" ψ(θ)="" k(θ)="" at="" capillary="" fringe="" θ="" characteristics="" of="" unsaturated="" zone="" capillary="" pressure="Matric" suction="" (ψ)="" ▪brooks="" and="" corey="" model="" (bc)="" o="" based="" on="" many="" measurements="" and="" numerical="" studies,="" bc="" suggested="" the="" following="" (brooks="" and="" corey,="" 1964)="" solve="" for="" ψ="" for="" practical="" use="" se="1" when="" |ψ|="" ≤="" |ψb|,="" why?="" ψb:="" air-entry="" pressure="" (low="" in="" sandy="" soil="" and="" high="" for="" clays)="" λ:="" model="" fitting="" parameter="" for="" the="" particular="" soil="" se:="" effective="" saturation="" (0="" ≤="" se="" ≤="" 1)="" note)="" see="" dingman="" ch="" 6.3,="" chow="" et="" al="" ch="" 4.3="" hydraulics="" of="" unsaturated="" zone="" se="" 11="" |ψ|="" cm="" water="" |ψ|=""> |ψb| ? = ?? ?? 1/? ▪Brooks and Corey model (BC) – cont. o kr: ratio of unsaturated K(ψ) to saturated Ks at a given matric suction Or o Read Green-Ampt infiltration equation for more detail (Chow et al. Ch 4.3) Se 12 Hydraulics of Unsaturated Zone ? ? = ?? ∙ ?? 2+3? ? ▪Brooks and Corey model (BC) o Soil water retention parameters (Rawls, Brakensiek and Miller, 1983) - Chow et al. Table 4.3.1 - Rawls, W.J., D.L. Brakensiek, and N. Miller. 1983. Green–Ampt infiltration parameters from soils data. J. Hydraul. Eng. 109:62–70. 13 Hydraulics of Unsaturated Zone n=θs |ψb| cm water ▪Brooks and Corey model (BC) o Soil water retention parameters (Carsel and Parrish, 1988) - Developing joint probability distributions of soil water retention characteristics. WATER RESOURCES RESEARCH, VOL. 24, NO. 5, P. 755, 1988 Note) Two tables are very close. 14 Hydraulics of Unsaturated Zone |ψb| ▪Brooks