ΐῒῑῌῐJ. Jpn. Soc. Soil Phys.
῏῍ῌῐῑ῎
No. 31, p. ,/῍-* ῎,**.῏

A Simple Estimation of Excess Rainwater Percolation froma Buried Container into a Vadose Zone
Katsutoshi SEKI*, Tsuyoshi MIYAZAKI*, Masaru MIZOGUCHI*, Hiromi IMOTO*,Kotaro NAKAYA** and Hiroshi MIYAZAWA*** Graduate School of Agricultural and Life Sciences, The University of Tokyo,+ῌ+ῌ+ Yayoi, Bunkyo-ku, Tokyo ++-ῌ20/1, Japan** Enlighten-Corporation, +ῌ-2ῌ+ Katsutadai, Yachiyo City, Chiba ,10ῌ**,-, JapanAbstractThis study evaluated the performance of a rainwater utilization system. Excess rainwater isdrained from rooftops into an underground container from which the water inﬁltrates from thebase and sides into the surrounding soil of a vadose zone. The saturated hydraulic conductivityof the soil where this system was used was very low at the surface and higher in the deeper layer
where the container was located. A simple method was proposed to estimate the steady recharge
rate of excess rainwater from the buried container into the surrounding soil of the vadose zone.
By modifying the steady recharge equation, which is widely used in the theory of the Guelph
Permeameter, a steady recharge rate from the container was calculated from the measured valueof saturated hydraulic conductivity and the size of the container.
Key words : Rainwater percolation, Rainwater utilization, Steady recharge, Hydraulic conductivity, Buried container+.

Introduction

Rainwater utilization is attracting a great
deal of attention, especially among people
living in regions where excess rainwater isavailable. In some cases the collected rainwater is stored in underground containers for use
in daily life and emergency. Excess rainwateris percolated to the surrounding unsaturated
soil to avoid inundation and surface runo# ofrainwater. Some people also expect that therecharge of groundwater may prevent the lowering of the ground level. When the rainwater
exceeds the capacity of the buried water tank,the management of the overﬂow is crucial forthe e$ciency of a rainwater collection system.
The potential of a storage system that captures overﬂow from the buried tank strongly
depends on the water retentivity and permeability of the soil of the surrounding vadosezone. In the +0th Century, people living on theAso plateau in western Japan dug rainwaterdrainage ditches around their residences (Japanese Association of Groundwater Hydrology,**+). The National Institute of Civil Engineering of the Japanese Ministry of Construction
implemented a system to recharge groundwater by collecting excess rainwater intoburied porous pipes, which drains the water
into the surrounding unsaturated soil zones
and, eventually, into the groundwater (Ishizaki+32/). The draft of the “Manual on the investigation and planning of a rainwater percolation
facility,” which was edited by the Society ofthe Rainwater Percolation Facility in +33/, provides information on percolation ditches andtrenches, U-ditches, and pavement. However,
the manual did not provide information forestimating the rates of inﬁltration from a watercontainer into the surrounding unsaturatedΐῐ῎῔῕ῑ ῒ 31 ῏ ῌ,**.῍26soils.
The objective of this paper is to demonstrate
a simple method for estimating the excess rainwater percolated from an underground container into the surrounding soil of a vadosezone.
,.

Table +

Parameters for Equation (-) (afterZhang, +332)

Soil texture

b+b,b-Sands
Structured loams and clays
Unstructured clays,4*1.
+433,,4+*,*4*3*4*3+*4++2*41/.
*402*40//

Materials and Methods,. + Study Site
The study site is located at Yachiyo City,
Chiba Prefecture, Japan. Boring tests revealed
that a dressed soil layer of about + m covers theKuroboku soil layer of *., to *./ m thickness.
Below the Kuroboku soil layer is a Tachikawa
loam layer of + to - m thickness. Both theKuroboku soil and Tachikawa loam are
Andosol, and they are known as Kanto loam.
,. , Soil Proﬁle Measurement
A ,-m soil pit was dug, and a soil proﬁle wasrecorded. The proﬁle of soil hardness wasmeasured in situ with the use of Yamanaka soil
hardness meter, which is widely used in Japan.
The empirical relationship between the reading of the Yamanaka soil hardness meter andthe soil hardness for the Kuroboku soil
(Watanabe, +33,) was used for obtaining soil
hardness values. Undisturbed cylindrical coresof /-cm diameter and /-cm height were taken tomeasure the saturated hydraulic conductivities, dry bulk densities, particle densities,and water content. Saturated hydraulic conductivities were measured by using the fallinghead method with these undisturbed cores. In
situ saturated hydraulic conductivities weredetermined with a Guelph Permeameter (Reynolds and Elrick, +321). In every measurement of
the Guelph Permeameter, the saturated hydraulic conductivity and the matric ﬂux potential were determined by least-squares methodby using three steady depths (/, +*, +/ cm)
measurement (Reynolds and Elrick, +321). In
the calculation of Guelph Permeameter, proportionality parameter, C, was determined byequation (-) using b+, b, and b- values of loam
soil in Table +.

Fig. +

Schematic diagram of a rainwater inﬁltration system.

Buried Container for Excess Rainwater
The rainwater inﬁltration system (Fig. +) is
brieﬂy described. Rainwater ﬂows from a rooftop to the ﬁrst buried storage container (C+).
The ﬁrst container preserves - m- of rainwater,and, when the rainwater exceeds this volume,
it ﬂows to a second buried container (C,). The
rainwater in the second container inﬁltrates
into the soil from its base and permeable walls.
A method will be shown here for estimating
the recharge rate from the second container tothe vadose zone ; the second container isreferred to as “the container” or “the cubiccontainer” in this paper. This system uses
excess water to recharge groundwater insteadof just draining the excess water into a drainage pipe. At the study site, the percolation
system container is buried at a depth of + to ,m and drains into the Tachikawa loam layer.
,. . Method of Estimation,. .. + Assumptions
A simple method is described to estimate thepercolation from a cubic container by calculating the percolation rate from a cylindrical container with an identical volume, i.e., the same,. -῕῔ΐῌῒ : A Simple Estimation of Excess Rainwater Percolation from a Buried Container into a Vadose Zone

base area and the same height. Two assumptions are made here. The ﬁrst is that the recharge rate from a cubic container and a cylindrical container is nearly equal when the areaof the base of each container is identical. The
second is that the matric ﬂux potential is negligible.
,. .. , ProcedureReynolds and Elrick (+321) developed a numerical model of inﬁltration from a cylindricalwell with a constant pressure to calculate saturated hydraulic conductivity using the Guelph
Permeameter method.
According to theirtheory, a steady recharge from a cylindricalwell into uniform and unsaturated soil is expressed as,pH,Ks,pHfm
Qῑ
῏pa,Ks῏ῌCCwhere Q (m- sῐ+) is the steady recharge, Ks (msῐ+) is the saturated hydraulic conductivity, H(m) is the steady depth of water in the well, a(m) is the well radius, fm (m, sῐ+) is the matricﬂux potential, and C is a dimensionless proportionality parameter primarily dependent on
the H/a ratio. The ﬁrst term on the right handside of Equation (+) expresses ﬂow out of thesidewall of the well, the second term expresses
ﬂow from the base of the well, and the thirdterm expresses the unsaturated component of
the ﬂow.
The matric ﬂux potential, fm, is deﬁned byῌῑfmῑ ῒ K῍y῎dy ; yi῔y῔*ῐ῎῍where y (m) is the soil water pressure head, yi(m) is the initial pressure head in the soil surrounding the well, and K (y) is the unsaturated
hydraulic conductivity (m sῐ+) at the pressure
head of y.
Zhang (+332) provided empirical formula todescribe C from the data calculated numerically by Reynolds (+320) :Hῌa ῎bCῑῌ῎῍b+῏b, Hῌa῏
where the values of b+, b,, and b- are shown inTable +.
Based on this theory, a simple method is27

shown for calculating the recharge rate from a
cubic container, (i.e., well), with a base area of S(m,). According to the ﬁrst assumption, thesteady recharge Q from the container is equal
to the steady recharge from a cylindrical wellwith an identical base area, where῏Sῑpa,By solving this equation with a, substituting
it into Equation (-), substituting the value of C
into Equation (+), and assuming fmῑ*, the following equation is obtained :῍῎b- ῒ,ῌb+
Qῑῐ
ῑ,pH ῍H ΐ ῏ ῏b,῏ ῏SΐKsῐWhen the values of Ks, S, H, b+, b,, and b- aregiven, the value of Q can be calculated, and thesteady recharge from the container using
Equation (/) can be estimated.
-.

Results and Discussion-. + Soil ProﬁleFrom the observation of the soil pit, from thesurface to *., m was a dressed gravel layer ; *.,to *.3/ m was a dressed soil layer ; theKuroboku soil layer was *.3/ to +., m from thesurface ; and the Tachikawa loam layer, at thebottom of the pit, was from +., to ,.* m. The
proﬁle of the soil hardness and volumetric percentages of the solid, water and gas phases areshown in Fig. ,. As shown by the proﬁle of thesoil hardness, the soils were remarkably harderat the surface *./-m layer and at the +.1ῑ,.* mlayer than at the layer of *./ to +.1 m. The solid
ratios of the dressed soils were .* to ./῕, andthose of Kuroboku soil and Tachikawa loam
were +3 to ,+῕.
Saturated hydraulic conductivities measured in situ by the Guelph Permeameter andthe falling-head method with undisturbed coresamples are shown in Fig. -. Each of the coresample values is the logarithmic means of ﬁve
replicated samples. The saturated hydraulicconductivities of the soil surface, i.e., thedressed soil layer, were in the order of +*ῐ+* msῐ+. The very low value of Ks in the dressed soillayer is because of extensive compression of
the surface soil to make a rigid ground for

28

Fig. ,Fig. -31,**.

Soil hardness and volumetric percentages of solid, water and gas phases.

Saturated hydraulic conductivity, Ks,
measured by the falling-head methodwith undisturbed core samples and theGuelph Permeameter in situ.

construction. The saturated hydraulic conductivities increased dramatically at a depth
between *.2 and +./ m from the surface to theorder of +*0 m s+, and they increased to theorder of +*/ m s+ at a depth of , m. Theseresults agree with the Ks value of about +*/ ms+ of the Tachikawa loam soil measured by
Tada (+30/). The bulk density of about *./ Mgm- in Tachikawa loam layer also agrees withthe measurement of Tada (+30/). This proﬁle isuseful to explain the merits of this inﬁltration
system in this region because the rainwater
does not percolate easily into soil if it falls
directly onto the ground, where the Ks is very
low ; however, when the rainwater ﬂows to theunderground and percolates into a much more
permeable soil layer by this system, the rainwater is recharged much more easily because
the Ks is higher.
The ﬁeld saturated hydraulic conductivity
measured by the Guelph Permeameter was
lower than the laboratory saturated hydraulicconductivity measured by the falling-head
method with undisturbed core samples fromthe depth of +.- and +.0 m (Fig. -). A possible
reason of this is that we compacted the innerwall of the observation well when we dug ahole for the Guelph Permeameter. According
to the Guelph Permeameter measurement, thematric ﬂux potential was +./ +*1 m, s+ at
the depth of +.- m.
-. , Calculation of the Recharge Rate
Parameters used for the calculation are
shown in Table ,. By putting the values of b+,b, and b- of loam in Table + and the parametersin Table , into Equation (/), the steady recharge rate was calculated as Q  1.2*+*/m- s+.ΐῒῑῌῐ : A Simple Estimation of Excess Rainwater Percolation from a Buried Container into a Vadose Zone

Table ,KsS
HParameters used for the calulation/4*῎+*0 m s῍+.41 m,*43. m-. - Evaluation of the Model-. -. + E#ect of the shape of the container
At ﬁrst, we will evaluate the ﬁrst assumptionthat the recharge rate from a cubic container
and a cylindrical container is almost the same
when the area of the base of each container isidentical. It is reasonable to assume that thesteady recharges from the bases of both wells
are equal because each base area is equal, and,inevitably, the depths of stored water are equalin each well. On the other hand, the side areasof cubic and the cylindrical containers are
di#erent, so it may seem inappropriate toassume that the steady recharge from bothsides of the wells is equal. Actually, simple
geometrical mathematics indicates that theside area of the cubic container is about +,.2ῌ
larger than that of the cylindrical container. It
is necessary to point out that the ﬁrst assumption and resultant estimation of the ﬁrst termof the right-hand side of Equation (+) may underestimate the recharge rate from side wall ofthe well, and it may be as much as +,.2ῌ larger
than the estimated value. From a practical
viewpoint, it is better to underestimate than tooverestimate the recharge rate because the underestimated value works as a minimum estimate of the percolation capacity of the container.
-. -. , E#ect of the matric ﬂux potential
According to the value of the matric ﬂux
potential measured by the Guelph Permeameter, the third term on the right of Equation(+) is +.1.῎+*῍0 m- s῍+, and it is only ,.,ῌ of therecharge rate calculated. Therefore ignoring
the matric ﬂux potential is justiﬁed in the condition of the experimental site.
However, the matric ﬂux potential depends
on the initial water content and soil type. According to Reynolds and Elrick (+321), the29

matric ﬂux potential component of Equation(+) increases in relative importance withdecreasing well radius (a), with decreasing
depth of ponding in the well (H), with ﬁner soil
texture, and with decreasing background soilwetness (decreasing yi). When applying thismodel to actual site, background soil wetness isa variable and the recharge rate calculated
from Equation (+) is a function of the initialwater content. Therefore a minimum estimateof the recharge rate can be obtained by assuming maximum initial water content. In thismodel, by assuming fm῏*, we get the minimum estimate of the recharge rate.
-. -. - Technical notes
The Ks of the permeable wall of the container
should be larger than the Ks of the surrounding
soil. Otherwise, the steady recharge is determined by the Ks of the permeable wall, not by
the Ks of the surrounding soil. Moreover, theKs of the permeable wall may decrease withtime by the e#ect of clogging, and therefore
the system should be maintained by cleaning
the permeable wall.
..

Conclusion

We showed a simple method to estimate
excess rainwater percolation from a buried
container into the surrounding soil of a vadosezone. In the study site where the rainwaterinﬁltration system was used, the saturated hydraulic conductivities of the soil surface werein the order of +*῍+* m s῍+, and they increased tothe order of +*῍0 m s῍+ at a depth between *.2and +./ m. They increased further to the orderof +*῍/ m s῍+ at a depth of , m. Using a Ks valueof /.*῎+*῍0 m s῍+, the steady recharge rate wascalculated as 1.2* ῎ +*῍/ m- s῍+. In the model
presented here, the e#ect of the matric ﬂux
potential was ignored. Ignoring the matric ﬂux
potential in the studied site was justiﬁed by thecalculation that the matric ﬂux potential was,.,ῌ of the recharge rate, but it must be notedthat the matric ﬂux potential becomes larger
when the initial water content is smaller andwhen the soil texture is ﬁner. The model pre-n{:­k; ® 31 ¯ °,**.±30

sented here may underestimate the recharge
rate because of two assumptions, and it gives aminimum estimate of the maximum possible
recharge rate from the container. At actual
construction site at Chiba prefecture, Japan,
the model has been implemented successfully
to estimate the rainwater percolation rate togroundwater.
References
Ishizaki, K. (+32/) : Inﬁltration capacity of a pipeburied in the ground and its application. Data
Nat. Inst. of Civil Eng., ,,.0 : -/ῌ/-. (in Japanese)
Japanese Association of Groundwater Hydrology
Ed. (,**+) : Inﬁltration of rainwater and fostering of groundwater. Rikou Tosho Co. Tokyo,
Japan. (in Japanese)
Reynolds, W.D. (+320) : The Guelph Permeameter

method for in situ measurement of ﬁeldsaturated hydraulic conductivity and matricﬂux potential. Ph. D. Dissertation. Universityof Guelph, Guelph, Ont.
Reynolds, W.D. and Elrick, D.E. (+321) : A laboratory and numerical assessment of the Guelph
Permeameter method. Soil Sci., +.. (.) : ,2,ῌ,33.
Tada, A. (+30/) : On the compaction curve of theKanto loam and its permeability +. Trans. Agr.
Eng. Soc. Japan, +. : -0ῌ.*. (in Japanese)
Watanabe, H. (+33,) : Studies on the soil proﬁlemodiﬁcation in humic Ando soils in uplandﬁeld. Special Bull. Chiba Prefect. Agric. Exper.
Stat., ,+ : +ῌ32. (in Japanese)
Zhang, Z.F., Groenevelt, P.H. and Parkin, G.W.
(+332) : The well-shape factor for the measurement of soil hydraulic properties using theGuelph Permeameter. Soil Till. Res., .3 : ,+3ῌ,,+.

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