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Civil Engineering

Research Article Volume 2 Issue 6

Porosity and Tuotorsity Effect on Flow Pressure in Lacustrine Deposition Applying Predictive Models

Eluozo SN,1 Oba KM2

1Department of Civil Engineering, Port Harcourt Rivers State of Nigeria, Nigeria
2Department of Civil Engineering, University of Sciences and Technology, Nigeria

Correspondence: Eluozo SN, Department of Civil Engineering, Subaka Nigeria Limited Port Harcourt Rivers State of Nigeria, Nigeria

Received: March 27, 2017 | Published: June 8, 2017

Citation: Eluozo SN, Oba KM (2017) Porosity and Tuotorsity Effect on Flow Pressure in Lacustrine Deposition Applying Predictive Models. MOJ Civil Eng. 2017;2(6):195-200. DOI: 10.15406/mojce.2017.02.00053

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Abstract

This paper studies the rate of permeability passage through Tuotorsity of fluid flow at different soil strata. The rate of fluid flow depends on the permeability of the soil. Such condition has other influences. However, this study monitors fluid flow reflection on the rate of soil permeability through Tuotorsity in the formation. The penetration of fluid is influenced by the structural stratification of the formation. Tuotorsity flows are determined by the structural depositional setting of the soil intercedes. Monitoring the fluid flow condition in lacustrine deposition was possible through the application of mathematical modeling method. The study monitored the permeable condition of the formation to phreatic zone through the effect of Tuotorsity of the formation. The developed model was simulated to express the rate of fluid flow through Tuotorsity to the phreatic zone. Theoretical values were generated from the developed model. The study expressed the rate of permeability through Tuotorsity flow to the phreatic zone. It was confirmed that the permeability was increasing with respect to change in depth under plug flow condition. Subject to this condition, the study produced 4.11E-05, which implies that the condition developed flow based on the deposition from Tuotorsity. This expression implies that the stated parameter influences the low yield rate of phreatic aquifers in the study area. Experts can now use the developed model from this study as a tool in exploitation of groundwater by monitoring the rate of Tuotorsity flow in the study location.

Keywords: Porosity; Tuotorsity; Lacustrine; Predictive model

Introduction

In years past, it has been noted that scaling laws for seepage velocity has been established and applied, but most researchers are yet to understand whether it is the Darcy’s permeability (hydraulic conductivity) or the hydraulic, expressed to be gradient that determines the function of gravity. Thus this has not been thoroughly addressed properly. This concern was investigated by Gooding’s,1 as he pointed out the diverse concepts for scaling flow velocity. Butterfield2 & Dean3 also discussed this issue. Other parameters such as permeability were considered by Pokrovsky & Fyodorov;4 Cargill & Ko;5 Tan & Scott.6 Recently, Singh & Gupta7 including other researcher’s defined permeability (k) to be directly proportional to gravity and hydraulic gradient (i).This implies that gradient is independent of gravity. Furthermore, it explains the reason why seepage velocity has a scaling law of N (m p v = N v).It has been observed that there is an alternative expression for the improvement of seepage velocity in a centrifuge. Schofield,8 Hussaini et al.,9 Goodings,10 & Taylor11 were able to further express how permeability becomes independent of gravity, thus developed through mathematical expressions. Drainage, evaporation and water-uptake are some of the parameters with relationship that determines the rate of water flow through the soil, which plays a significant role.12,13 More so, the relationship of three parameters such as (water, gas and solid) in three phases of the soil are influenced by properties such as texture, structure, biological activity, weather and soil management.14 Relating it in terms of porous media, it can be grouped in volume and function; this has been observed to be of tremendous importance to assimilate the processes associated with water, air and heat transport in soils.15-17 Meanwhile, the volume of soil is influenced by mechanical stresses (e.g. tillage-induced soil compaction, Blackwell et al.;18 Horn et al.;19 Horn et al.;20 Ball et al.;21 McNabb et al.22 and internal forces (e.g. wetting and drying cycles, Peng & Horn19; Bartoli et al.20). The quantity changes and are controlled by such mechanical stability of the soil or through the main in comparison with previous internal stresses. Recurring swelling and shrinkage develop tensile and shear induced crack formation in blocky structure thereafter in a sub-angular blocky structure (Horn & Smucker,14). The influences from soil compaction on soil structures have been investigated by several researchers. Finally it is also observed that soils are able to shrink & swell.14

Governing Equation

φ ¯ K t = Q n e K 2 Z 2 Λ ¯ K Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaiaaykW7juaGdaWcaaGcbaqcLbsacqGHciIT caWGlbaakeaajugibiabgkGi2kaadshaaaGaaGPaVlaaykW7cqGH9a qpcaaMc8UaaGPaVlaaykW7caaMc8Ecfa4aaSaaaOqaaKqzGeGaamyu aaGcbaqcLbsacaWGUbqcfa4aaSbaaSqaaKqzGeGaamyzaaWcbeaaaa qcLbsacaaMc8Ecfa4aaSaaaOqaaKqzGeGaeyOaIyRaam4saSWaaWba aeqabaqcLbmacaaIYaaaaaGcbaqcLbsacqGHciITcaWGAbWcdaahaa qabeaajugWaiaaikdaaaaaaKqzGeGaaGPaVlaaykW7cqGHsislcaaM c8UaaGPaVNqbaoaanaaakeaajugibiabfU5ambaajuaGdaWcaaGcba qcLbsacqGHciITcaWGlbaakeaajugibiabgkGi2kaadQfaaaaaaa@6E2D@ (1)

Nomenclature
K             =              Permeability [LT-1]
Q             =              Flow rate [LT-1]
ne            =              Porosity [-]
Λ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaacq qHBoataaaaaa@377C@    =   Void ratio [-]
T             =              Time [T]
Z              =              Depth [L]

φ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaiaaykW7aaa@3A76@            = Linear velocity [LT-1]

Let K=T,Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlb GaaGPaVlaaykW7cqGH9aqpcaaMc8UaaGPaVlaadsfacaGGSaGaamOw aaaa@40EF@

φ ¯ T 1 Y= Q n e T Z 1 Λ ¯ T Z 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaiaadsfalmaaCaaabeqaaKqzadGaaGymaaaa jugibiaadMfacaaMc8UaaGPaVlabg2da9iaaykW7caaMc8Ecfa4aaS aaaOqaaKqzGeGaamyuaaGcbaqcLbsacaWGUbWcdaWgaaqaaKqzadGa amyzaaWcbeaaaaqcLbsacaWGubGaamOwaSWaaWbaaeqabaqcLbmaca aIXaaaaiaaykW7caaMc8EcLbsacqGHsislcaaMc8UaaGPaVNqbaoaa naaakeaajugibiabfU5ambaacaWGubGaamOwaSWaaWbaaeqabaqcLb macaaIXaaaaaaa@5CE1@ (2)
φ ¯ T 1 T = Q n e Z 1 Z Λ ¯ Z 1 Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaKqbaoaalaaakeaajugibiaadsfalmaaCaaa beqaaKqzadGaaGymaaaaaOqaaKqzGeGaamivaaaacaaMc8UaaGPaVl abg2da9iaaykW7caaMc8UaaGPaVNqbaoaalaaakeaajugibiaadgfa aOqaaKqzGeGaamOBaKqbaoaaBaaaleaajugWaiaadwgaaSqabaaaaK qbaoaalaaakeaajugibiaadQfalmaaCaaabeqaaKqzadGaaGymaaaa aOqaaKqzGeGaamOwaaaacaaMc8UaaGPaVlaaykW7cqGHsislcaaMc8 UaaGPaVNqbaoaanaaakeaajugibiabfU5ambaajuaGdaWcaaGcbaqc LbsacaWGAbWcdaahaaqabeaajugWaiaaigdaaaaakeaajugibiaadQ faaaaaaa@644F@ (3)
φ ¯ T 1 T = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaKqbaoaalaaakeaajugibiaadsfalmaaCaaa beqaaKqzadGaaGymaaaaaOqaaKqzGeGaamivaaaacaaMc8UaaGPaVl aaykW7caaMc8Uaeyypa0JaaGPaVlaaykW7cqaHYoGylmaaCaaabeqa aKqzadGaaGOmaaaaaaa@4C83@ (4)
Q n e Z 1 Z = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamyuaaGcbaqcLbsacaWGUbqcfa4aaSbaaSqaaKqzadGa amyzaaWcbeaaaaqcfa4aaSaaaOqaaKqzGeGaamOwaSWaaWbaaeqaba qcLbmacaaIXaaaaaGcbaqcLbsacaWGAbaaaiaaykW7caaMc8UaaGPa VlaaykW7cqGH9aqpcaaMc8UaaGPaVlabek7aITWaaWbaaeqabaqcLb macaaIYaaaaaaa@5010@ (5)
Λ ¯ Z 1 Z = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqGHsi slcaaMc8UaaGPaVNqbaoaanaaakeaajugibiabfU5ambaajuaGdaWc aaGcbaqcLbsacaWGAbWcdaahaaqabeaajugWaiaaigdaaaaakeaaju gibiaadQfaaaGaaGPaVlaaykW7caaMc8Uaeyypa0JaaGPaVlaaykW7 cqaHYoGyjuaGdaahaaWcbeqaaKqzadGaaGOmaaaaaaa@4FDC@ (6)
[ Q n e Λ ¯ ] Z 1 Z = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aamWaaO qaaKqbaoaalaaakeaajugibiaadgfaaOqaaKqzGeGaamOBaKqbaoaa BaaaleaajugWaiaadwgaaSqabaaaaKqzGeGaeyOeI0IaaGPaVNqbao aanaaakeaajugibiabfU5ambaaaOGaay5waiaaw2faaKqbaoaalaaa keaajugibiaadQfalmaaCaaabeqaaKqzadGaaGymaaaaaOqaaKqzGe GaamOwaaaacaaMc8UaaGPaVlaaykW7cqGH9aqpcaaMc8UaaGPaVlab ek7aITWaaWbaaeqabaqcLbmacaaIYaaaaaaa@56CD@ (7)
φ ¯ dK dt = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaKqbaoaalaaakeaajugibiaadsgacaWGlbaa keaajugibiaadsgacaWG0baaaiaaykW7caaMc8UaaGPaVlaaykW7cq GH9aqpcaaMc8UaaGPaVlabek7aITWaaWbaaeqabaqcLbmacaaIYaaa aaaa@4C56@   (8)
φ ¯ d 2 d t 2 = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaKqbaoaalaaakeaajugibiaadsgajuaGdaah aaWcbeqaaKqzadGaaGOmaaaaaOqaaKqzGeGaamizaiaadshajuaGda ahaaWcbeqaaKqzadGaaGOmaaaaaaqcLbsacaaMc8UaaGPaVlaaykW7 caaMc8Uaeyypa0JaaGPaVlaaykW7cqaHYoGylmaaCaaabeqaaKqzad GaaGOmaaaaaaa@515F@   (9)
Q n e dK dz = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamyuaaGcbaqcLbsacaWGUbqcfa4aaSbaaSqaaKqzadGa amyzaaWcbeaaaaqcfa4aaSaaaOqaaKqzGeGaamizaiaadUeaaOqaaK qzGeGaamizaiaadQhaaaGaaGPaVlaaykW7caaMc8UaaGPaVlabg2da 9iaaykW7caaMc8UaeqOSdi2cdaahaaqabeaajugWaiaaikdaaaaaaa@4FDD@ (10)
Λ ¯ dK dz = β 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa0aaaO qaaKqzGeGaeu4MdWeaaKqbaoaalaaakeaajugibiaadsgacaWGlbaa keaajugibiaadsgacaWG6baaaiaaykW7caaMc8UaaGPaVlabg2da9i aaykW7caaMc8UaeqOSdiwcfa4aaWbaaSqabeaajugWaiaaikdaaaaa aa@4B17@   (11)
d 2 z=[   β 2 φ ¯ ]=dz MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGKb qcfa4aaWbaaSqabeaajugWaiaaikdaaaqcLbsacaWG6bGaaGPaVlaa ykW7caaMc8Uaeyypa0JaaGPaVlaaykW7caaMc8Ecfa4aamWaaOqaaK qbaoaalaaakeaajugibiaabccacqaHYoGyjuaGdaahaaWcbeqaaKqz adGaaGOmaaaaaOqaaKqbaoaanaaakeaajugibiabeA8aQbaaaaaaki aawUfacaGLDbaajugibiaaykW7caaMc8UaaGPaVlabg2da9iaaykW7 caaMc8UaamizaiaadQhaaaa@5CD0@ (12)
d 2   β 2 φ ¯ dz MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa8qaaO qaaKqzGeGaamizaSWaaWbaaeqabaqcLbmacaaIYaaaaaWcbeqabKqz GeGaey4kIipacaaMc8UaaGPaVlabgkHiTiaaykW7caaMc8UaaGPaVN qbaoaapeaakeaajuaGdaWcaaGcbaqcLbsacaqGGaGaeqOSdi2cdaah aaqabeaajugWaiaaikdaaaaakeaajuaGdaqdaaGcbaqcLbsacqaHgp GAaaaaaaWcbeqabKqzGeGaey4kIipacaaMc8UaamizaiaadQhaaaa@5457@ (13)
dz=   β 2 φ ¯ z+ C 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGKb GaamOEaiabg2da9iaaykW7caaMc8Ecfa4aaSaaaOqaaKqzGeGaaeii aiabek7aITWaaWbaaeqabaqcLbmacaaIYaaaaaGcbaqcfa4aa0aaaO qaaKqzGeGaeqOXdOgaaaaacaWG6bGaaGPaVlaaykW7cqGHRaWkcaaM c8UaaGPaVlaadoealmaaBaaabaqcLbmacaaIXaaaleqaaaaa@500F@ (14)
dz =   β 2 φ ¯ zdz+ C 1 dz MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aa8qaaO qaaKqzGeGaamizaiaadQhaaSqabeqajugibiabgUIiYdGaaGPaVlaa ykW7cqGH9aqpcaaMc8UaaGPaVlaaykW7juaGdaWdbaGcbaqcfa4aaS aaaOqaaKqzGeGaaeiiaiabek7aITWaaWbaaeqabaqcLbmacaaIYaaa aaGcbaqcfa4aa0aaaOqaaKqzGeGaeqOXdOgaaaaaaSqabeqajugibi abgUIiYdGaamOEaiaaykW7caaMc8UaamizaiaadQhacqGHRaWkcaaM c8UaaGPaVlaadoealmaaBaaabaqcLbmacaaIXaaaleqaaKqzGeGaaG PaVNqbaoaapeaakeaajugibiaadsgacaWG6baaleqabeqcLbsacqGH RiI8aaaa@6468@ (15)
z=   β 2 φ ¯ z 2 2 + C 1 + C 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG6b Gaeyypa0JaaGPaVNqbaoaalaaakeaajugibiaabccacqaHYoGylmaa CaaabeqaaKqzadGaaGOmaaaaaOqaaKqbaoaanaaakeaajugibiabeA 8aQbaaaaqcfa4aaSaaaOqaaKqzGeGaamOEaSWaaWbaaeqabaqcLbma caaIYaaaaaGcbaqcLbsacaaIYaaaaiaaykW7caaMc8Uaey4kaSIaaG PaVlaaykW7caWGdbWcdaWgaaqaaKqzadGaaGymaaWcbeaajugibiaa ykW7caaMc8Uaey4kaSIaaGPaVlaaykW7caWGdbWcdaWgaaqaaKqzad GaaGOmaaWcbeaaaaa@5CC4@ (16)
z=   β 2 φ ¯ z 2 + C 1 z+ C 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG6b Gaeyypa0JaaGPaVlaaykW7juaGdaWcaaGcbaqcLbsacaqGGaGaeqOS di2cdaahaaqabeaajugWaiaaikdaaaaakeaajuaGdaqdaaGcbaqcLb sacqaHgpGAaaaaaiaaykW7caWG6bWcdaahaaqabeaajugWaiaaikda aaqcLbsacaaMc8UaaGPaVlabgUcaRiaaykW7caaMc8Uaam4qaSWaaS baaeaajugWaiaaigdaaSqabaqcLbsacaWG6bGaaGPaVlaaykW7cqGH RaWkcaaMc8UaaGPaVlaadoealmaaBaaabaqcLbmacaaIYaaaleqaaa aa@5EDC@ (17)
z=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG6b Gaeyypa0JaaGPaVlaaykW7caaIWaGaaGPaVdaa@3DE5@

z=   β 2 φ ¯ z 2 2 C 1 y+ C 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWG6b Gaeyypa0JaaGPaVlaaykW7juaGdaWcaaGcbaqcLbsacaqGGaGaeqOS di2cdaahaaqabeaajugWaiaaikdaaaaakeaajuaGdaqdaaGcbaqcLb sacqaHgpGAaaaaaKqbaoaalaaakeaajugibiaadQhalmaaCaaabeqa aKqzadGaaGOmaaaaaOqaaKqzGeGaaGOmaaaacaaMc8UaaGPaVlaado ealmaaBaaabaqcLbmacaaIXaaaleqaaKqzGeGaamyEaiaaykW7caaM c8Uaey4kaSIaaGPaVlaaykW7caWGdbqcfa4aaSbaaSqaaKqzadGaaG OmaaWcbeaaaaa@5BE3@ (18)

  β 2 2 φ ¯ z 2 + C 1 y+ C 2 =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacqGHsh I3caaMc8UaaGPaVlaaykW7caaMc8Ecfa4aaSaaaOqaaKqzGeGaaeii aiabek7aITWaaWbaaeqabaqcLbmacaaIYaaaaaGcbaqcLbsacaaIYa qcfa4aa0aaaOqaaKqzGeGaeqOXdOgaaaaacaaMc8UaamOEaSWaaWba aeqabaqcLbmacaaIYaaaaKqzGeGaaGPaVlaaykW7cqGHRaWkcaaMc8 UaaGPaVlaadoealmaaBaaabaqcLbmacaaIXaaaleqaaKqzGeGaamyE aiaaykW7caaMc8Uaey4kaSIaaGPaVlaaykW7caWGdbWcdaWgaaqaaK qzadGaaGOmaaWcbeaajugibiaaykW7caaMc8Uaeyypa0JaaGPaVlaa ykW7caaIWaaaaa@6C0F@ (19)

Auxiliary Equation becomes:

  β 2 2 φ ¯ M 2 + C 2 m+ C 2 =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaaeiiaiabek7aITWaaWbaaeqabaqcLbmacaaIYaaaaaGc baqcLbsacaaIYaqcfa4aa0aaaOqaaKqzGeGaeqOXdOgaaaaacaaMc8 UaamytaSWaaSbaaeaajugWaiaaikdaaSqabaqcLbsacaaMc8UaaGPa VlabgUcaRiaaykW7caaMc8Uaam4qaSWaaSbaaeaajugWaiaaikdaaS qabaqcLbsacaWGTbGaaGPaVlaaykW7cqGHRaWkcaaMc8UaaGPaVlaa doeajuaGdaWgaaWcbaqcLbmacaaIYaaaleqaaKqzGeGaaGPaVlaayk W7cqGH9aqpcaaMc8UaaGPaVlaaicdaaaa@6357@ (20)

Applying quadratic expression, it can be express as:

M 1,2 = b± b 2 4ac 2a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGnb WcdaWgaaqaaKqzadGaaGymaiaacYcacaaIYaaaleqaaKqzGeGaaGPa Vlabg2da9iaaykW7juaGdaWcaaGcbaqcLbsacqGHsislcaWGIbGaey ySaeBcfa4aaOaaaOqaaKqzGeGaamOyaSWaaWbaaeqabaqcLbmacaaI YaaaaKqzGeGaeyOeI0IaaGinaiaadggacaWGJbaaleqaaaGcbaqcLb sacaaIYaGaamyyaaaaaaa@4F0A@ (21)

M= C 1 ± C 2 4cz ( β 2 ) 2 φ ¯ C 2   β 2 φ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGnb GaaGPaVlaaykW7caaMc8Uaeyypa0JaaGPaVlaaykW7juaGdaWcaaGc baqcLbsacqGHsislcaWGdbWcdaWgaaqaaKqzadGaaGymaaWcbeaaju gibiabgglaXMqbaoaakaaakeaajugibiaadoeajuaGdaahaaWcbeqa aKqzadGaaGOmaaaajugibiabgkHiTiaaisdacaWGJbGaamOEaKqbao aalaaakeaajuaGdaqadaGcbaqcLbsacqaHYoGylmaaCaaabeqaaKqz adGaaGOmaaaaaOGaayjkaiaawMcaaaqaaKqzGeGaaGOmaKqbaoaana aakeaajugibiabeA8aQbaaaaGaam4qaSWaaSbaaeaajugWaiaaikda aSqabaaabeaaaOqaaKqbaoaalaaakeaajugibiaabccacqaHYoGyju aGdaahaaWcbeqaaKqzadGaaGOmaaaaaOqaaKqbaoaanaaakeaajugi biabeA8aQbaaaaaaaaaa@67CE@ (22)

M 1 = C 1 + C 2 2 C 2   β 2 φ ¯   β 2 φ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaaMc8 UaamytaSWaaSbaaeaajugWaiaaigdaaSqabaqcLbsacqGH9aqpcaaM c8UaaGPaVNqbaoaalaaakeaajugibiabgkHiTiaadoealmaaBaaaba qcLbmacaaIXaaaleqaaKqzGeGaaGPaVlabgUcaRKqbaoaakaaakeaa jugibiaadoealmaaCaaabeqaaKqzadGaaGOmaaaajugibiabgkHiTi aaikdacaWGdbqcfa4aaSbaaSqaaKqzadGaaGOmaaWcbeaajuaGdaWc aaGcbaqcLbsacaqGGaGaeqOSdi2cdaahaaqabeaajugWaiaaikdaaa aakeaajuaGdaqdaaGcbaqcLbsacqaHgpGAaaaaaaWcbeaaaOqaaKqb aoaalaaakeaajugibiaabccacqaHYoGylmaaCaaabeqaaKqzadGaaG OmaaaaaOqaaKqbaoaanaaakeaajugibiabeA8aQbaaaaaaaaaa@62B1@ (23)
M 2 = C C 1 2 2 C 2   β 2 φ ¯   β 2 φ ¯ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGnb WcdaWgaaqaaKqzadGaaGOmaaWcbeaajugibiaaykW7caaMc8Uaeyyp a0JaaGPaVlaaykW7juaGdaWcaaGcbaqcLbsacqGHsislcaWGdbGaey OeI0IaaGPaVNqbaoaakaaakeaajugibiaadoealmaaBaaabaqcLbma caaIXaaaleqaamaaCaaabeqaaKqzadGaaGOmaaaajugibiabgkHiTi aaikdacaWGdbWcdaWgaaqaaKqzadGaaGOmaaWcbeaajuaGdaWcaaGc baqcLbsacaqGGaGaeqOSdiwcfa4aaWbaaSqabeaajugWaiaaikdaaa aakeaajuaGdaqdaaGcbaqcLbsacqaHgpGAaaaaaaWcbeaaaOqaaKqb aoaalaaakeaajugibiaabccacqaHYoGylmaaCaaabeqaaKqzadGaaG OmaaaaaOqaaKqbaoaanaaakeaajugibiabeA8aQbaaaaaaaaaa@63AE@ (24)

Assuming this discriminate is complex; therefore, equation (23) and (24) can be expressed as:

K[ TZ ]= f 1 Cos M 1 z+ f 2 Sin M 2 z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlb GaaGPaVNqbaoaadmaakeaajugibiaadsfacaWGAbaakiaawUfacaGL DbaajugibiaaykW7caaMc8UaaGPaVlabg2da9iaaykW7caaMc8UaaG PaVlaadAgalmaaBaaabaqcLbmacaaIXaaaleqaaKqzGeGaaGPaVlaa doeacaWGVbGaam4CaiaaykW7caWGnbWcdaWgaaqaaKqzadGaaGymaa WcbeaajugibiaadQhacaaMc8UaaGPaVlaaykW7cqGHRaWkcaaMc8Ua aGPaVlaadAgalmaaBaaabaqcLbmacaaIYaaaleqaaKqzGeGaaGPaVl aadofacaWGPbGaamOBaiaaykW7caWGnbqcfa4aaSbaaSqaaKqzadGa aGOmaaWcbeaajugibiaadQhaaaa@6D88@ (25)

But if T = d V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaSaaaO qaaKqzGeGaamizaaGcbaqcLbsacaWGwbaaaaaa@398A@  and V = V.t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGwb GaaiOlaiaadshaaaa@390B@
The expressed model can be written as:

K[ T,Z ]= f 1 Cos M 1 d v + f 2 Sin M 2 d v MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlb GaaGPaVNqbaoaadmaakeaajugibiaadsfacaGGSaGaamOwaaGccaGL BbGaayzxaaqcLbsacaaMc8UaaGPaVlaaykW7cqGH9aqpcaaMc8UaaG PaVlaaykW7caWGMbWcdaWgaaqaaKqzadGaaGymaaWcbeaajugWaiaa ykW7jugibiaadoeacaWGVbGaam4CaiaaykW7caWGnbWcdaWgaaqaaK qzadGaaGymaaWcbeaajugibiaaykW7juaGdaWcaaGcbaqcLbsacaWG KbaakeaajugibiaadAhaaaGaaGPaVlaaykW7caaMc8Uaey4kaSIaaG PaVlaaykW7caWGMbqcfa4aaSbaaSqaaKqzadGaaGOmaaWcbeaajugi biaaykW7caWGtbGaamyAaiaad6gacaaMc8UaamytaKqbaoaaBaaale aajugWaiaaikdaaSqabaqcfa4aaSaaaOqaaKqzGeGaamizaaGcbaqc LbsacaWG2baaaaaa@765A@ (26)

And

K[ T,Z ]= f 1 Cos M 1 v.t+ f 2 Sin M 2 v.t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcLbsacaWGlb GaaGPaVNqbaoaadmaakeaajugibiaadsfacaGGSaGaamOwaaGccaGL BbGaayzxaaqcLbsacaaMc8UaaGPaVlaaykW7cqGH9aqpcaaMc8UaaG PaVlaaykW7caWGMbWcdaWgaaqaaKqzadGaaGymaaWcbeaajugibiaa ykW7caWGdbGaam4BaiaadohacaaMc8UaamytaSWaaSbaaeaajugWai aaigdaaSqabaqcLbsacaaMc8UaamODaiaac6cacaWG0bGaaGPaVlaa ykW7caaMc8Uaey4kaSIaaGPaVlaaykW7caWGMbWcdaWgaaqaaKqzad GaaGOmaaWcbeaajugWaiaaykW7jugibiaadofacaWGPbGaamOBaiaa ykW7caWGnbWcdaWgaaqaaKqzadGaaGOmaaWcbeaajugibiaadAhaca GGUaGaamiDaaaa@73B1@ (27)

Materials and Method

Standard laboratory experiments where performed to monitor the rate of flow using failing head at different formations. The depositions of the strata were collected in sequences based on the structural deposition at different locations. These samples collected at different points generate at different depths, producing different migration of fluid flow, developing at various levels of flow and at different strata. The experimental results are applied to compare with the theoretical values to determine the validation of the model.

Result and Discussion

Results and discussion are presented in tables including graphical representations of permeability on Tuotorsity flow conditions Tables 1-7. The figures from the graphical representation of permeability and Tuotorsity show the following behaviour of the system. Permeability, as is called is defined as the ability to permeate. It is the measurement shows easily a fluid can flow through a porous medium. Most especially in geotechnical engineering, the porous medium is soils and fluids are definitely the water at ambient temperature. In general conditions, the coarser the soil grains, the larger the voids and larger the permeability. Based on these factors, it is confirmed that gravels are more permeable than silts. Hydraulic conductivity is another term used for permeability especially in environmental engineering literature. In another development on soil structural stratification, it is obvious that when water flows through soils, from upstream to downstream, due to difference in water levels, some energy is lost in overcoming the resistance provided by the soils. This loss of energy, expressed as total head loss is simply the difference in water levels. The pressure is the pore water pressure and therefore pore water pressure at any point in the flow region will definitely influences the behaviour of flow under the geological settings of the soil. The express figures were found to be influenced by these conditions as exponential state of permeability generating Tuotorsity were graphically expressed in such linear direction. The influences from homogeneous setting of structural stratification may have influenced the behaviour of the flow, although it is not always at regular intervals, but the condition of the geological settings from this dimension was found to have been influenced by the system. The simulation values were compared with other experimental results for validation of the model, but parameters from Figure 1-6 expressed in graphical representation show that the maintained exponential state of flow in such linear phase developed lots of homogenous influences within the intercedes of the formation. The expressed alluvium deposition in the deltaic environment may also pressure the behaviour of the flow under the influences of Tuotorsity.

Depth

Flow Rate [m/s]

3

6.45E-08

6

1.42E-07

9

2.22E-07

12

2.88E-07

15

3.57E-07

18

4.33E-07

21

4.85E-07

24

5.64E-07

27

6.37E-07

30

6.96E-07

Table 1 Flow rate at different depths

Depth

Flow Rate [m/s]

3

6.45E-08

6

1.42E-07

9

2.22E-07

12

2.88E-07

15

3.57E-07

18

4.33E-07

21

4.85E-07

24

5.64E-07

27

6.37E-07

30

6.96E-07

Table 2 Flow rate at different depths

Time Per Day

Flow Rate [m/s]

10

6.45E-08

20

1.42E-07

30

2.22E-07

40

2.88E-07

50

3.57E-07

60

4.33E-07

70

4.85E-07

80

5.64E-07

90

6.37E-07

100

6.96E-07

Table 3 Flow rate at different depths

Time Per Day

Flow Rate [m/s]

10

3.41E-06

20

8.35E-06

30

1.29E-05

40

1.72E-05

50

2.17E-05

60

2.34E-05

70

2.77E-05

80

3.32E-05

90

3.79E-05

100

4.23E-05

Table 4 Comparison of theoretical and measured values of flow rate at different Depths

Depth [m]

Theoretical Values [m/s]

Measured Values[m/s]

3

6.45E-08

6.11E-08

6

1.42E-07

1.35E-07

9

2.22E-07

1.89E-07

12

2.88E-07

2.80E-07

15

3.57E-07

3.33E-07

18

4.33E-07

3.43E-07

21

4.85E-07

4.66E-07

24

5.64E-07

4.54E-07

27

6.37E-07

5.41E-07

30

6.96E-07

6.55E-07

Table 5 Comparison of theoretical and measured values of flow rate at different Times

Time Per Day

Theoretical Values [m/s]

Measured Values [m/s]

10

6.45E-08

6.55E-08

20

1.42E-07

1.35E-07

30

2.22E-07

2.32E-07

40

2.88E-07

2.82E-07

50

3.57E-07

3.52E-07

60

4.33E-07

4.29E-07

70

4.85E-07

4.88E-07

80

5.64E-07

5.61E-07

90

6.37E-07

6.41E-07

100

6.96E-07

7.11E-07

Table 6 Comparison of theoretical and measured values of Flow rate at different Times

Time Per Day

Theoretical Values [m/s]

Measured Values [m/s]

10

3.41E-06

4.08E-06

20

8.35E-06

7.75E-06

30

1.29E-05

1.21E-05

40

1.72E-05

1.67E-05

50

2.17E-05

1.87E-05

60

2.34E-05

2.33E-05

70

2.77E-05

2.84E-05

80

3.32E-05

3.38E-05

90

3.79E-05

3.64E-05

100

4.23E-05

3.99E-05

Table 7 Comparison of theoretical and measured values of Flow rate at different Times

Figure 1 Flow rate at different depths.
Figure 2 Flow rate at different at different Times.
Figure 3 Flow Rate at different Times.
Figure 4 Comparison Theoretical and Measured values at different depths.
Figure 5 Comparison Theoretical and Measured values at different depths.
Figure 6 Comparisons of Theoretical and Measured Values at different depths.

Conclusion

The study has expressed the behaviour of permeability in the soil over the Tuotorsity flow condition in deltaic formation. The rate of strata permeation are structured through the geological settings in the study location. The expression from the formation has been able to express its pressure on the Tuotorsity flow condition in the study location. The simulation was able to establish the depositional level of the fluid within the intercedes of the strata. Graphical representations of the flow conditions show linear phase in the strata. The study has determined the rate of flow in the formation. The rate of flow was found to be in average condition. It implies that the structure of the formation deposition reflected on the pressure of flow in the strata. The developed model simulation results generated theoretical values that were compared with other experimental results. Both parameters developed a best fit. The values from the simulation implies that the flow yield rate may not occur as shallow depth yield experienced are very low. The formation may be predominant silty formation, and such stratum may develop permeable conditions of an average flow within the intercedes of the formation. The study is imperative because experts will apply the model and simulation values to monitor the rate of permeability and Tuotorsity flow conditions in the study location.

Acknowledgements

None.

Conflict of interest

The author declares no conflict of interest.

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