0038-07 5C / 99 / 1 648-s27 -34 1

August 1999
Vol. 164, No. 8
Prinred in U-S.A.

Soil Sciencc

Coppight @ 1999 by Lippincott Willianrs & Wilkins, inc.

TECHNICAL ARTICLESESTIITATION OF SOIL HYDRAULIC PROPERTIESWITH THE CONE PER {EAIVIETER: FIELD STUDIESRadka Kode5ov6r, Sondra E. Ordway', Mollv M. Gribbr dnd JiiiSim0neke'We present field application of the cone perneameter method for es-

tirnating soil hydraulic properties: the soil-rnoisture characteristic curve,0(h), and the hydraulic conductivity function, K(lr). The cone penneameter was designed to inject water into the soil under knourn pressure.
The cumulative inflow volume and pressure heads measured with tensiorneter rings at fwo locations above the water source are recorded intirne. The observed data sets are analyzed using an inverse modelingmethod to predict the soil hydraulic properties. The device was fieldtested for the first time in two fypes of sandy soil. Tests were always conducted with two sequentially applied pressure heads of dilferent magnitudes for different experimental runs. After the water source was shutoff, tensiometer measurements were continued to monitor the redistribution of water in the soil. To study
impact of one or two steps ofapplied-pressure head on estimates of-thewetting soil hydraulic propeities,
we carried out nurnerical inversions for data Fom the injection (iettingj
part of experirnent, first with only one supply press,tre head and thJn
with rwo supply- pressure heads. For selected testJ we analyzed, data fromthe. entire expeqrnent t-9 inv-estig-ate hysteresis of the soil hydraulic properties. The resulting soil hydraulic properties correspond well withihoie
obtained with standard techniques. (Soil Science lE99i164tSZ7-541)
Key words: Inverse solution, cone pelTnearneter, soil hydraulic properties, unsaturated hydraulic conductivity function, soil-moisture ctraracteristic curve, field studies.

rf1lfi soil-moisture characceristic, 0(h), and hyI draulc conducriviry, K(/l), curves are rwo

an appropriate governing equarion and analyticalexpressions of K(h) and 0(lr). The unknown pa-

basic hydraulic properries of soils. Current direct
laboratory and in situ merhods for their determination are often time consuming and costly. Parameter optimizadon is an indirect approach thatmakes it possible to obtain K(/r) and 0(/r) simul-

rameters of K(fi) and 0(ft) are obtained by minimization of an objective function describing thedift-erences berween some lneasured flow variables and those simulated with a numerical flowcode. This methodology was originally applied
to laboratory one-step (Kool et aI.1985;Parker etal. 1985; van Dam et d. 1992;'Wildenschild et al.
1997) and muld-step (van Dam et aJ. 1994; Eching and Hopmans 1993; Eching er al. 1.994;Zwmiihl and Durner 1998) outflow data. Paramerer
esrimation has also been used with data obtainedusing the evaporation method (see, for example,

taneously from fransient flow data (Kool et al.
1987). In this case, a florv event is modeled with
rDcpertmcnt ol Civil & Environmentrl Enginccring
Univcaity of South Grolina,

300 l{rin Sr., Columbi., SC 99908. Dr. Gribb i: coneponding author. Eoail:
gntb@sc.cdu

iU.S. $linity uborarory, USDA-ARS, a5O W. Big gpring Rd., Riveride, CA
99507.

Santini et al. (1995); Ciollaro and Romano

Rcccivtd Jan. l?, 1999; accepted Aoril 16, 1999.

(1995); Simrinek et al. (1998b)). For field deter-

* l.-

528

Sor Scnruce

KooeiovA. Omwav, GRrss ANo Sru0Nex

minacion of soil hydraulic properties, parameter
estimation methods were appiied to ponded infiltration flow &ta (Russo et al. 1991;Bohne etal. 1993), and tension disc infiltrometer flow data

(Simtnek and van Genuchten 1996, 1997;

Si-,ih.t et al. 1998a). Another field techniquefor gaining information about the soil hydraulicproperties via multi-step soil water extraction
and parameter optimization was developed byInoue et al. (1998). Both the tension disc in6ltrometer and multi-step soil water extraction experiments are applicable only in the near surface.
Gribb (1996) proposed a new cone penetrometer tool (e.g., cone permeameter) and use of parameter optirrdzation to estimate soil hydraulicproperties at depth. A protofype was further
developed by Leonard (1997).A detailed description of the protorype as weI as its use under saturated and unsaturated conditions were previously presented by Gribb et al. (1998). The cone
permeameter rvas designed to inject water underknown pressure into the soil. The cumuiative inflow volume and pressure heads at flvo locations
above the source are measured during the injection (rvetting) part of experiment. Only the pressure heads are recorded during the redistribution
process after the water supply is shut oft-. The
protorype u.'as previously tested in the laboratory
aquifer. Kodeiovl et al. (1998, 1999) discussed resulcs of the numericai analysis of data from thewetting parts of one-step appiied pressure headcone permeameter experiments, which were
performed in the laboratory for one soil rype but
under different inirial and boundary condirions.
They discovered that higher applied Pressure
head and lorver initial pressure head conditions
resulted in higher va-lues of saturated soil moisture content, 0,, and saturated hydraulic conductiviry, K,. They also studied the influence of cone
permeameter placement (pushed vs. buried) on
estimates of soil hydraulic properties and the possibiliry of including soil moisture content information into the optimizadon process. They
found that soil densification caused by pushing
the protorype to the tesdng depth resulted inslightly lower values of 0, and K,. They also

showed that additional measurements of soil
moisture content would be useful for more Precise estimation of 0,. Simrinek et al. (1999) andKodeiovl et al. (1999) examined both the wetting and redistribution parts of cone permeameter experiments to determine the wetting anddrying branches of the soil hydraulic properties.
In cases where the parameter 0, was overestimated, they investigated the potendal for opti-

mization of addicionai parameters, such as thepore conne$ivity parameter in Eq. (8) (see below) and the anisotropy factor (expressing the rado berween horizontal and vertical K,values), to
obtain better fits of measured fow responses
when 0, was fixed at a reasonable value.
Here we show resuls from field application of
the cone permearneter. We have modified themethod of placement and the test procedure basedon previous experience. Before placement of thecone permeameter in the soil, a soil core of smaller
diameter was removed with a sampler. This reduced possible discurbances caused by the directpush of the permeameter into the soil. In addition,
carefirlly exrracted samples of known volume wereused to determine the initiai moisrure contents ofthe soil at the tensiometer locations. Initid moisrure content values were paired with the corresponding initial tensiometer readings and includedin the oprimiza[ion as poins of che soi]-moisturecharacterisric, 0(/r). The cone Permeameter infiltration tess were performed immediately after thecone permeameter was placed in the soil and themeasured pressure heads reached equilibrium.
Tests were always conducted with rwo sequentially applied pressure heads of different magnirudes for each test. The parameters describing thesoil hydraulic properties were estimated ftom thefirst part of the experiment alone as a one-steP ex-

periment or &om both paru as a two-step experiment. Finaliy, the redistribution, or third part ofthe experiment, was included in the parameter
optimization so that the effects of hysteresis could
be srudied. The resulring soil hydraulic properties
were compared with those determined with standard laboratory and field techniques.

THEORY
Experimental Setup and Problem D$nition

A protorype cone permeameter has been discussed in detail by Gribb et al. (1998). A
schematic of the device and the experimental
setup are shown in Fig. 1. The cone Permeameter is placed in the soil, and a known head of water is then supplied to the s-cm-long screen using a microprocessor-controlled solenoid valve
assembly. The cumulative inflow voiume infi-ltrated into the soil through the screen is determined from scale readings of the mass of water
removed Gom the source. Progress of the wetting
front is measured with tensiometer rings 5 and 10
cm above the screen. After the water supply valve
is closed, the tensiometers monitor the redistribution of water in the soil profile.

Vor. 164 - No. 8

EstrvratroN oF SorL Hyonqulrc pnopenrtrs

529

B TIII

ugrwcoMP(nR

slogr
IOITCBDAqBOOEANDDBK6ETRD

scAt;BDXSP!-f,Y

Tensiometer Rings
ScreenPR TOTTFts

Fig, 1. Cone permeameter test set uo.

The cumulative inflow and pressure headdata are then analyzed to obrain estimate s of 0(ft)and K(ft) functions. The flow responses are modeled with an appropriate, variably sacurated flow
equation-, augmented with parameterized hy-

draulic functions of K(/r) and 0(h), and suitableinirial and boundary condirions. The unknown
parameters of rK(ft) and O(ft) are determined byminimization of an objective function describing
the dift-erences berween measured flow variablei
and those simulated with a numerical flow code.
During the minimization process the initial parameter estimates are iterarively improved until
the desired degree ofprecision ls obiained.
Coverning Flout Equation

HYDRUS-2D (Simrinek et al.1996) is used
to simulate the cone permeameter test in initiallyunsarurared soil with the finite element dis-cretization of the flow domain shown in Fie. 2.
The governing flow equarion for radially sfmmetric, isothermd Darcian flow in an isorropic,
rigid porous medium, assuming the air phase

plays an insignificant role in the liquid flow
process, is (Richards 1931):#=+*l'"#] . ri["(#.')](1)

where r is the radid coordinate (L), z is rhe vertical coordinate posirive upward (L), r is dme (T),ft is the pore water pressure head (L), K is rhe hy-

draulic conductiviry (LT-t), and d is the volu-

metric moisrure conrent (L3L-3). Eq. (1) is solved
numerically for the following boundary and initial conditions:h (r, z,t): h,(r, z),t:0(2)h(r,z,t):fi'(r) _(r_r)
LI11)
r = ro, zo5 a z 1 zo* i, O a r a r,,,'-'|

v,(r, z, t) = 0, r = ro,|.o- i ( z(zo * i, ,_< t1t,

(4\

\'/

Kon*ovA, Onlway, GRlnr a-no SrudNrx

s30

Sorr- ScENcr

during the period tu,_r 1 t < t,, ho, is calculatedwith Eq. (6) ftased on the geometric character-

isrics of the interior of the cone body), where Z
and V,-, (L3) are the volumes of water at the current rime and at the time l._,, respecrively, andis the actual infrltrarion rate (L3T-') corresponding to the specified boundary conditions. For details,see Simrinek et al. (1999).The otherboundaries are defined as no-flow boundaries.

f

Uns aturate d Soil Hy draulic Properties

The van Genuchten (1980) expressions formoisture content and hydraulic conductiviry,0(h) and K(fl, are used in this work:
A(h\- n-'0--''''' e,- e, = ( + laftl)''.fi<01(7)0,= 1,h>0
K(q = K,0j[1 - (1 - stt-1-f'z,tt<0

K(O=K,h=o

60 cm

Fig. 2. Finite el€ment discretization of the flow domainused for modeling cone permeam€ter tesb. UT : Upper

Tensiomete4 LT = Lower Tensiometer; SA = Screened
Area.

where fi, is the initial pressure head in the soil (L),fto is the supplied pressure head imposed at thecenter of the screen (L), .zo is the coordinate of
the center of the screen (L), L is the length of thescreen, ro is the radius of the screen (L), t,, is thetime when infiitration is completed (T), t, is thetime when the experiment is terminated (T), andu, is the flux in the radial direction (LI).Suppliedpressure head, ft', is variable in time and definec
as follows:

14=ho,,rr_, (r<ti,jtzo= flv(t))1(5)<t<t,,,(6)=7,.,w-: t(r*,-,JrtOa,),

',,-,

(8)

where 0. is the effective moisture content(L3L-), K, is the saturated hydrauiic conductiviry(LT*'), 0, and 0, are the residual and saturated
moisture contents (L3L-), respectively, / is thepore connectiviry parameter (-) (/ : 0.5), and e(L-'),, and n (= 1 - 1/n) are empirical Parameters (-).

'When the hysteresis of the characteristic

curves is taken into account, the drying and wetting curves are described with Eqs. (7) and (8) us-

ing the parameler vectors (ei, 0i, ad, nd, Kd,) and(0Y, 0:', du', n'', K",), respectiveiy, where the superscripts d and at indicate drying and wetting, respectively. Considerarion of hysteresis (e.g., descripcion of scanning curves) in the simulation

procedure and commonly used restrictions aredescribed in detail by Kool and Parker (1987)
and Simrlnek et al. (1999). In our study the following simplifications are used:

0!=01=0, 0!--E:9,, nd=n"=n, Kf=KJ'=4 (9)The hydraulic characteristics defined by Eqs. (7)Equation (5) describes a pressure head boundary
condition, which can be changed in steps, wherefi', G) is the pressure head applied during thetime period t - 1<t<t , t, is the time when the applied pressur6 head hu, is changed, and t,,-, is thetime when the water supply is shut off and only
the water remaining in the cone body infilnates
into the soil. The decreasins actual pressure headand (8) contain the unknown parameters K,,0,,0,,n, q"', and oy', which are found by optimizacion.
Formulation of the Inuerse Problem

To derive estimates of the hydraulic parameters using parameter optimization, an objective

funcrion, @, expressing the difi-erences berween

flow responses measured with the cone perme-Vor. 164 - No. 8

EsrrruatloN oF SorL HyoR-aulrc PRopeRrrrs

ameter and those predicted using a numericalmodel u'ith parameterized soil hydraulic properties. is minimized:
frq\1963), which combines the Newton and steepest
descent methods.

MATERIALS AND METHODS

ftsi

6(b, q, p) =2u,2*,,,!a',@, tS-q,(x, t,,b))2

Desciption of Studied Locations

i=l

J=t

np nn,(10)+ >4 )n,,, [t,@) - pj@,, b)j,
J= t

JJ.t

i=]

where the first term on rhe right side represents
deviations berween measured and predicted
space-rime variables (e.g., pressure heads ormoisture contents at different iocations and/or
fimes, or the cumularive infiltration rate vs. rime).

In this term, ra- is the number of difierent sets ofmeasurements,"and nr.is the number of measurements in a particular measurement set. Specificmeasurements at time t, for the jth measurement
set at location x(r, z) are represented by qi(r, t,);41(x, t,,6) are the corresponding model predic-

tions for the vector of optimized parameters 6(..g.,.4, 0r. o'.,!0,n, K,);and v,andw,rare weights
associated with a parricuiar measurement set orpoint, respectively. The weighting factor, u,, isgiven by the inverse of the number of measurements muitiplied by the variance of those observarions, and w,, is equal to 1 in this work. The
second term r6presents differences befween independently measured pi(0 ana predicted p,(0,,b) soil hydraulic propeiries (e.g., 0(h), K(A or
K(ft) data), whereas the terms mr, npj, Tj.and tu,,,have meanings similar to rhe first teim, bur now
apply to the soii hydraulic properdes.
Minimizarion of the objective function @ isaccomplished by using the Levenberg-Marquardt
nonlinear minimization rnechod (Marouardt

Tests were carried out at rwo sites in PoinsettState Park, located southeasr of Columbia, South
Carolina. This area is composed of interbedded,
unconsolidated sands and clays of the Atlantic

Coastal Plain (Pirts er al. 1974). Soil profiles inboth cases were quite homogeneous and consisted ofwvo layers ofsandy soil. Site t had a darkgrayish-brown suface layer and a pale brownsand subsoil, and Site 2had a dark reddish-broq'n
surface layer and a darker reddish-brown sandsubsoil. The top layers contained organic marerial and were approximately 10 cm deep. Tesrs
were conducted with the center of the screen at
a depth of 50 cm so rhar rhe weming front would
not reach the upper organic iayer during the expe riments. The tested materia-ls had dift-erent particie size distributions, as shown in Fig.3. The soil
at Site 2 was more compact and had a higher clay
content (5.3% vs.0.6%), higher silt content (2.3%
vs. 1.8%), higher bulk densiry (7.72 g/cm3 vs.
1.56 g/cm3),1ower porosiry (0.345 vs. 0.4) and,
consequently, difierent hydraulic properries rhan
the soii at Sire 1 (See Tables 2 and 3 in Resultsand Discussion). The hydraulic properties of rhesoils were determined directly using several standard methods. Capillary rise (Lambe 1951) tesrs
were performed to evaluate the wetting curves ofthe soil-moisture characteristics. The nonlinear
optimization program R-ETC (van Genuchten etal. 1991) was used to fit 0(l) data to Eq. (7).
Falling head tests (ASTM D-2334) were per-100.007o

80.007o€-.- Site 1 Sieves-r- Site 2 Sieves-o- Site I Hydrometer

6o.oovo

R 40.00Vo
20.00Vo

0.00Va10.0000

1.0000 0.1000 0.0100 0.0010 0.0001
Grain Size (mm)Fig' 3. Grain size distributions for tested materials at Sites 1 ond 9 determined via sieve and hydrometer analyses.

s32

KooeiovA, Onoway, Gnisr AND Su.,r0Ntx

formed in the laboratory, and Guelph perneameter tests @ouwer and Rice 1976) were done
in situ to obtain the saturated hydraulic conductiviry, K,, of the soil. Muiti-step outflow tests (vanDam et a\.1994) on undisrurbed soii samples andnumerical inversions of observed transient flow
data using HYDRUS-1D (Sim0nek et al. 1998c)

were carried out to obtain estimates of soil hydraui-ic parameters describing the drying curvesof 0(h) and K(/r). To define soil hydraulic properties accurately in the approximate range of pressure heads measured in the field with the cone
permeameter, the mulfi-steP outflow tests were
run with the foliowing pressure heads applied at
the center of the samples: - 10, -25, -55, - 100,
* 170 cm. During each pressure head step, equilibrium rvas achieved so that the soil moisture

contents paired rvith the applied pressure heads
could be included as points of the soil-moisturecharacteristic in the optimization process. In thiscase, the pore connectiviry parameter, /, was also
optimized. Soil samples for iaboratory tests weretaken close to the screen and tensiometers after
the cone permeameter tests were completed. In
siru Guelph permeameter tests were performed
before cone permeameter testing and far enoughaway so as to not influence the flo"v region during cone perneameter testing but close enoughto obtain properties of approximately the samemateriai.
Cone Pernteanrcter Tests\Y/- ^-J^---r c,,- tests at different locations
at each site. Before the cone permeameter wasplaced in the soil, a soil core was taken with asampler of smaller diameter (3.2 cm) than thecone permeameter (4.06 cm). This reduced possible disturbances caused by the direct push of
the cone permeameter into the soil. The soil core
was divided into sections of knoq'n volume, andthe initial soil moisture contents were determined. The cone permeameter was then inserted
into the sampler hoie. Tests were performed im-

mediately after the cone permeameter wasplaced in the soil, and the measured pressure
heads reached equilibrium. Tests were always
conducted with rlvo sequentially applied Pressure
heads. For the first three tests (A, B, and C), pressure heads of 30 and 50 cm rvere applied to thecenter of the screen, which corresponded to single-step applied pressure head (30 or 50 cm) experiments performed previously in the labora-

tory and andyzed by KodeSovi et ai. (1998, 1999).:.
and Simrinek et al. (1999). To demonstrate rypr-

cal flow responses, we show as examples the

Sor ScrcNcr

courses of Tests B at Sites 7 and 2 (Figs. 4a andb). Recorded pressure head changes during thefirst applied pressure head considerabiy outweighed changes during the second applied pressure head for both tests (Table 1). To ger more

sigrrificant information about the soi.l-water
regime, it would be more desirable to obtain similar pressure head changes duiing both steps, withmaximum pressure heads close to zero. Therefore, rve carried out Tests D with the appliedpressure heads of 27 and 108 cm at each site.
These pressure heads represent the lowest andhighest possible heads that can be supplied withthe present prototype.As shown in Figs.4c and d,
the measured pressure change during the first applied pressure step dominated that measured during the second step. In addition, in the case of
Test D at Site 2, the overly high applied pressure
head and corresponding high flow rate probably
disturbed the soil structure. u'hich resulted in adecrease in the initially high infiltration rate, as
s'ell as the pressure heads during the second applied pressure head step. Finally we conducted
Tests E with applied pressure heads of 21 and 80
cm. The effeccs of structural changes resulting
Gom the higher applied pressure head is again evidenr, but appear to be less significant than for
Test D (Figs. 4e and f).
Tests were run for different lengths of time
according to the measured responses, as shown in

Table 1. The total time necessary to perform a
protofype test is increased by the time required
for test preparation, which depends on the technique used. We are currently using a rack jack assembly (Geonor Inc.). This involves placement of
soi-l anchors, after which the insertion frame must
be secured, and, finall,v, rhe soil sampler and thecone permeameter can be pushed into the soil.
This takes approximately 40 min. It takes another10 mi!. to assemble the cone permeaneter set up
as shown in Fig. 1.
Inuerse Solutions

Cone permeameter experiments with onJy
one applied pressure head were analyzed in previous studies (Gribb et al. 1998; KodeSovl et al.
1998, 1999; Simrinek et al. 1999). Therefore, we
performed numerical inversions for data (cumulative inflow, upper and lower tensiometer Pressure heads) collected during the first infiltration
part of the experiments, e.g., for appiied pressure
heads of 30 (Tests A, B, and C) or 21 cm (Tests D
and E). To study the effect of the second appliedpressure head on estimates of the soil hydrauhc
properties, rve then carried out numerical inver-Vor-. 164 - No. 8

EsrtuarloN or Son Hvonaullc pnoprR.rrEs

Site I, Test B

Site 2, Test B

m

0

0

-so
E
E

-2000

' 8 -100

Lower Tensiometcr

g -150Upper Tensiometer

4000

trn
!io6-<n

t
g
-8000

-2000

g -150* 6 _200* -250-12000 E
U-6000

L,ower Tensiometer-8000-10000^ -zsa3000 6000 9000

12000

Time [sec]

o

-4000

8 -loo

-6000

8 -zw
ts

ra

0

-10000Upper Tensiometer-120003000 6000 9000

12000

Q

Time [sec]a)b)Site I, Test D

is0
.q.Fn
oJi
-5000

0

0

.9, -50

I -1ooUpper Tensiometerg -150Lower Tensiometerfr -zw* -250Site 2, Test D

Fi-10000-15000Inflow-zL ,,t.

3000 6000 9000

0
-2000

E
E.5O
S
9 Ti -lso

Upper Tensiometer

-1oo

E
E -

-8000

o

-10000-250-120003000 6000 9000

Timc [scc]

4000
-6000

Inflow.,* Lower Tensiomeler
.F

12000

u

r2000

U

Time [sec]d)Site I, Test E00

6. -so
S -1oog -150-F-2000
Lower Tcnsiometcr
Upper Tcnsiometcr

4000
-6000
-8000

fi -2oo-10000-250-120003000 6000 9000

12000

Site 2, Test E

o
cfl

dt

e

g-s0

E
-F
e
'56

3 -100g -150*

6 -200

=F

U=

-tsn

-2000
-6000
Lower Tensiometersecond parts of the experimens with appliedpressure heads of 30 and 50 cm (Tests A, B, andC), or 21 and 108 cm (Test D at Site 1 only), or
27 and 80 cm (Test E). Test D at Site 2 was notanalyzed because of soil structural changes that
occurred during the second pressure head step.
Findly, for seiected rests we analyzed dara &om
the entire experiment (e.g., the wetting and redistribucion parts) to srudy hysteresis of the soil
hydraulic properries. In ail cases, the initial soil
moiscure content determined at the position of

-8000

C)

-10000Upper Tensiometer-1200012000

Time [sec]0Fig. 4. Observed cumulative inflow volumes and pressure heads for Tests B, D

sions for data collected during both the first and

a

-4000

3000 6000 9000

Time [sec]e)0

and E at Sites 1 and g.

the upper tensiometer was paired with the initialpressure head reading and included in the opdmization using the second term of Eq. (10).
Inirial pressure heads in the domain were set
equal to the initial upper tensiometer reading forelevarions at or above that of the upper tensiometer. Similarly, the pressure heads at the elevation of the lower tensiometer or below wereset equal to the iower tensiometer initial readine.

The pressure heads benveen the two tensiomJters were linearly distributed. The externalboundaries were ser as no-flow boundaries. The

Koos5ovA, ORoway, GRrss ANo Slu0Nx

534

screen was modeied as a constant head boundary,o$s€or9so+
sv$ot6nh*+
tlttlttttl

E9owith water pressure head ranging from 27.5 to
32.5 cm (or 18.5 to 23.5 cm) from borrom ro rop
for the first step and from 47.5 to 52.5 cm (or105.5 to 110.5 cm or 77.5 to 82.5 cm) for thesecond step. For the third (redistriburion) part of

F3
i .al
tr./

I;-)

:v

0r
at

nNO€O\\C6O€V
vshooo660t

rrrtlttttl

the experiment, the screen was defined as a

9*known head boundary, described by Eq. (3) for
the inirial infilrration of water remaining in rhe
cone body after the water supply was shut offando^^^F

cooNo6:oNo
t49O+t:C.6€

then as a no-flow boundary after the cone was
empry.

al\tctot\ooNoroosnc)ss€oroorroovr\,
E
N

-'t!

E
a.

=-

sl

rlPI :-

rttlt+
F--

6$NO€€rNNt--N

llttltlJ

that it is only possible to estimate both parameters, 0, and 8,, u'hen the initial soil moisture con-NN

tent is included in the oprindzation process.

I

Without this information, one of these parame-

-

^i.

iOdV

ters must be set at a reasonable value, and only
one can be optimized from analysis of our test
data. Initial escinates for resuits shorvn here rvere
aiways set as follows: 0,0.09; 0, = 0.38; a*

IFNF

:

I

I
I
I

I
I

Ea

I
I
I

:'i ac=^o< "\J

3.=53

6N@-FCO@r-oONOOA€..)

N
P

I

F il:
>:
:9
:3

F=

g

=

a=

ttl

--orA946O
NCiN
INN.iAN

a:.

NI

-l
=L!
6o

K,. When we considered hysteresis, the parameter ad was also estimated. It must be mentioned

-:F
NN+

ttltltt!

<l

9a

--

F

AI

oe

All inverse soiutions were obtained with thesame sets of optimized parameters, 0,, 0,, a*, n and

EI

*l
o-l

I
I

=

I
I
I

^l
el
TI

:l

O

=

F

2l 3

6VNT9OOON
6rO\C+NONN
so6€oNNoc*99C.S9n6N
NNN-OOttO

rtlltttrt

I

9l

A-l

:Iol

66-nNr€66

E-l-FN_NFNNF<l t-.;l rrttttlll

N
I

'-l

-l
I

I
I

F

F
I

3C*O9ONNTNOAHOO.iS
INNNN:--N

tttttlll

hours to analyze rhe rwo-step tests and from 2 to
10 hours for the enrire experiment on a Pentium
II Pro 200 MHz.
NRESULTS AND DISCUSSIONSI

The soil hydraulic parameters obtained from6L.

c€N900Noct
6*6NOrOiO
eN-NNNail numericai inversions of cone permeameter

rrtlllttl

N

F+NNNN
q9qAqoUqU
q6n6u)v)q6aN

data and those obtained using standard techniques are presented in Tabies 2 and3 and in Fig.
8. Measured and simulated cumulative flow andpressure head data are shown for Tests B and E
from both sites in Figs.5, 6,and7.

I

.;
.=

F

F

:

0.035 cm-1; n = 4.0;K, : 0.002 cmlsec; and od: 0.035 cm-r.'We restricted Daramerer /r to therange of 2.01 to 7 (or 2.01 ro 5 for Tests A anc
D at Site 2) and parameter 0, to the range of 0.2
to 0.6. To investigare the uniqueness of rhe optimized parameters, we also carried out inversions
for some tesrs with different initial esrimates of
the hydraulic parameters.'We obtained almost thesame resuhs, without significant deviations. On
the other hand, we had to resrricr paramerer fl to( 5 due to nonconvergence of solution in the
rwo cases noted above.
The computarional time required for inverse
solution depended on the length of rhe rest, theinitial parameter estimates, and che eftciency ofthe computer. In our case, it took from 1 to 5

-TOO€€ON6
N5nta66i-FNOAN

il

-l
?

Sou. ScrsNcr<deatd<dud

X

One- step Pressure He ad ExperimentsF.

the one-step pressure head experiments: Test

Figures 5a-5d show the results of analysis foroVor. 164 - No. 8

EsrruarroN oF Sotr HyoRaulrc pRoprnrles

53s

TASLE 2
Hydraulic parameters e', d, n,0,, 0,and, K obtained &om difi'erent
tests at site l,where rhe measured
bulk densides and porosiries ranged berween 1.45 and 1.70 g/cm3,
and 0.350 and 0.45g, respecdvely

Tcst merhod

Hydraulic panmcrerst'(e/d(cm-1)

r (-)(cmlsec)

Capillary Rise (1 of 2 Columng

0.067

7 10

Multi-Srep Ourflow (1 of 2 Sanrples).

0.000

0.028

3.86

0.1 40

Guelph Permeamerer (4 Test Holes)
Laboratory Falling Head (9 Sampleg
Cone Permeametcr A, &o = 30 cm
Cone Permeameter A, fio = 30, 50 cm
Cone Permeameter B, lo = 30 cm
Cone Permeameter B, ho = 30,50 cm
Cone Permeameter B. lu = 30.50 cm,& redisrribution
Cone Permeameter C, lo = 30 cm
Cone Permeameter C, fio = 30,50 cm
Cone Permeameter D, /ro : 21 cm
Cone Permeameter D, lo = 21, 108 cm
Cone Permeameter E, fio = 21 cm
Cone Permeameter E, ho = 21,80 cm
Cone Permeamete r E, /ro = 21. 80 cm,& redistribution

0.380
0.400

0.00140.0025--0.0038

0.001H.0044

0.037

J.t /

0.088

0.035

4.81

0.089

0.037

J.v)

0.088

0.035

4.79

0.089

0.035/0.026

4.46

0.088

0.034

J,Of

0.033

4.04

0.082
0.083

0.047

z.)3

0.055

0.044

3.1 1

0.069

0.035

3.19

0.087

0.031

4.09

0.031/0.026

4.02

0.089
0.089

0.379
0.377
0.400
0.393
0.390

o.00220.00200.00180.00160.0016

0.433
0.449
0.443
0.447
U.JJJ

0.001i0.00110.00400.00360.0011

U- J)TJ

0.00i 00.0010

0.349'Pore connectivity parameter, /, in Eq. (8) was also optimized (l= _ 1.57)

1 (Fig. 5a), Test B-Site 2 (Fig.5b), Test!-!i*
E-Site 1 (Fig.

5a, c, and d) for the inirial increase of pressure
head at rhe upper tensiomerer (Fig.5b). The sim_5c), and Tesr E-Site 2 (Fig.5d).
In all cases, the cumulative inflows were well sim_
ulated. Oprimized pressure heads corresponded
closell' with observed values, except for th. partwhen pressure heads measured with the upper

ularions did not match rhe initial decreases ofpressure heads measured with the upper ten_siomerer (c and d). These measured preisure headdeclines were probably caused by air thar was

tensiometer approached their final ,oal,_,es (Figs.

forced ahead of the wetting froni and, as such.

TABLE 3
Hydraulic parameters a'", d, n, 0,, 0,andK, obuined from drfferent
tese ar Site 2,where the measured
bulk densities and porosities ranged between 1.6r and 1.95 g/cm3,
and 0.304 and 0.391, respectively

Test methode (e'/d) (cm-(cmlsec)

Capillary fuse (1 of 2 Columru)

0.052

t1n

Multi-Step Ourflow (1 of 2 Sampleg.

0.018

3.46

Guelph Permeameter (4 Test Holcs)
Laboratory FaUrng Head (6 Sample$
Cone Permeameter A, lo = 30 cm
Cone Permeameter A, lto = 30,50 cm
Cone Permeameter B, lo = 30 cm
Cone Permeamerer B, fio = 30,50 cm
Cone Permeameter B, lro = 30,50 cm,& redistriburion
Cone Permeameter C, ho = 30 cm
Cone Permeameter C, io = 30,50 cm
Cone Permeameter D, fio = 21 cm
Conc Permeameter D, fio : 21, l08 cm
Conc Permeameter E, ho 21 cm=
Cone Permeameter E, ho = 21, 80 cm
Conc Permeameter E, fio = 21,80 cm,& redistriburion

0.0s5

n 114

0.380
0.350

0.000130.00044-{.0007s
0.00011-{.00064
0.030

5.00
4.98

0.026

s.29

0.026
0.025/0.018

5.07

0.176
0.116
0.124
0.124

4.05

0.1 200.321

0.000250.000250.00026

0.38s
0.386
0.303

0.000300.000290.000960.385

0.000740.000670.00066

0.031

0.022
0.022

J.t6

0.142

3.24

0.1 43

0.036

5.00

0.i20

0.032

4.07

0.031

4.96

0.031 /0.024

4.89

0.099
0.099
0.099

'Porc connectiviry parameter, l, in Eq. (g) was also oprimized

1l= _ 2.rrr.

0.309
0.303

0.000610.00061

0.331

0.328

0.381
0.381

Sor ScmNce

Koor5ovA, ORowav, Gn tsn aND Su"lriNpr

536

Site 1, Test B

ao

;trH

Upper Tensiometcr

4000

i,>,

Inflow

-5000
-6000
-7000

I -toog -150I -200-2502000 4000

0
-1000
-2000
-3000

EF

-1000
-2000
-3000

Lower Tensiometer.E -soSite 2, Test B

(.1

0

E

.E

!

E-so
E -rooe -l5oLower Tensiomeler

6 -200Upper Tensiometer- -zso06000

Time [sec]- Measured Data -a)Inverse Solution- Measured Dau -b)lnvene Solution

Site 2, Test E

0
Lower Tensiometer

3 -tooi0-1000 6'tr

6 -200(.r

02000 4000

I -100tt

C -150!

-250

s -200- -zso-4000
Upper Tensiometer2000 4000

6000

I

-2000
-3000
Lower Tensiometer

Time [sec]Measured Data

-r000

E-so

2

!

Upper Tensiometer

0

;
-2000

-3000 cts
-4000
-5000
-6000
=rf
-7000

Inflow

E -150-6000

0Jf -)u

-5000
-6000
-7000

Time [sec]Site I, Test Ec)2000 4000

4000

q)

-5000
-6000
-7000

6000

Time [sec]Inverse Solutiond)- Measured Data -Inverse Solution

Fig. 5. Observed data and simulated cumulative inflow volumes and pressure heads resulting from analysis of first
infiltration part of experiments with one applied pressure head; ho = 30 cm for Tests B at Sites 1 and 9, and ho =91 cm for TesG E at Sites 1 and 2.

cannot be described with the numerical model.
The pressure changes at these low pressure heads
correspond to a very small change in moisture
content for these soils. Therefore, we assumed
that the air phase had iittle influence on the wa-

muiative inflows were again weil simulared.
Modeled pressure heads during the first steP responded in the same way as for the one-step experiments. Simulated pressure heads during thesecond step followed measured data from the up-

ter flow regime.
The soii hydraulic properties estimated fromper tensiometer better than those from the lou'er
one. Logically, the simulations did not reproduce
the initiai increase and subsequent decline in thepressure heads observed after application of the

all cone permeameter experiments at Site 1 werevery similar (Table 2). At Site 2, the estimatedproperries varied to some degree, but such variabiliry was also observed using the other experimentai techniques (Table 3). This suggests thatthe proposed cone permeameter method provided consistent results. Inclusion of the initialmoisture content in the objective function
yielded realistic estimates of 6, values that corresponded well to measured porosiries.
Two-Step Pressure Head Expeiments

Fig.6a-6d shows the resulu of analysis for the
rvvo-step pressure head experiments: Test BSite 1 (Fig.6a), Test B-Site 2 (Fig.6b), Test ESite 1 (Fig. 6c), and Test E-Site 2 (Fig. 6d). Cu-

second pressure head. The pressure decrease wasmore obvious for the lower tensiometer. As discussed previously, this was likely caused by soil
structural changes.
In previous snrdies, higher vaiues of 0, and {were obtained for one-step experiments withhigher applied pressure heads (50 cm) than forexperiments with lower applied pressure heads(30 cm) (KodeIovi et al. 1998, 1999;Simrinek eta]. 1999).A similar eflect was not found in thiswork. The applicarion of higher pressure heads inthe wvo-step experiments did not influence theresulting soii hydraulic properries gready when
comoared with those obained from the one-stepVor. 164 - No. 8

EstruartoN or Solr_ HyntauLlc pnoprnrrrs

experiments (Tables 2 and 3). Of course, the resuits from the rwo-step experiments were still
controlled mainly by the first steps. However themeasured data during the second step wererracked well, especially the cumulative inflows,which primarily influenced values of K.. The
benefit of performing and analyzing rwo-step
experiments (even u'ith such small impacc on
observed pressure heads during the second part)was that the inverse problem was better defined,
thus preventing the inverse algorithm from wandering into arex of paranreter space that could
cause numerical instabiliries.'When analyzing the
one-step experiments, the inverse algorithm attempted several times to make a step in the direction of the n parameter (if unconstrained) that
resulted in numerical insubiliries (Site 2, Tests A
and D). Better definirion of the inverse problem
also improved the stabij.iry of the inverse solution. Since the higher supply pressure heads during the second step extended the ranges of measured pressure heads at both tensiometer rings(Table 1), the optimized parameters are expected

to be representative for wider ranges of pressure
heads.In addition, rhe optimized hydraulic properries better define behavior near saturarion. The
accurate description ofrhe soil hydraulic proper-

ries close to saturation has recently receir.,edmuch attention (van Genuchten and Leij 1999).
Three-Step Expeiment (Two Applied
Pressure Heads and Redistribution)

Figures 7a through 7d show the results ofanalysis for the three-step pressure head experi-ments: Test B-Site 1 (Fig. 7a), Test B-Site 2(Fig.7b), Test E-Site 1 (Fig.7c), and Test E-Site
2 (Fig.7d). The simulated flow responses during
the first and second parts of the experiment rvere
similar to those obtained for the swo-srep experi-ment. The pressure heads during the ridisriiburion part were modeled satisfactorily, excepr forthe pressure heads measured u,ith tLre lowei tensiometer for Test B at Site 2. In this case, the measured pressure heads decreased in nvo steps. The
numericd model with the prescribed boundan'
conditions could not simulate such behavior.

Site 1, Test B

Site 2, Test B

?0-so

0

.E

-2000

3 -r00g -150*4000
Upper Tensiometer

-250

0

n

o

E -so

o

3 -r00o -15n

-6000
-8000

fr -2oo-10000a -tnn-12000-2502000 4000 6000

U

a)

-

-

0

-2000
Inflow

Upper Tensiometer-2000
Lower Tensiometer

4000
-6000

g -150-8000

fr -zcnUpper Tensiometer

-250

0

-12000-10000-r20002000 4000 6000

oo

- Measured Data - Inverse Solution

Inverse Solution

0

I

0

-so

-2000

S -too

-4000

o

-6000

g -150
Lowcr Tensiomelerfi -zoo* -zsoUpper Tensiometer

-8000

{)

-10000-120000Time [sec]c)-10000Site 2, Test E

c.l0

I -100a2000 4000 6000

- Measurcd Data -b)Site 1, Test E

E -so

-8000

Time [sec]Inversc Solution

0

q)

-4000
-6000

Lower Tensiometer

0Time [sec]Measured Data

537

2000 4000 6000

U

Time [secJd)- Measured Data -lnverse Solution

Fig' 6' observed data and simulated cumulative flow volumes and pressure
heads resulted ftom analysis of first andsecond infiltration parts of experiments with two applied pressure heads; fr" 39 and50 cm for Tests B at Site 1
r 'u= -and 9, and ho= 91 and 80 cm for Tests E at Site 1 and Q.

538

Koor,SovA, ORpway, Gnrse nNo StM0r.\EK
Site 1, Test B00E

Jr -50

I

-2000

-100

g -150Lower Tensiometer

4000

Upper Tensiometer

-6000
-8000

n -200-10000Inflow-250-1200003000 6000 9000

12000

Site 2, Test B

an
trF

-

Measured Data-:

3 -100g -150o>a! *8
E -zsot)0
Lower Tensiometer

-2000
-4000
-6000

-8000
Upper Tensiometer

-250

0

-10000-120003000 6000 9000-

Measured Data

-Inverse-r00000-120003000 6000 9000

12000

;
E
7,
>=

!

E

Inverse Solution

Site 2, Test E

An
EF

u

E-so
5 -roo-2000
Lower Tensiometerfi -zoo* -rsn-8000

I-10000Upper Tensiometer-120003000 6000 9000

12000

o

-4000
-6000

e -150Time [sec]

c)

-8000

Upper Tensiometer- Measured Data -b)Site 1. Test E

fi -zoo-6000
Lower Tensiomeler-zoo

Inverse Solution

3 -100g -150

-2000

4000

Time [sec]

0

E -so

0

E E-soTime [sec]a)Sou- ScrrNcr

12000

Time [sec]Solutiond)- Measured Data -Inverse Solution

Fig' 7' Observed data and simulated cumulative inflow volumes and pressure heads resulting from analysis of thefirst and second infiltration parts of experiments with two applied pressure heads, i,o = 30 and 50 for Tests B at
Sites 1 and 2, and ho = 91 and 80 cm for Tests E at Sites 1 and g, and the third redistribution part with no infiltration through the screen.

The pressure head decreases for all cases dur-ing the water redistribution process were small
compared r',.'ith the totai pressure head increases
during the infiltrarion parts of rhe experiments.
Thus, it would seem that the information obtained rvould be less significanr. However, the inverse solurions did yield reasonable esrimates ofparameter ad defining the drying process, and theresulting soil hydraulic properries characterizing
the wetting curves were almost the same as forthe rwo-step experiment (Tables 2 and 3). The
dift-erent c parameters for the wetting and drying
curves illusrrated hysteresis (Fig. 8).
Compaison oJ Soil Hydraulic Propefties Obtained
uia Inuerse Solutiotts and Other Techniques

Soil-moisture characteristics obtained withnumerical inversions correspond weli with thosemeasured u'ith the mulri-step ourflow techniquedescribing drying curves and sarisfacrorily wirh
the curves from the capillary rise tesrs characrerizing the werring curves (Fig.8).It must be notedthat the capillary rise tests were performed on
repacked soil columns. To measure properties
similar to those determined on undisturbed sampies, it is necessary to ensure rhe same densiry ofmaterial. This was difEcult to achieve (especiallyin the case of rhe soil from Site 2),and, as a result, higher saturated soil moisture conren$ wereobtained. In addition, the soils were inirially very

dry, and, therefore, the data obrained described
the limiting wetting curves, and the optimized
residual soil-moisture contents were lower thanthose determined by the other methods. On theother hand, the residual soil moisture contentsfrom the multi-step ourflow tests were higher
than those obtained from the other tests. Multistep oucflow tests were performed with pressure
heads ranging berween 0 and -170 cm, and thedetermined parameters are characteristic for that
range. It is probable that the value of d. would belower if tests were run for lower pressure heads.
Nonetheless, the curves predicred iy inversion ofcone permeameter data lie predominandy be-Vor. 164 - No. 8

EsrtuarroN or Sort_ HvoR-q,ulrc pnoprnrrrs

rween multi-srep ourflow and capiilary rise
curves.

The esrimared sarurated hydraulic conduc-tivities were in the range of measured data ob-tained wirh the laboratory falling head rest andnear the lower limit of values obtained with the
Guelph permeameter in rhe fieid. We consider
such correspondence to be exceilent.

CONCLUSION
In this articie we document the applicabiliryof a protorype cone permeameter for determin-

100

sonable value.

360
An

9, zv
0

0

0.1 0.2 0.3 0.4 0.5

*A
*E

*B
+dB +C+dE-CR-MO

Moisture Content [_]+)Site 2
100

The technique for obtaining the initial moisture content of the soil and use of this informa_tion in the optimization process proved to bevery useful. Inclusion of the initial moisrure content, paired with the initial rensiomerer reading,ailowed for realisric esrimation of 0.and d..,aluei'Wirhout
this informarion, only one of rhese pa_
rameters can be optinrized, and the orher one
must be set at a reasonable value for our experi_
rnentai data sets. Anall,sis of one- a,rd rwo_step
tests yieided similar paramerers. presumably be_cause of the dominanr influence of the first steoon the inverse solutions. However, addition of
the second step better defined the inverse prob_

lem. stabilized the numerical and inverse solu-

tions, and resulted in paranteters representadve ofa rvider range of pressure heads. Application ofhigher applied pressure heads to force pressure
head readings closer to saturation was pioblem-

5. 80

360

atic. The higher flow likely caused destruction of
the existing soi.l. strucrure and, consequently,

94n
o

8zo

changed the soil properties. Thus, rve do .rot ..._

0b)

previously discussed by SimLinek er al. (1999) andKodeiovi et al.. (1999).Analysis of cone p.r-._
ameter tesrs in an anisorropic laboratory aquifer
soil returned unreasonably high estimaie, of e,.
They found that an anisotropy factor expressing
the relationship berween horizontal and-vertica-l

simulated flow responses if d. was fixed at a rea-

880

a)

ing hydraulic properries of sandy soil in the field.
The tested materials (the second layers of the soil
profile$ were very homogeneous, without obvi_
ous layering or anisotropy, and, as a result, opti_
mi_zation of parameters 0,,0,, a,,,cd, l, and K was
suficient for describing che observed flow responses. The solurion, including anisotropy, .rvas

hydraulic conducrivities could be optimized roobtain good agreement between observed andSite 1o

539

0

0.1 0.2 0.3 0.4 0.5

*A
*E

+l
+dB +c +p*dE-CR -MO

Moisture Content [-]Fig. 8. Soil-moisture characteristic curves obtained withstandard methods and those obtained kom inverse solutions for all tests. Only the curves resuldng ftom analysis of the following dato are presented: Test D 6t Site 9(one-step), Tests A, C, and D at Site 1, and Tests A 6nd
C at Site g (two-step), and Tests B and E at Sites 1 and
9 (three-step), where dB and dE refer to the drying
curves. CR and MO refer to the curves obtained fromthe capillary rise and multi-step outflow experiments,
respecWely.

use of appiied pressure heads higher
9".*:1dthan

80 cm with this device. The wetting"\_

draulic paramerers obtained from anaiysis Jf theentire experimen$ were consistent *irh ,hor"obcained from analysis of only rhe wetting parsof the rwo-step experiments. The drying c (afwas lower, as expected. The different a values described the effect of hysteresis. The estimated hydrauiic properries corresponded well with thoseobtained with standard techniques.
'We
have studied application of paramerer esrimation to cone permeamerer data in difi'erent
sandy soi1s, and for this rype of soi1, this experi_mental technique seems to be fuliy applicable.
Furure work will include field suiies- i, othe.

soil ffpes.

Son Screxcr

Koor,SovA, OrowRv, Gnnn aNo SIr,a0Nex

540

ACKNOWLEDGMENTS

The authors thank S. Anderson and M.
Mwamba for performing some of the laboratory
tests, and the Nacional Science Foundarion CA-

R€ER Grant CMS-9501772 and U.S. Army
Research Ofice Grant DAAH04-95-1-0228 forsupport of this project. The authors also acknowledge the anonl'mous revieu'ers.

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^/^^daEching, S. O., andJ.W. Hopmans. 1993. Optimizationof hydraulic functions from transient outflow andsoil water pressure data. Soil Sci. Soc. Am. J.
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Eching, S. O.,j.W. Hopmans, and O.Wendroth. 1994.
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