\ . I .//' " J , ;" ----"" ,- > " " " The Simulation of Rillenkarren. \ '! - • ,.
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The Simulation of Rillenkarren. \
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Tl!ESlHULATIO!{ OF ~ , . I, •. .. ".::
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JOHR R. GtEw . ,
A Thl!ais ,
Submitted to the School ofCraduate Studies
in, Psrtial FJ1lfi1ment of'the Requirements
for the, Degree
Master of, Science
HcKsater University
April1976
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j CE> JOHN R. GLEW 1977 ",,-" 11'
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MASTER OF SC.IDlCE (1976) -(Geograp'hy)~-
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. McMASTER UNIV~ITY Hamilton,' ·Ontar.io-
TITLE: The Simulation o~, Rillenkal-reri
,AUTHOR: , Jphn R. Glew B.Sc. (Trent !1nivereity)
SUPERVISOR: Dr. D.C. Ford
NUMB'Ut OF PAGES: X, 116
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ABSTRACT '
- " " The development of Ril.lenkarren surfaces on plaster sad
, . salt has been s1mul4ted in a serie,s of enalogue ezperiments using
e laboratory rail1fa~ simulator.
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The axpen-nts 'determined that rainfall 18 the daad.uaut r "" • '(.o!;;
process controlling the ,development, of'Rilleukarren. The length of
'rills 18 related to the angle of slop~ of the. ezposed' surface. The
/ rill cross-section approaches that of a ,parabolic channel. The width,
of tl18 rill appears to be determined by properties of the materia1: , , . . ; ~
on plaster sud 'sBlt Charac\le:P.atic widths and depths were establlihed., .. .;. : . . \ No ezperimeute ~ere carried out, On limestone in the laboratory.
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The development of Ii R111eukarreu ~urface in, uat~e 18
unique. The laboratory ezper1meuts have determined that such a s?rface
• repreaeuts one of rim effect adjusting to the proces.s of rainfall
(the rsudOlll distribution of water dropleta of a size rsuge less than
0.2 mm to approximately 4~S mm in diameter, falliug at speeds close
to their terminal velocities). The pbys1ca of such a phjmaDeuou do
not appear to have been investigated sud it is suggested that very
~ , considerable dyuam1c analysis would be required to further the
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observations reported1!ere.
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, ACIQIOWLEDGEHER'r~ , '. " \ ,'. , " -\.
The author ill indabted to hill .upe~lIor, Dr. D.C. Ford\ , ... ", ' '\
wholle ~tilllll:l.a81ll for the proje'?t and- lIupport and 'direction" made, 1\ p~ss:f.b1e this study; to Dr. W.P. Adame of Trent University whose
\ ebiHo/ to extract a concise draft from the accumul.a~ed exper1mental \
\ data was :l.nvaluable, and to ,Dean J .L. Rob:l.nson of Durham/College for
many uSeful ideas ~hat were incorporated into the model. / ' '
\ , Particular thanks are due t9!4'. Robert' Bignell~ saaior
. ~ technician and Hr. Rick Zablocki, technician with the Geography
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. Department along with Hr. J1m, }layer in the machine shW and eng:l.neer:l.ug
supply; for a great deal of technical support.
Finally I would 'like to thank Hiss Rosanna Wan for typing
the' theais.
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Chapter
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1:2
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A\BSTRACT, ACKNOWLEDGEMENTS TABLE' ere CONTENTS LIST OJ? fiGURES LIST OJ? TABLES
mTBODUCTION ,
Description o~ the Ri11enkarren'SurlACII , \ ,
SOIII8 Unique AsPects of RiUenkarren \ \
. .\ 1:3 Hypotheses Regarding the Rillenkauen Surface
, 2 THESIHIJI;ATION HODEL ,
2:1 General Simulation Conaiderati
2:2c,> The Hardware Hodel
2:3
2:4
2:5
Rainfall Simulation /"'\ ' ,
The Jehavior of the ~clware kde1
Droplet Velocity and 1'-I>118tiIJ:
3 EXPERDIEIiiTAL RESULTS <"'-
3:1 escription of the Experiments
3:2 er1mental Measurements
3: 3 Expe,~lIe%ltal Results
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Ri Length and" Slope Angle Relationahips
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~ laster SurfaCes '
Rill' wi tha on Plaster Surfaces "'-
, '" Rilla get'! rated on Sali:' Surfilcea , '~
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- . . Cross-section of the Rill 47'
Solution Rate fo?: the Ex,per1l11enta1' Surfaca' 50
3:4 Processes Operating on the Experimental Surface 55
4 CONCWS'ION 6 j,.
4 q. SUIIIIia~ of the Experimentalllellults 67
4:2' The Ril1enltarren Surface, what it Represents 69
BIBLIOGRAPHY 72
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APPENDIX .B 85
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LISTOP'P'IGuaES
P'igure Page ,.
1 Physical regimes of water and its relatiOl18hip to Karren developlIIIIDt.· ,
J. Ri~enkarren on landslide blocks i1\ the Surprise Valley. J.asper Nlitioaal Park Canada. 4
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3 General schematic,diagr8111 shovUlg interre1aUonahips between various elements within. the model and, ita " operation. Hatched elements are th08ethat can ,be adjusted to modify conditiOl18; dashed lines :lsldic'at;e a ,feedback effect. In tllis case R11.1en1tau;eu represent the major modification to surface !'b'ape,' 13
4 ,Drop size distribution of simulated rain (at 35 mm/hr) compared 'to Laws t. (1941), medium intensity data. 15
" ''5 The terminal velocity of raindrops for three obs~rved experiments and -two calculationa, (data from Gurm and Kinzer, 1949; Laws, 1941; ,Ima1, 1950; Schmidt, 1909 and Spilhaus, 1945. lS
6 Simulation velocity of drOillets. 19
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Plaster block dimensiona.
Salt block dimenaiona.
Modified plaster block dimensions. '\ "
Guide plate d1mens10118. • \
11 Development of rill partition at J.50, 350" 450 and
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'550 hours. ' \, ,29 .
12 Rill length histogram;' block number J.,'
13 Rill length histogr8lll, block .nUlllber 3.
14 Rill length histogr8lll, block number 5.
15 Rill length histogr8lll, block nUlllber 6.
16 . Rill length 'histogr8lll, block .number 9.
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17 Rill length pistogram. block .number 1.
18 ,Rill length histogram, block ·.nl.lllber 7.
19 Rill 'l~gth histogram, block .numbsr 8 •. ,
\ ;l0 Rill length histogram. block number 10.
- ;l1 Rill 1ength.hi~togram, block .number 4.
:z:z Plot of ri.!l length vs. sl~e engle.
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;l3 Time profile, 100, 300 end 500 hours. 4;2
;l4 Development of a rill crOSB grading .network, (after Horton, 1945), li'1g. 19a, compared. to the development of Rillenkarren; Pig. 19b. Note different scales end the' chenge in net flow direction associ-ation with'crOBs grading. 46
, ;l5 Comparision of three characteristic rill widths.
Simulated rills on plaster, salt end .natural 1ime·stone (Pa1iser limestone, 'Jasper National Park). '
;l6 Partial cross section of enatural Rillenkarren surface on limestone, (above) 8Ild a simulated plaster surface, below. Both profiles 8 em from crest; experimental
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surface 60·, natural slope appx. 70·.. 51
;l7 Cross ~ectional shape of a rilled surface approximated by balf circles A, Intersecting circles B, and :llttersectiug" parabolas C. . 52
;lS Rill deepening over time, conforming to parabola: y .. lIS). (s2). Profile flOlD block number ;l, 1;20 brs to 504 brs, S em profile zone 5. \ .'
;29 Plot of surface reduction against time;/
30. Estimated surface,erosion plotted against slope gradient, after Horton, (1945) end Renner, (1936).
31 Sustained volume of water/Vs. surface inclination.
3;l Theor~tical dissipation of energy over a parabolic surface.
33 . General arrangement: McMast.er University Rainfall Simulator.
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The McH4ster University Rainfall Simulator.
Nozzle spacification. W Cr';\Ue ·top view, 1/4, scale. .~.~; ~ ~
: water' circ4·la~~on·.·di~gram; Plaeter block. specification.
Block mould, !lross-section. __
Photo POsitiODll, with block ·inclined. '{-,
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Camera and 'projector positions, with block inclined. i
,Projector, gen6ral arrangement.
Projector detail.
Oil bath, l/l scale.
4S . EXpo8ure ap~aratus for raindrop meaeurement.
46, Aperture plat!!.
47 General arrangement of the aperture gauge for measuring film flow thieleness over block surface.
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LIST 01 TABLES
Table, .•
,2.1 Terminal veloci tie.. for raindropa 0.5 111m to 3.0 JI1ID .
3.1
3.,2
. diameter. (attar Ounn IIIId Kinzer, 1949).
Mellll width. ot rilb _lIured at ,3'; 5, IIIId 10 em po.ition. tor varioUi .lope 11118le& . '.' I .' Mean width ot' rUb mea.ured at,26%, 43% IIIId 87%
. ot mean rill lensth. trom crllt ~t Ilope. . . ,"
3.3 eompari.on ot rill width. dave~ped.on aalt, column A aimulated, column ,B natural rain.
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3.4 Simulated rain tall intllllaitie., and teat inclination • . tor plaster bloclta 1 - 10. ..
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3.5 Volume ot water intercepted by the. experimental 'surface at selected anSle., (lit res per hour).
3' •. 6 Surface reduction.
B.l. '. Simulator; Settinss Experiments No. 1-10.
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CHAPTER ONE /'8"
ImRDDUCTION
D~CriPtion of Lhe Rillenkarr~ Surface.
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Rillenk8n::en or, lapies are small scale features attributed
to the solutional weathering of readily soluble rocks such as carbonates, , , \. '
sulpiultes and halides. Uilder the heading of karren are grouped all such
smaii'sCale surface soluti~ features. Because of the great variety
of surfaces' and' a world wide distribution, an tiliun~,ce of names and a
large v'olume of literature,have accumulated: , The ,nm.enc1ature[ used
, throughout ,this thesis is that of, Bogli et 8,1. (1960); part: of his
classification system is also used here.
RillenJcaJy:en may be ,considered as a apecific surface form.
belonging .to a larger group of karren features. Karren surfaces have
been reCQgnized by Bogll (1.9"60), Miotke (1968) and Jennings (1971) as , "c" CQmprising three_~":\llc groups; texmed free, half-free and CQvered. Such
a division s1mplif:1~"the classification by separating fundamentally,
different types by process-fo,rm relationships. figure'l illustrates
tlie likely development of various karren forms in assoCiation with the
dominant process involved. Rillenkarren are sh""", as belonging to the
free-karren group, developing eS,sentially on bare rock surfaces wi'Ch
out the influences of vegetation or soil~ in direct response to the
rainfall process.
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Free falling rain' >--. striking bare' rock
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RILLENKARR£N
\ SPfTZKARR£N
\ KAM£NITZAS TRITTI<ARR£N
\\ .\ . SH££T SOLUTION
LARG£ SOLUTION PITS AND BAS}NS
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\'''' \ Half free \
. Subsurface \
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. RINN£NKARR£N .... =.~ =- ¥. =<;}.===--=";'~ """-.... =~,~
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Standing wa.ter in association with vegetation and soil
~ ~ ~ ~ ~ ~ -;Q ~ ~ ~. '" ~. ~ -z. -z.
Surface runoff over rock
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!<==rSLilsurfoce flow 0
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13 Surfat:t! flo\ll ,
Fig. 1.
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Physical rBllimes of water 'and its relationship 10 Karren development .
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/ . Rill"nkarreri surfaces are· not common to all karst regions, ,
, , but have been des-cribed in a wide variety of locatioas on many different
lithologies and under greatly differing climatic conditions. Because
of the;l.r yery distinctive appearance; Ril1enkarren were one of the-first
types of solution sculpture to be classified. The name 'Rillenkarren' \
(literally translated 'grooved karren') refers to surfaces solutionally
weathered to a form dominated by efficiently 'packed parallel grooving·
which is aligned, down the steepest part of the inclined exposure
(Fig. 2.). The Ril1enkarren surface is unique smong channel erosional "
features developed at the earth's / . '
surface, with no known similar
morphological form existing elsewhere in nature on other rocks or . ,
at other scales.
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Two attributes of the surface are distinctive. Fi~~ erosional channels appear to be propagated from the highest part of
the slope: This is a reversal of the mcn:e usual form of channel
erosion described by Horton (1945). in which an up-slope, or crest I .
area exists in which no channel development is possible. This zone - , 'was termed by Horton 'the belt of no erosion'. Second, the channels
on the R11lenkarren surface are eroded to form the optimum pacldng . .>-. ......... . . . ,
arrangeJDent such that sdjacent cruJini$ or rills form partitions or
boundary walls that are knife like.
1:2 Some Unique Aspects of Rillenkarren.
General;'observation indicates' that slopes- from about 10 degrees
to almost 90 degrees can develop Rillenkarren.' Ford (unPu?') measured
I R1l1enkarren on a series of fifty l.andslide blocks of limestone in the
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Surprise vaU~, Jasper National. Park. It was observed that rilling
was .absent on slopes of less than 10. to 15 degrees and that the rill
forms tended to break' down to'a shallow scalloped surface on s10pes ' ,
greater than 70 degrees. W:f:thin the 10 to 70 degree range of slopes '
no statistically significant relationships between slope and rill·
length could be established, I;l1though casual inspection rather than
precise measurement suggested that rilla were generally longer on
steeper slopes.
The individ,ua1 rilla are frequently deepest on the highest
part of the slope and tend to flatten or wash-out dOwn slope. The .' , ,
characte~tic cross sectional profile of the rilled surface reveals
a strong modality, having been descr:!l>"d_as-a-~et of flutes,
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similar to the decorat·ion on Ii doric column (Eckert, 1902; Civijic, 1924).
The ·stra1ghtness of the' rill psttern in plan-form is most unusual in
naturally weathered . surfaces; the rill packing across'the surface is
partly responsible for the uniform width and cross-sectional shape
" of the rill form. The packing can be said to be almost perfect with
'" no surface, flat or othet:Wise, existing between individual r1l1a,
"-....-... !;"om_"'.'~,I'l3~~,!neItt~~E! in the'Surprise Valley. Ford (UDpub~) reports
a packing br rill ----ity ranging from 23 to 26 per foot from fifty
measured samples.
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1:3 Hypotheses Regarding the R11l'~Urface. Al.though R111enka=en have long been re ognized as a surface
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• characterized by uniform shape and habit,
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inexplicabfhen~. HSny have been advanced to explain their
'existence; '-g(;~~ are-ones involving ice,wind and w~ter,as well , }' '
as a cOmbination of pro~ses. AlthoughlllO/!t of these hypotheses have
now been rejected in favour of one 'ihvolving rainfall, a great ,deal
of speculation still exists regarding how the process operates and how
/ ' , other controls of clilVSte affect the rate at which such/surfaces, evolve.
/
Sweeting (1972) maintains that Rillenkarren represent a
surface form that. is established very rspidly," citing as examples rill
development on surficesthat have Onlyrecen~ exPosed, as in
quarries. Both J~gs (1971) and Sweeting (1972) regard climatic
___ '-c- variation as a signifIi~-ac.tOi:-.in 'the general distribut'ion of , .~.. -~
Rtllenkarren and the form of rill ,pevelopment, the rill length being
greater in warmer and wetter regions than in temperate zones; also
finer (smaller sCale) rills ,are' found in semi-arid regions, receiving
less than 250 mm of rainfall annually (Wilford and Wall, 1969). The
means by which the formative processes are modified under these
different' cl1matic regimes are not made specific, other than by ,
suggesting crude limitations imposed by severe envirOIllDeDts such as
exist in periglacial or semi arid-zones. McMaster lhdversity fi.eld
parties have noted many Rillenkarren in the Nahanni karst which is
in a periglacial region. Rates of formation, while sUsl'ected as
beiIig rBllid, have not been measured even in what are coDsidered
the most favourable climates.
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Hitherto,the problems associated with -Rillenkarren formation
have been addressed only in terms of- theoretical l'ossibilities.
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Ci vij ic (1924). while ,dis~s:l,ng in some detail the enlargement of large , .
lapies. advanded no theoxY on the development of 'young lapies'. I Lehmann (1927) and Rathjens. (1939). summarized in BogH (1960).
approached the problem of r::I.l1 deVelopment by hypothesising that tlie
ch~c:al aggressivity of rainwater vas reduced substantially as it ,_ Ii .
flowed from the crest of an inc;:lineCi surface down-s1ape. and that
this was a major factor in determ:l.ning tb.e position of r::I.11ing that /'
characteristically develops at the ,crest. Miotke (1968)' regarded the
. -chem:f.c:al differences of the solution on the surface ~ insignificant
from the ,pOint of view of r::I.ll development. adopting instead an
hypothesis invOlving the preferential movement of low velocity air
over the surface. parallel to the axis .of r::I.lling. This theory is
similar to one put forward by Blanckenhorn (1915).
The purpose of the ser::l.es of experiments reported in this thesis
'is to approach the problem of r::I.11 fonnation by direct s:llllulation • •
SUch~proach enables the accurate d~termination of the fonnation
processes and at the same time provides a means for establishing some
explanation regarding the occ:u=ence of such surfaces in nature.
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CHAPTER TWO
THE SIMULATION HODEL
2:1 General Simulation Considerations • • Rillenkarren surfaces were generated on plaster and salt .
in the laboratory using a rainfall simulator. Thecpurpose of the
rainfall simulator is to produce. in a precise manner. droplets of , '
water whose size. ',fall 'velocity and random distrib,ution. are similar'
to those which make "J?; natural' rain. Only by closely ,replicating
, natural rainfall conditions can some approll.ch--be made to the generation
of, the erds;live e~rgy that is present at the intercepting s~face ". ~. ~ .
. :'", -simulation· of the surface response. the erosional form.
and
to the
Explanaticfu of the formative processes and their significance ,~
"in the de;velopment'!lf Rillenka=en' can be attempted if. under controllfc1
experimental conditions. geometrical similarity between the experimental-. ,. , .
. ' surfaces and natural Rillenkarren developed on limestotie is achieved. , ,
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Hardware models of various types have been used ili' Karst' studies
and related research to inVestigate the solution'rates of limestone.
(Purdie.19721 Weyl.1958). and the d~elopment of solution-formed surfaces
(Goodchild and Ford. 1~71). The latte,r authors studied the development
of erosional scallops or flutes which were simulated upon plaster
surfaces in the base of a small flume. Waterman (1975) and "
Ewers (1916 in litt). used hardware models in the studY of conduit po.
network development along simulated bedding planes. Such
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quite closely wi.th those ~~und in t~e \~81 wor~~, \ " \ \" \ ~"-R1ll~rren are one of the smSflest fe~t~s classified as
.\ \ 1"\\\ "karren. For tllis' ~on,laborQ;tory s:1inulatd.on was regarded as beiJig
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straightforward ~d" probably' tlieiiiO;~economkal "form'of \ vestigat:f:on
witti re/lpect., tq. ;~th time and equi~ment:~~pproach t6 ,\e study '. . .'. ". \~ \ ....... .
. has three main 'advantages. First. no' great 'change. in phyaica~cale"
was envisaged. th~ r8!nfal1simulator. being capab1~of .. pro~' \', )QUC1ng ,
conditions sim1.1ar to thoae prevai1iJig in the natural ~ronment. ' . " .
SecOnd .. ,~ h~~dware model offers the advantages of precis 'contro~\f the key aspects of rainfall intensity. :a1nfal';a"r~,tion. ~ test \
surface configuration. Third. the continuous operat~ of. th~e
model for extended periods of t~ provideathe opportuDi~ for ewing
, ' " the development of an eroaional surface which under natur81 conditions
~\ .\ would evolve only over very long time periodS.
2.2 The Hardware Hodel. •
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\\ some general dea crip tiona of the model operation are reviewed. , . Yalin (1971) recognized relationships that are important iJi
hydraulic modeling. These are not directly applicable to some aspects"
. of raiJifall simulation but do serve to describe the three ma:1n associ-
ations present withiJi the simulation model. Correct replication by a
simulation model may fall iJito three' categories of s:lJrl1arity-
geometric, kinematic and dynamic. Geometric similarity is maintaiJied'
, ...
~, if e its proportions are the same
'counterpart. e 'mOci~s-anematiCallY the same 1£
", it's .. natural '''', .
the 1l havior of , '. ~ ~ ,
tbe"~~uid fl is. dmUar i~ all parts' to that of the natural ~ototype.
Thirch.y~ dynamic similarity is\uamtained if all parts of the mo~ ,
,;- liqU:f.d,~lid and gasebus, are s~ect to the s~ net forces ,that ar
present und~~'natural Cond~ons. ~ The normal scaling problema that~ most significant in
affecting the dynamic, geometric and kinemati~lationshiPs in modelling
\\operat~ons were not encountered in the design 'of ~ rainfall simulator
• due to the maintenance of dynamic and kinematic CODdi\ions close to
natural magnitudes. In this narticular hardware model \ e geometric \ ~" \
similarity is to be regarded as a consequence of the 'other' two '\ .
~elationships. , ~e development of a rilled erosional surface of a c figu-· - , , '\
ration simil~that of natural Rillenkarren is the result oj accurate
replication of the d~ kinematic relationships. Such relation
ships are manifest in the mod~l~e of raindrop size,
droplet size distribution, fall velocity and rilin£all intensity. It
was the failure to produce simulated r~all wit~oplet --~----..
size and terminal yelocities which prevented characteristic rills from .' ".
developing in the experiments of Hoffmeister and Ladd (1945) and
Purdie (1972). In fairness to these workers,~owever,such scale factors
were not considered because in their experiments spraying types of
"\equipment were used only to apply and maintain fairly thick films of
~~lvent to the experimental surface.
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2:3 Rainfall Simulation.
Many investigations have been made into the energy
relationships and the physics of rainfall, ,e;g.', Gunn ,and
Kinzer (1949}.,Jones (1959}'and'Free, (1960). Application of
,rainfall simulati,on teclm1queS in the: study, of,eroding',soils
!
has produced eVidence s,upporting the view that a close association ~
exists between rainfall intensity and the erosional rate of materials
such as sand (Elllson,194l), and sol1s (Wiscbmeier,1957; Hudson 1971).
Only a few at;tempts have been made tostudy.-the effect of rainfall on
th rate of rock erosion Oioffme1ste~and Ladd,1945; Purdie,1972}.
Unlike he work carried out on erosion of unconsolidated materiills, .,0-
with close ontrol and precise ,measurement of the simulated rain, '
littl) attempt' as made"~ these investigations to reproduce accurately
natural racteristics. This,fact is possibly due to the
general concepts regar g the nature of unconsolidated material and
ts susceptibility to eros on slopes, and the supposition that
rock under similar conditions not eroded by rainfall. It is thus
not surp sing that few attempts Ii ve been made to study the solution
of rock'sur ces in this way, the rate f surface removal being assumed
to proceed so s ly that laboratory mode~ is impracticable.
Some expe ental work has been car~ out where the rate
problem has been overc by substitu!=ing the sOl~en~ (water) with a
more aggressive solution ~uallY Hel} e.g. Purdie '(l:~72). Tbeoreti-
" ~
11
cally both the "solvent and the'splute -can be substituted in 'e, ,simulation '" "
processmode~ providing that the dynamic an~ kinematic relationships
. ,
~
/ are maintained. Inspection of Figure 3 however indicates hoW difficult
in reality this may become.
~, For the present series of experiments no alternative solvent
u '............... \'
~or'water was considered for two reasons; first, the substitution of \
"-.......,........ . . ~,
another liqUid ,:I,n the rain simulation process induces changes in the '"
relationships betwe~;t'variou8 parts of the system that would require
adjustment in other parts of thelnodel. Second', the handling and
discharge of some solvents particularly the more corrosive types.
present difficulties in the design of the machine and limit its use.
A substitute solute in the form of cast plaster of paris or
salt was used in the present series of experiments. Use of plaster
also substituted'the calcite/carbOnic acid solution system with a less
complex ionic dissociation process. The behavior of plaster is well
understood under such dissolving conditons while being at the same
time inexpensive snd easy to h~le. A number of other successful
experiments have used such materisl as a substitute for limestone,
e.g. Goodchild and Ford (1971).
Becsuse the experimental surface was of homogeneous compos i\
tion, containing few voids and only a small insoluble fraction, it
represented an erodible surface which is unnatural in as much as such
conditions are seldom to be found in natural rocks. Variations in rock
solubility and 'porosity caused by original depositional characteristics
and lithification, as well as variations in the permeability due to
small seale fissures, bedding planes and joints, were not incorporated
in the model. surfaces. The experimental surfaces therefore represented
12
'-.
Fig. 3.
"
. VI,coslty .~
Dropl.t alz. ~ of liquId ~ , ~
Fall velocity of droplet
Surface tonslon I-' Specific weight , effect
'\ of liquid
General schematic diagram showing interrelation ships between various elements within the model and its operation. Hatched elements are those that can be adjusted to modify conditions, dashed lines indicate a feedback effect, in this c~e Rillenkarren represent the major modification to surface shape.
,"
0
" ;'
, , ,
SI •. " I'J " ,~p, o~~." ,
.
, Kinetic .nergy at Intercepting
aurfoc. Permeability: --- .. pore lpace,
grol n poc:kl ng. ---, ---i etc.
~ .. ~ "~ Saturated ,
~Large leal. ~ boundo ry layer l'lurfoCl shape ~ conflgurotl\ln ~"'" ,.
t ' . I
, I I I
1------- ./ Rat. of removal
of solut. " ,
'j:o-w
'.
-'
" , .
a simplified soluble substitute having similar physical attributes to
those of natural limestone.
2:4 The Behavior of the Hardware Model
There are two maicodifferences between the simulated rainfall
produced by the 'machine and natural rain. These are lower average fall
velocity and a s1Il8l1er size distribution of droplets produced, by the
14 ,
"
I ,ulachine(Fig. 4). ~- I
The difference in the fall velocny '1s-direct:ly-__ . ____ _
attributable to the size limitations ,of the simulator. The maximum fall
height for the droplets i~ approx1mately.2.6 meters, depending on the
p,ressure at the spray nozzle and the size and inclination of the
experimental surface (Appendix A ; Fig. 33 & 34.).
For the purpose of the experiment it was impractical to
increase the fall height for two reasons. First, a headroom' restriction
inside the laboratory limited construction height to four meters; second,
an increasing degree of difficulty was encountered in the control of
overall rainfall intensity when droplets were allowed to fall through
distances greater than two meters. This second problem is due to the
tendency for the droplets to disperse in an unpredictable manner as
they fall through the simulator.
2:5 Droplet Velocity and Kinetic Energy
The kinetic energy present at the experimental surface was
calculated from the data of Gunn and Kinzer (1949). Table 2:~describing
the velocity and dropl<>t. size,is part of their ~re extensive work
------' involving the measurement of droplets ranging from 0.08 mm to 5.8 mm
, ; ~
, 1 ,
::
,:\
~ :3 g
~ ~ "-C)
~
~ 15 Q;
16 -
14
12
10
8
6
4
2 I I
---'
SIMULATED
-r-"\.._" I r
I, ... -,
I r--' I I
r-..1 I I I
r-~ I . I I __ J
I I . ,-_,NATURAL
I o·
I I I --,
I I,
L_, I I I
'--, I I
~ "':.~~; ':-,' "
.\. L.._-,
I 2 3 '
DROP DIAMETER (mm)
I
'--.' L_
4
" :. ~ .
• .;\~
F/g-;'4. Drop size distrlbution of sImulated raIn (at 35 mm hr) compared to Lows 1941 medIum IntensIty data.
6
, ' "
~"
\
,.
I·~.l·' . \ :. .
'\ ..... 1 . ",' .
:-.1,. . : J \ ,
.... ,
TABLE 2.1
~nW. VELOCITIES FOR RAINDROPS: 0.5 111m to 5 uml DIAMETER (AFTER GUNN AND KINZER.i949).
Drop Diam. (em)
0.05 0;06 0.07 0.08 0.09 0.10 0.12 0.14. 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38
...... 0.40 0.42 0.44 0.46 0.48 0.50 '
\
Termdnal Ve1oc!ty(m/sec)
2.06 2.47 2.87 3.27 3.67 4.03 4.64 5.17 5.56 6.09 6.49 6.90· 7.27 7.57
·7.82 8.06 8.26 8.,44 . 8.60 8.72 8.83 8.92 8.98 9.03 9.07 9.09
\ 16
"
. .
in diameter. Gunn and Kinzer's results differed from earlier work
und~rtaken by .Laws (1941) by only'3% •• Figure A 'compares Gtmn and
Kinzer's work and Law's with the values obtained by Schmidt ~1909),
Spilhaus (1948) and Imai (1950). There appears to be close agreement
betWeen the,calculated and the observed data for smal1,drop1ets, up
to 1: 5 mm. diameter. The reason for the variation, in. the higher
velocities is possibly due to tbe unstsb1e aerodynamic behaViour of
the larger droplets.
To' facilitate comparisons with this work and to calculate
the energy developed at the exp'erimental surface by the rainfall
.. ' simulator the drop1'ec'size and 'size distribution were determined for
two intensities, '30 and 40 mm/hr (Fig. 45, Appendix B)., The
terminal velocity for droplets from the size range 0.05 to 0.50 em "
in diameter (Table 2.1) was used, to determine actual droplet velocity
as a percentage of terminal velocity. The, calculited percent terminal
velocity for a range of drop1e't sizes ,is plotted in'Figure 5, with the
incr~t1values derived from Figure 6: The kinetic energy values
calculated at the 2.(> m level' ~ere determined using these values , I
in conjunction with the size distribution data in Figure 4.
Under essentially still air conditions, it can be assumed
that natural rain droplets ariiving at 'the Rillenkarren surface are
, fallin{ at theii respective terminal velocities. In turbulent air
conditions, the droplet velocity will vary widely. In the present series
of experiments,drop1et velocities of one to four meters per second were
attained (55 ,to 90 percent of the respective terminal velocities for
17
10
9
8
~ ~ 7 '" ~6 III e: I 5 ~ '0 oS! qj 4 ::. -tJ .S 3 E ~ 2
I
0
!
,- -
V ,
,
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i ~ " ;;-
,,/J 1-" , --,,'"
A V,/ f .... .-
i1'b{(
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I I I
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/\ ,
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",'
L --1- .... --
... ..... ..... ...... '
.
.
_0-·- -- The fer
~- for three 0
fwo coleulot Kinzer 1949 Schmidt 19
Gunn, observed
Laws, observed
Imai, calculated
Sch,mldt. observec
Spllhaus, calcu/al
Inol velocity of raindrops bserved experiments and
'ns, (data from Gunn end Lows 1941, Imal1950,
9, and Spllhous 1948 •
"
---::-. ----d --------.
a 0,5 I'O! 1,5 2{) -.2·5 3'0 3-5 40 4'5 5{) .,
Drop diameter. - mm rn
- Ff9~5.J
\
.... OJ
,.
~
/i 100
90
80 Percent ofl
terminal veldelty
70
60
50
\
'\ SImulation velocIty of droPlets]
\~ .. Simulation Fall height of 2·59 m
~+ (after Bryon) 1970
. + -I- ..
~ ,
,
~+ ......... I
I j
. l + •
I
I
. j .
i
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:
f 2 3 4 5
Drop diameter (mm)
1-F!gS-]
":
,
.... \0.
J
/ ./.
,
I
----~--- - - ---- /'
/' the drop sizes generated). The effect of such deviation, producing a
lower energy rainfall on the experimental Ri11enkarren sur~aces, has not been determined. The 'change in Phys~cal process however is regarded
both intuitively and from the simulation experiments to be ,one of degree.
only, not kind.' Its effect is to possibly slow down the formation of
rills and the rate of surface reduction.
,-"
...
I
-----.!..- -
20
CHAPTER THREE
,
EXPERlHENTAL RESULTS
,
3:1 Descripd.on of the Experiments.
Ten experiments were conducted us~ng rainfall intensities
of 35 to ,40 mm/hr, upon plaster surfa'ces and a further five experiments .". - , were carried out to 'investigate specificphenOll1ena using salt. Three
preliminary experiments 'were carried out to test the rainfall. simulator
and to estahlish the rate and nature of erosion ,on the plaster surface. Two
experiments were run for 650 hours and a 'third' for 800 hours. Each of the ,.-
main sedes of experiments was run for 500 hours, this time period having
~eenldetermined as 'sufficient to produce a stable surfacer.;£orm in the
longer preliminary experimental runs. A 'stable surface' or mature surface
is implied here to represent a solutionally-modifiedsurface configuration
that remains unaltered after a period of initial development or growth;
after such a period the surface continues to be reduced by solution but
the surface form remains. the same. ~l simula~ed Rillenkarren surfaces
conformed to this development sequence on plaster. The high sOlutiorj
rate of 'salt coupled with the limitation imposed by a smaller block
size did not permit salt surfaces to be determined as mature.
In each experiment the rainfall intensity remained constant.
The surface angle of inclination was also fixed for the duration of'
each experiment and all surfaces were, initially smooth. Such experi-
mental limitations enabled the experimental results to be eaSily
compared. The plaster blocks consisted of cast rectangular prisms
if
21
"f... '-:
"
,(Fig. 7), ~he surface finish of the block after cas~ing being in ~he
er orde'i"'of 250 microinches, excluding voids that were seldom larger than
one millimeter" in diameter (Appendix A).' The surface of the salt
blocks was somewhat slIlDOther, blocks used in the experimen~s being
cut from large 50 lb ct?"""ercial salt licks (Fig. 8).
Under certah exper~talcon!iitions the effect of the long '. l·
symmetrical block edge tended to produce 'crest development of a type " ",
not obsenved in natural rilled surfaces. This effect was eliminated '~ ,
by modifying' some blocks before the experiments were run'to,increase , "
the included angle of the upper expos~d edge (Fig. 9). '--.........."'~
22
3:2 Experimental Measurements. """,~
Because the experimental surface represented a complex and
changing shape, a number of standard measurements were taken on all
surfaces at fixed time intervals throughou~ each experiment. These
measurements were supplemented by photographic coverage usually taken
every 24 hours. The three main types of measurements made while the
experiments were in p~gress are summarized below.
The selection of the rainfall intensities, surface angles
and the particular factors investigated for each experiment are listed
in Appendix B. The measurements made during each experiment varied
to s?me extent, ru:did the photographic schedule.
(1) Measurement of the total surface reduction, usually undertaken at
100 hour intervals. The initial surface position for these measure-
ments was referenced by casting four 10 mm diameter brass pins in
the plaster block, the,tops of the pins being set flush with the cast
surface. Up to 25 height measurements could be located using a
/'
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(£ 3dAL) V . i (~3dAJ.) Cf..! rc
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a~-/c=? --r V ~
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(2)
,~' , '--....
<guide plate.. (Fig. lOh~
The degree of riii formation ~er-time was ascertained by measure-. ~,-:-.. ~-
ment of :individual rills and by comparing tlie-rtiled area of the ~~
surface to the non-rilled area. Use was made of a line projector
and multiple time exposures to contour the surface and establish
the position of rills over time, described in Appendix B; "
26
(3) General stereoscopic photography was taken, usually-every;~24._llour_s" ~=~=~=
five frames of 35 mm' iiim being exposed at fixed stations along a
pre-aligned optical fixture (Appendix B, Fig. 40).
3:3 Experimental Results.
, Collectively the data from the experiments support the theory
\ tbat\Rillenkarren are a rain-induced phenomenon~ In all ~~~ __ ri __ l_l~ ________ ~.~
dev~~pment was·propagated from the uppermost edge of the inclined '-,
surface\, (the crest). This form· is. characteristic of rills found on
natural efPosures. No substantial change in the slope angle,w~as~--------__________ __ "
\ observed to occur during the experiments; the change in surface form
from that of a rilled to a smooth surface was not associated with any
measured change in the amount or rate of surface lowering.
The extent of rill development and the final stabilized
length was determined for a number of slope angles. In all experiments,
the deepest part of the rill developed close to the crest and flattened
or washed-out at a p'osition downslope. Erosional development was
characterized by the initial rapid growth of the rill partition from
the crest down the slope. After approximately 200 hours,the lengthening
slowed and rill deepening accounted for the greatest change in surface
\
..
..
... ~ ~
I
I I
I /
') .
A Dowel position
!~~·r4;:J ~ ,uide plate dimensions I
II I·_ .. l.)-ii/I_-.--
~--------~r-~~--~ I'
• -+ -$- -$- +7 I '
-$ • #r -$-!! c:>
• • .J. i . ~ ~~ ~+ Ql " t ~ 1 ~ .. -+ ~ t . ~ .~.. .. (
! ' I / i ~ Ir 0·937
I. 22 /25" 'I I. 2 . 00 -4--+---"-1
All dlmens/on~ in )ncnes
I I
\ .. I, \
I I
I I ,
'A' HO/~ forn.ers, drill 0·257,. top 5 6- IS. oil other holes O· 2/9 dio drill thru..
'I! .. ,I
l! I Fig. 10.'
/
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N .....
.~8
, " "" "'J..f" ,. .>
shap,e after this time. Four stages of psrtition growth are shown as
diametric cross sections in Figure 11. These represent stages after
250, 350, 450 and 550 hours, when rill deepening predominates and the
lengthening of the rill is very slow.
Rill Length and Slope Angle Relationships on Plaster Surfaces.
For th~ experiments carried out on Ylaste~s~rfaces, a direct
relationship between the· stable mature rill length and the slope angle
selected pes det-e-rminedi hi all experlriienfs "rill -growth- developed._f_a.i~test
along the side edges of the test surface, the partitioning of&rills
becoming unstable close to the ends of the block. ·To elimin~te these
effects which are comparable to the wall effect in flume~, the outer edge
(10 em wide at eaCh end of the block surface) was excluded from the measured
area. The mean rill lengths derived from the data in Figures 12 .. - 21 are
¥lottedllgainst the slope angle in Figure 22. For the determination of tlilo
length data, a me·asurement of the length of the rill partition from the
crest to the point where it was extinguished was made; rather than attempting
estimates .along the rill trough. The plotted measurements in Figures 12 - 21
were made at the 500 hour mark.
The log-linear relat·ionship between the length of mature rills
and the surface inclination, between 22 1/2 and 55 degrees, sppears close.
Estimates of rill length at inclinations greater than 55 degrees were
limited by the size of the experimental block. Such rill length and
slope angle'relationships have not been observed in the case of natural
surfaces. Two main complicating factors are possibly responsible for
,
Rill partition ofter 250h
I Ion offer Rill part·t· 350 "~;.....,,.-.-//
/-,'~
Rill partition ofter , 450hrs _I ~--1
I Ion ofter Rill port·t·
/;
-
'.'
- ;--------
29
---"7<""--- -:* ~~nUI!:
II' .!-'-/.::I:-7:J' -J' ;,:c-~- ,
Fig II. (}evel partilion at o';;l6nt of a rill 450 and O. 350 • 550 hours. •
\
/' /
,~
20 •
, Number
10 (0' • 4·66)'
10 20
, ---.
I'
if? ItIlengfh hlst~g~amJ
Slope angle 45 0
blo,ck no 2. (500 hrs)
30 40 . 50 Rill lentjth (em).
2· 5 cm class Int~rval i
\
60
L jO"g. 12: I
UJ o
•
\.
-20
Number
-10 (CT • 3·57) p
• 10 20
[Rill length histog,;,;;]
Slope angle 35° )
block no3 ,(500 hrs)
30 40 50 Rill length (ern)
2· 5 cm class Interval
'-
, ;
60 ')
,rFlg·13. I
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I
~ 1
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w ...
20
Number
10 (eT" 17· 29 J
10 20
[ Rill lengthhlstOg~am I
Slape angle .30°
block no 5 , (500 hrs)
30 40 Rill length (em).
1·0 cm class Interval
50
./
r
"
60
I Fig'. 14. l'
~ '\
w
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2
Number
10
«(I". '·07)
,
10 "-- 20
Rill length hlstogrom "
Slope angle 22,~o
block no 6. (500 hrs) /
'\
30 40
Rill length (em J. 1·0 cm class Interval.
J
,
50
/
-~ 60
I Fig. 15.]
/
w w
, ,
'.
\
20
Number
10
'-
10 20 ~-
~
Rill length histog-;:;;-riJ J
Slope ongle 50° block no 9. (500 hrs)
(0"" 5'48)
30 ·40
RlIl length (em).
2'5 em class Interval
./
50
£.
60
•
J F10-:-16-:-]
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.:
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20
.,
Number
10·
10
{cr- 4·06}
20
.... --.
I Rill length hlstogr~-I
. Slope angle 45°
block no 1 (500 hrs)
30 40 50
Rill length (em) . . 2·5 cm class Interval
-----
----
60
" r- Fig. 17. - I
'w ,/ VI
20
Number
10
10
I Rill length histogram I
Slope angle 45,0 '
block no 7, (500 hrs).
(rT:: '·73)
20 30 40
RI/I length (cm)
2~5 cm closs Interval
50
-----
J!;.
,-Fig 18~ I
'-
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20
Number
10
---" -
10
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I R;II-'-engthNstogro~-1
Slope angle 45 0
black no 8, (500 hrs).
(0-. 11 4·90)
20 30 Rill length (cm)
2·5 em class interval
40 50
. [Fig. 19-1 -.
r
,
.... ....
-
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Number
20
70
_ 10
-,
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Rill length his to g7c;;-]
Slope angle 60°
block no 10 (500 hrs)
((T_: 2·64)
201 " /
30 40 . 50
Rill length (em) " -2·5 cm closs Interval
,"
,
--.....
Fig. 20 -I '\
-w '" '"'-.. -
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20
f
Number
10
10
,
~.~~,':J,..j~.s~;: I;";;'> ~.; .• " - 1~·~_.
r------- I Rill length histogram
Slope angle 55° block no 4, (500hrs).
(CT" 17·02)
·20 30 Rill length (em)
2·5 em class Interval
40 50
t
..
•
'ij"
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\
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,
--
W ID
"
Surface Inclination
( deg)
60
50
40
30
20 2
0
0
0
0
-- - --
.3 45678910 15 20 .30.
Rill length (em)
Plot of rill length vs. slope angle.
.Incllnotion Mean length
60 25·0
55 23-4
50 23·3
45 1/-2
35 '7·4
30 6·.1
22vz 4 :,
1- FIg.22}
" ..,. o
I l
!
--,.-.--
this. First, the greater variatfon in surface roughness and at lsrger
scale the uneven slope angles effectively produce greater variability
in the developed rill length on natural surfaces. Second, the rainfall
"'. intensity and the variation in prevailing rainfall direction may be
significant in. some locations, although Ford's measurements investigated
aspect as a determining factor in the Surprise Valley and found no ~
relationship, (Ford, unpub.)
Rill Widths on PlaSter Surfaces.
Data for the measurement of rill cross-section and rill width
" were obtained initially by using the line profiles at three, five and
ten centimeter parallels below the crest (Fig. 23).
After completion of six experiments it was found that this
type of profile described the rill width poorly, due mainly to the
absence of measuremen~at lower slope positions. In the case of slope
angles over 45 degrees, which produce longer rills, only the upper
portion of the rilled area was measured. Consequently, the smaller rill
forms close to the crest appeared more Significant. This can be seen
in Table 3.1 where rill widths appear to become smaller at higher
slope angles. To provide a better adjusted sample of width measure-
ments the profile position was repositioned down the surface propor-
tional to a fixed percentage of the mean length developed after 500
hours. In order to make the repositioned profiles comparable with
the original selection of 3, 5, and 10 em, these values were calculated
as a percent of a rill length mean of 11.5 em (the mean length developed
!
41
/
:3 em from erest -
" \' ~, ~ \~cm from crest --+-
10 em from crest __
20cm from crest
I \ I
I \ I \
" \ I :.J:;'" \
L__ ~~.;~;~ i',:~ __ ~\
~~.~
~~.~ •
-W8~~ 100 hr .300 hr 500 hr
Time profiles at 100, 300 and
500 hours.
. r-Fi9~NJ· .0-N
I ..
TABLE 3.1
, .-. MEAN WIDTHS OF RILLS MEASURED A:r 3, 5, ~O em , POSItIONS FOR VARIOUS SLOPE ANGLES. '
Rill width iti DIm measured along profile 'distance (from crest)
.~,
Slope 3em Scm 10em
22.5 7.43
III CD 30'.0 7.02 8.59· -~:l , :"
,--..' , ' .f"
I ij~ 35.0 6.89 7.27 --1Il~
,
!~ 45.0 6.24 6.76 8.06 '"
5b.0 5.33 6.19 7.81
60.0 5.01 5.38' 7.00
...... J" "
I , ~ ~ .. ;:; ". ~ ,
.~ "
'"
TABLE 3.2
MEAN WIDTll OF RILLS MEASURED AT 26%, 43% and 87% - OF MEAN -RILL LENG'l'llS-FROK ~ST- ·OF StoPE
Rill width in mm meaaured along profile· (percent of rill length)
Slo,~e 26% 43% 87%
22.5 7.50
cu co 30.0 '6.55 6.63 8.50 ~~ i~ 35.0' 6.02 7.21 8.47 cu-8
!~ 45.0 6.24 6.76 8;06 til
50.0 6.28 6 .. 81 8.15
60.0 5.51 7.03 7.91
/'
on plaster surfaces at 45 degreea). The rill width measurements obtained
using this proportioned profile appear in Table 3.2. Using this data
no significant· change -in the rill widths- were associated with the . variation-in slope angle.
~ In the initial series of experiments the developing surface
was characterized by the development of two types of rill; micro-scale
rills which only diss~cted the crest area and could be observed within
a ~ew hours of surface erosion, and large scale rills that develop
44
"
/
later and are o~y well established after approXimately 100 hours of
sustained rainfall. The larger scale rills appear t~orm by the
coalescence of the micro foJ:IDS -and the length to which the micro-
rills develop before coalescing is dependent on the slope
angle of the surface. The coalescence 6f micro-rills appears to be \
fundamentally different from the, concept of micro-piracy described by . -
Horton in which cross-grading was regarded as being responsible for the
change from the parallel rilled surfsce to one approaching one of . . '
dendritic plan form. On the Rillenkarren surface all rills tend to be
of a width that is uniform along the developed length. The wic\.tlls 'Vary,
micro rills being in the order of five to ten times smaller than the
mature rills. The characteristic parallel rill form appears to be
preserved even in the micro foJ:IDS, the' change in rill width frQlll micro
to mature size is accomplished by ,the extinction of the micro rill
partitions across the developing upper- axis of the .maturerill and
not by cross grading (Fig. 24j' The proportion of micro"rilling to
the total rill area appears ~o be the same, approXimately 10%, during
the development s~age, regardl~ss of the set slope angle.
The absence of the micro rUling phenomenon on outcrops of
natural limestone and on soma ,~ow angle plaster surfaces ,(22 1/2 and
30- degrees) prompted experiments utilizing"blocks with a modified crest. - , '
Thes8,bloc:lts ~ere positioned in the rainfall simulator with a truncated
cr~st uppermost such that'a greater included angl~, existed between
~djacent surfaces. The expe~ents with blocks of this modified type
resulted in the elimination of mi~ro rilling on the mature surface at
45
, ApproxImate scale-
1m
-----CREST
'Belt of no erosion'
I Fl~1 l ~ , r F1g,24b.1
"
\ ,. -, ::;1; I ;:;.-; -;~ I.:.E; \
11 Net flaw dIrectIon
-\ ~J ,
,
\.
v
--'A'~'A'
:x··~,x"
'/ --- 1
,I 5 mm '.
CREST
o
"
l tl Net flCM direction
~ i ~ -
Development of a rill cross grading network, (after Horton 1945), Fig.19a, compared to the development of R111enkarren, Fig. 19b. Note different scales and the change in net flow direction associated with cross grading.
I Fig.24. I .... 0>
-, '
slopes up to and including 4S degrees. No experiments were carried out
at greater slope angles.
Rilla gene~ated on Salt surfaces. , ,
, ' Five experiments with salt bloclcs were carried out at a
rainfall intensity of 3S f1l1Jl/hr., identical to the experiments using
plaster. The salt'blocks were smaller then the equivalent plaster
caatings, (Fig. a),.and the resulting edge,effecta made determ1n~tion /'
of the mean rill l~th impractical. Two important relationships were
noted however.- -The rill form developea was identical to that developed ~.
on plaster. '!be size.of the rill, the cross sectionalform,was larger
on salt ~ on pl~er. Fig. 2S compares the width of rills developed
on salt with those on plaster and on l:I.meston!ls" '
Supplementary to the five experiments was the exposure-of a
salt surface of identical shape and size to a number of natural,rain-
storms. Subsequent comparison of this surface w~th those exposed to
artificial rainfall provided an opportunity to determine the degree
of replication produced by the simulatar , (Table 3.3); Only direct
COlDp'arisona of this sort could be made ua1ngsalt such comparisons
could not be made with plaster because of the duration of rainfall
requil:ed and because of, the hygroscopic effects of plaster surfaces
that are well ventilated and 'aubject, to ~ast drying.
Cross-section of the Rill.
Rill cross-section was measured at vario~ stages during the, . . '
experiments in a number of ways, i.e. direct mechanical measurement
47
Number . of rills
'5
'0
5
\
i:
~ ..
.-/
I'J ; ; ;. P'aster mace .
Umesfone (natura'
'urface)
/centimeter class inferval •
\
, ~
Cemparison of three characteristic rill widths. Simulated rills on plaster and salt, and natural limes~one. (Paliser limestm:l.e,1 Jasper National Park).
----
I Flg.25 I ..:~.
\
~
""
".
TABLE 3.3
COMPARISON OF RILL WIDTHS IN MILLIHBTRES ON SALT, COLUMN A SIMULATED, COLUMN B NATURAL RAIN.
-!. JL ~.
14 13 -20 14
14 14
13 15
14 15
13 16.
14 16
15 16
15 17
25 . 16
18 13
15 -17
20
49
!
~ -;
..
\
1
J \-. .'
utilizing a height gBuse, by taking casts of the surface, by sectioning, .
and by the use of photography in conjunction with the projection of
inclined contours. A combination of these techniques was utilized to
plot the profiles in Fig. 26. Using these profiles, an approximation
I of rill.cross-section using a number' of basic shapes for comparison was
attempted (Fig. 21). It was found that most rill cross-sections
approached a parabolic form. Because the rill width ia fixed, deepening
by solution overtime prOduced a rill shape that conformed closely to
the equation:
/ y • lIn ( x2 ).
For simulated ,ril(l,s developed on plaster and salt the In I value varied' '\. I
, . . from approximat~ 10 in· the early stages of development to a low value
around 3 f~r very mature rills (Fig. ~8). Rills on a sample, of . the
. Palliser limestone {Fig. ,26)/ appear to approach the same range of In I
values.
Solution Rate of the Experimental Surface.
The overall reduction rate of the surface depended direc~ . .
on the rainfall intensity and· the aurface inclination; these two
factora 'of intensity and slope determine the amount of water that the •
surface intercepts and t~ereby regulate the amount of iolution that
can take place. Fig. 29 iB a, plot of surface reduction, after 500
hours of. sustained uniform rainfall, against different surface
inclinations •. The maximum rate of surface reduction occurs at
approximately 45·. ThiB curve can be compare~ to the empirical
/'
50
51
\ o·
Ii 't> e 0
• <> .... /'
t: - ~ ~
>C
<> 5 Q.
.... ::a go e: .§ • co -- .. - E?
co
-II: CI .. ::a
t\I
• -- 't> - CI
C.
~ (; ;;: e: of 0-
Ii:
::a 0 -..... Q. CI : ID
e: .c: <> - •
l; .Q <> III
.. .2 ~ e: - ~ <> • l: ::a -- e: <> .. .. <> - -• - u .. ... <S.
<> .. -.. e .- e: .. .. ::: .. E
~ ~ -e: .. .. •
a <> ::a' ~ II
.. - • 1: .. .. ~ ~
:!! -.. 7;-::a .!! ·S .. Q.
/'
,
I ,
" ./
"'\
.-',{ :f\ " '/1 + + 1J,4.~'1 \ I . \ II
I I
\. 9 __ '.i ____ _ ~----------... -------
,,~,1
'I , I ,
, I , I , I
\I .
,. I • -1----"---- -----X----
~A..;;.<~~~ .. <.;, .. :, J~'._'.
I I I I , I I
- -- t"
t-
"
" ~
Fig. 22
A. Profile: Semi circle, rill depth - 1/2 rill width, crest line coincident with profile cen~res,(segment - half circle)
(2r)2/7fr2 Area ratio:
2
B. Profile: Intersecting circle, crest line below I?rofile centres, minor arc 9
Area ratio: -
1/2 r2 (9-sin9)
v---..
2 . 1/2 r (9-sin9) - (~-(cos .9/2 r»(2sin 9/2 r)
C. Profile: ,.
Paraoola intersecting, crest line above focal line.
Area ratio: - y. 3/4 x2
I Fig. 27. I ~:~ ,-....
.. ~~,,'
/'
.." N
v -
I , ....
n = 10 .~
•.
, /
Fig. 28
/
~~~~,,~~'®
Rill deepening over t1llle, conlprm1l8 to parabola: y • lIn (x2). Profile frolll block 1l0lllber 2 120 hra ·to S04 hra, 8 ClII profile zone S.
) /
--.,
S3
25 .. ~ E E 10 IQ - 20 0
~ .. :a 0 .c 0 0 10 15 .. CD -.... 0 c: .2 -u :a 10 .,. ~
3 0 .... .. :a C/)
5 20
~
/
-$22'4 . . 21·3
19-5
30 40 50 60 Surface angl. In degr ...
Fig 29. Surfac. raductlan at ./ght -b/oca plott.d aga/n.t IIope angle.
54
:.
-----_.\ .. ,
relationships of slope and erosion rate as determ1ne~ by Renner (1936)
and Horton (1945) for larger scale inclines on which the classical ~,
sheet, rill and gully erosion were operating (Fig.~).
Because the rainfall intensity and surface slope were • J oJ.
~ changed for different experiments (Table 3.4), it ip important to ~ , .
determine the volUDie of water which comes into contact with the ----------..............
surface over a period of time. This value is given by the relationship: ", -"
Vol of water (litres/hr) • Intensity (cm/hr) . (Surface area) (Cos apgle)
,1),00 ... ~ . -.. .
Table 3.5 gives some selected values for inclinations. and . ,
intensities appearing in Table 3.4, plotted in Fig. 31. Although the
overall r~e of surface reduction, as measured from the reference points,
differed slightly, it was generally commensurate with the total ~all ./ received and the inclination. The observed. differences are within the
limits set by the variation in the plaster castings. Table 3:6 includes
the surface reduction values for eight experiments along with the total
received rainfall for the surface at 500 hours.
3:4 Processes Operating on the Experimental Surface. . ,
The maintenance of a uniform rate of erosion on surfaces which
develop a two zone form, rilled and un-rilled, under sustained rainfall . .
implies that whilst the solvent capacity of the water is similar at all
points on the surface, two distinct eroding processes are lOcalized.
It is hypothesised that this difference in erOsional pro'cess, is alUed
to the .water film thickness and to the.degree of turbulence propagated
in that film by impacting droplets. An alternative hypothesis, that
the surface is a response to the differing a88resaiv1ty of the water
55
I
80
" : ..... - ",-
60 ~
z 0 C/) 0 II:: 1&1
- o 20
", .. -.'.--~-----
"
40 60 80 100
GRADIENT '"
'\
fig 30. Estimated surface erosion ploHed against slope gradient, after Horton,1945 and Renner. 1936 .
56
:
., , . ~
'.
SIMULATED RAINFALL INTENSITIES, AND TEST INCLINATIONS FOR PLASTER l\LOCKS.~ - 10.
;'.
) '. )
, 57
• 0
·'
_ ..... __ .... ..-.:..,.-----------'----""""'"-,..------------,...-'
TABLE 3.S .
VOLIlMR OF -WATER INTERCEPTED BY THR RXPI!lWIRNTAL SURFACE AT SRLRCTED ANGLES, (LITRES PER HOUR).
Inclination Degrees
o
22
.30
4S
60
Effect:l.ve Area (eq ciD) .
216
200
187
lS3
108
...
TABLR 3.6
- Suatained Volume at SO mm/hr. . at 2SlIIII/hr. '"
1,080 S40
1,000 <. .SOO
93S 468 '
76S 382 ::" ,
S40 270
• .. .. SURFACE REDUCTION '\
;)-
Total Rainfall Surface Reduct:l.on Slope' Experiment No. ·:l.n L:l.tru' at 0500 hn in CIII
2,2.S 6 3S2.5 10.05
30.0 . 5 330.0 16.2
35.0 3 312.5 ' 19.05
4.5.Q 1 270.0 21.3
4S.0 2 270.0 22.4
50.0 (In:l.t:l.al 2) 245.0 20.4
050.0 7 210.0 16.8'
60.0 8 162.5 11.3
58
· \
Surface lnclinaJlon {defTees}
------------
"
60
I 50
.' I \
40
\ ..J
Sustained lIOlume of wafer CNeT block w. surface Inclination.
~3fjl
\ \
30 1 '1 1 I 1 I 1.1 1 I 1 '.1 I I 1\ I I I 1\ I I I It. I I I" I I "I I I. I I .'
I 20 II I I I I I· I l ~'I I ~ I I I ~ I I I f\, I , 1\ I I 1\ I I f\ I
I "
\.
-,
~~~~~~~~~~~~~~~~~. -. I ..
Sustalnedvolutne (ml/hr of' water.) r
---'" '"
I.
.,
-'
\
, ., >
' .. ;.
)
'"
.. ' , ,0
as it move. downllop., (Boa1:l. 1962, R.thjenl 1939, end Lel\Qnn 1927),. ' . ~ '.,.
il rea.rd.d .1 unlikely dUI to thl ,Uicient,mixina end r.pleniahment
, of the film by dropl.tl Itrikina allover the lurf.ce, end .imply
bec.uee erolion rate h .. b •• n Ihewn to b. con.tent in both 10n.l.
~ Althouah aqual amountl of wat.r are d.liver.d to the lurfaci
by the adjuetment of the intenaity end drople~ diltribution within the
'rainfall .imulator, the amount of wat.r on the intercepting .urfac.
vari.l. Any .mall portion'of th"inclin.d lurfac. may b. conlid.r.d
to rac.ive direct rainfall plue a volume of flowina wat.r (run-off) - I'.
from the ar.a of Ilop. above it. An inolin.d' lurface und.r luetain.d . " . '
rainfall will ther.for. tend to carry mar. wat.r on itl lower .1op.l,
then at the crelt,'th. film thickne.1 on the low.r part of the Ilope " I •
being partly a function of the lurface rouahn.11 that prevent. the
flow from acc.l.ratina, to any'dearae on the'inaline. No dir.at
1IIIalUra1lllnti w.re mad. to d.t.rmin. the ,eli •• d of the Uowina film on
the lurfac. or, to mealur. the d'ara. to which the flow aac.l.rat.d
down the lurfaa. of the blofk. Bxp.r~1IIIntl carri.d out with dye to
_alura the thickn ... of the film, (Appendix B), fail.d to ihow any'
mark.d inar .... in Ip •• dof the flow OIl the low.r ~Iu;faa .. ,.q,f, the block,
'bllow the rill.d Ion ••
~h. inareal' in wat.r film th1ckn •• 1 from a minimuR valul,
alai' to the cralt t, 10l1li Itlbl. alllOunt dictatld bY' the flow raaim.,
of-the ~llm il ,raapondbl. for the diffa«nt1at10n of 'the lurfaa. form
Charaat.r1ltic ofth. R111ankarran lurfac ••
•
60
'l , i ,
, , '.\
.. ~
~
~ :1 5 ;~ ~
" '.
"
u\ ..
Tha· variation of fl1l11 thiclcn .. s and ita suociation vUh the
rats of srosion (solution) of ths supportina surfaca vas racogni.ad
by Hoffmaister and Ladd (1942), and by Smith ahd Albritton (1945),
whan attemptins to a.tabli8h a sen.~al thaory reSlrdins the rai.ad
edsa. ~ormed'on sOllla'westhared clint •• Their study e.tlhli.had that
variation. in tha f:l1111 thiclcn ... , particularly the thillDina of tha
fl1l11 cloae to ~h. a~se. of tha t .. t blocb,vu .rractiva in raducina 1
the rate of .olution th.re. Thi. they tarmed 'dill .ffact'. It vu : ..
evident frolll-tha.a pre.ant axpariment., and from thoaa of Purdia (1972), , . . . . . \ that this sffact i. aelf-anbancina in u lIIuch a. tha psr.i.tanca of an
are. of thin fillll tbiclena.s vill reduc. th. .olution rata, b.csua. of •
th. reduc.d velum. of vat.r. Ov.r t1llla this aree wili hacOllla alavatad
vith re.pact to it •• urroundina surfeca., t~ua reducins tha fillll thickP
n .... ;to an evar sraltsr extant.
An analoloua but oppol1t. aUact, (a depolitioual charlctar:l.. tic), . -can b. ob .. rv~ILin th. a~th of dlllltena (calcU.) d81111 on xcuah
flow.tona .urflc •• in naturAl. cavarn.. Thua, in an Aqu.oua res1llll, . .
th. rat. of d.po~iton i.·.nhanc.d.vh.ra filllll ara thinn.d ovar a "
politiva' rouahn.... Th •• ffact 11 •• If-p.rp.tuatinl and att'r1butad
to th. acc.l.rat.d rat. of CO2 d.-Iu.inl. '- ,
61
In th. initial •• ri •• of .xparilllant. \!tina plutar .urfacu~h.r. wa. . . , ~.
a .ymm.tricll. cr •• t formad b~ th •• djac.nt .mooth lac •• 'of th. cutina. , .
It vu fxclII thi. cra.t 11n. th.t 1:1~11 war. pxcp .. at.d in avary axp.ri-
lllant. Th. CHit can b. r.la1'd.d u thtin1t:l.1l '1'illl' owr "h:l.cb no
p.rIIIII\.nt lolution fl1l11 can b. ma1nta1n.d;· Th. 1':1.11 lanath hu now'
\ '
I
(
, ,
, (/ f
/' been determined ~imentally andcollforma cloaely to the extent of
the area that could be claaaified aa a rim effect lone • •
However, the width, depth and aeneral morpholoay of the rill,
aa well al.it. packina "dona the crut, po.ethe quastion of why rill.
develop. In term. ofa,procel.-form ralation.hip, the problem can be
.tated I the lolution .urface torm deftloped under a totally random , ~
fall'of rain droplet. on an expo.ed aurface (inclined to the'
extent that it 11 unable to maintain a thin f:l.lm of water ov.r it,' '
cre.t) i. rilled in a non-random mann.r. The caUl. of the tran.for-
mation of a .mooth .urfac. to that of a .at of .clo.e pack.d rill. of
.traiaht plan form and of parabolic cro •••• ction i. not auy to
determine: From the re.ulta of the tollill •• rie. of experim.nt.,
thirteen pla.t.r, includina thr.e pr.liminary block., and five
experiment. ut:l.lil1na ... It, it i. apparent that the linearity and
packina of th. ' rill. developed on the aurface i. not 'due to any form
of,.y.tematic.rror introduced by the mcd.l, or to any .pacial charac
ted.tic. of the .urf.c. material Ulad :l.n the exp.r.1ment.. Th., caUl ••
of r:l.ll dev.lopment mUit th.r.for.,b •• ouaht :l.n the n.tural proc ••••• ~ " . \, .
and ~h.ir .U.ct.. ,Two ~clUl. may b. cona:l.d.rad. ',The\f:l.rat :I.e the \
un.1d:l.r.ctional arav:l.tational compon.nt, and the •• cond :I.. that, r.latina , .
to the .p.c:l.al prop.rt:l... po •••••• d by the form of the r:l.ll cro ••
•• ct:l.on, a quadtat:l.c parabola.
Th. atra:l.ahtn ••• of the rill part:l.t:l.on.,'wh:l.ch .ra alway.
d:l.rected down-alqp. at an anal. a. clQJ. to the vert:l.cal aa :I..
" p.rmitted by the elope, .tronaly .uaallt a dominant arav:l.tat:l.onal )-
62
•
••
) \ ,1;
\ 1 , · 1 ·
"', · • ~
· I
~
\'
/ component whfch i, effective in directing the eurface flow. the falling
. -. c
droplet and the IIplaih produced by the droplet. on impact with the
.urface. The .econd factor. th!l form of the rUl. i, one relating to
the unique prop~rtie. of the qUAdratic parabola. notably that of the
deflection of parallel force, through a focal point. A. all droplete
·are falling in parallal motion before Itr:l.k:l.ng the lIurface the parabolic
rill appear. related to thi. factor.
For any uniform random droplet intenaity the rill IIhape in . /
the mature form (n < 6. Fig. 28) may be regarded .. an effic:l.ant .hape ,
~---that minim ... droplet impact thereby reducing the diaaipata'd anergy . . '.
over the rill partition and allowing only a narrow portion of the rill . ,
trough to lIU1ta:l.n droplet impact directly. (fig. 32). •
/
.J
... - ...... -.--
63
, ·
.. • •
,
64
... 0
,/
~~ aI 0
.--' ~i aI ~ rn ~Z
] ~ "
\
.. 8 ~ 9:1 fJiI~
/"
,
- . 'if IR
l I fi
" "-',~ ,at
,
I
~ .. ",,~ ..
I ..
" , , ~ ~ ,'"
:~'
.~
"" " ," :;;. ,
, "
.",
" ' , ,
, '. ,-',
'.. "
•
!
/
The cross section of the rill arid its characterist1cstre1sht
p'lan form, while anablins .ffiCient flow to be ~nta1ned alona its
troush axis, ia radically diffarent from tha flow-formad conventional
channel. Thie ie evidencad by the wuhinS out of the rill at a
position'on the alope wh.re a continuous film flow ia presant.
Rills, u Horton (194S) referred to them, only basin to ba establiahed
once the film flow reachaa an unstable thickness further down the
alope, thS(flOW velocity at this'point ,.nabltns channels to ba cut into
the aurface byturhulent flow.
Rinnankarren (Boali,' 1961; a.e F1a. 1), tranelated u runnel
karren are the keratic equivalent of Bortone corruion rills. Like
tha latter, R1nnankarran haad below. 'belt of no channel erodon', and
frequlntly coal .. ca and expand in dimenaion downalopl. Thl R1nnankarren
channela er.aepa-atld by planar interfluve elopas and are much brsar
acale features than Rillenkarren.
The dear .. to which dllina may be propeaated over a surface
ia limited ~o the, aone over which ~ thin or intermittent water film
i. pre.ant, the relative .iae of thi. aona bains proportional,to the
.urface inclination (Seation,313). No direct meuurament of tha film ,
thickn ... wu po.dble in tha cre.t ar... the problem bains' co'uq,Ucatad
by the rUle the.al.n." in tha ,undllad portion of the experimental
.urface the film thickn ••• wu lIIIIuurad. On plutar .urface. inclined
at 45 deara •• a .ustained rainfall of 3.5 IIIII/hr. produced a film flow
• thickn... of 0.006 to 0.008 inch.. ,(0.1.5 to 0.20 II1II) below the rill aona.
6S
, .
The flow thicltneaa -is in part. de.terudned by the aurface
rougbnaaa and thia factor i8 also fundamental in deterudn1ns·the . .
area of rUling on an inclined surface. The magnitude of the ril}.
cross aection aeama alliad to the material used in the experimental
plaater rills are smaller. than natural limaetone rille and thoae
developed on salt, larser" The procee ... reeponaible for ~terial
characteristic rill size wer. not determined in the presant experimenta.
/
\ ,
\ ' .,' ..
66
. I ....
... -'
CHAPTER FOUR
CONCLUSION
411 Summ'ry 'ofthe 'Experimental Re.ult ••
The .im of thll .tudy was to provide an explan.tion of the
,Rillenkarran .urfac. which.until the pra.ent.wa. not wall undar.tood.
The .imul.tion ganar.ted Rillankarran on pluter'and .elt .urf.ce ••
T~erie,.of .xper1mant. are' ras.rd.d 'u b.ina important.
fiut in the detet1llin.tion of the dominant proce •• involved in the
formation of the Rillenkarran .urf.c ••.• nd .econd in e.t.bU.hing
oth.r ral.tion.hipath.t could not be made uaing conventional fi.ld
ob.erYationa.
Th. experimant. dat.t1IIin.d rainfall to be the .dolllinant
proca .. controlling tha devalopina Rill.nk.rren .urf.ce. Tbe mo.t
, remarkable rel.tion.hip i.that inth •• b .. nce 0' any other proc ...... . - ...... . the ,random f.il o.f water SoPl.ta of • .iI. rang. clo.e to th.t compri-
lina n.tural rainfall~ ov.r timatran.f~rma •• mooth. '1ncUn.d .nd
.• olubl •• urf.ce to on. of • h1ghly unUorm rUl.d conf:laur.t1on. 'With-, , ,/ '
1n the l~mit. impo •• d by the ~.rimant.l'lIrogram and' notvith.tandina
,the l1m:1.t.tiona of, the Iimul.t10n modal it •• if the Rillank.rr.n
phenomanon,th. re.pon •• of an1nt.rc.pting .urf.c. to • random proc •••• ,
.pp •• re to b. po.libly • univereal on ••
Th. d.t.t1IIin.tion of the rill cro ..... ction and the rill •
l.ngth-.lop.,angl. relation.h1p h.ve b •• n accUr.tely .atabliah.d for
67, •
. I plaster surfaces.
, . Such determinations are difficult to establish in .
• ----- the field where they cannot be accurately related to ·the formation' .
.. ~rocesses. The shape of rill' cross-section and the rill-length to .
slope-angle relationship are regarded as being the most significant \ . \
in the formation of the RillenkArren surface.
The relationship existing betwaan the rill length developed
on the surface and the slope angle.is one determined by the amount of
water resident on the lIoUd surface. A critical lIIIIOunt 18 raquired to
prevent the developmant of rilling. On anylloping lIurface the~ ,
'existll a theoratical lone extending lome diltance from the creat in
which the rill forming procell (raindrop impact) is significant • . "-
The extant of thill lone ill determined'by the surface Ilope. An
insufficient number of experiments has been carried out to ass IllS
whether the mature rill length i. directly controlled by the estabUsbld
lone about the cralt. or it' the developed r1ll-lanath to 10m. degree
e~endl the initial lone down-slope by overcoming the film flow. For
materials lIuch all plaster,that have a fairly uniform. surface rouahnell . .
and are therefore able to maintain an even thickn .. 1 of lurface flow
68
under conditionl of luatained rainfall. a crelt. lona in whiCh rill
developmant occurs il eltablilhed for Ilopi &nal.1 exce.dins approximat.ly
1.5 dearaal. .. <.
The parabolic sh.p. of the rill cro •• -•• ction i. d.velop.d
ras.rdl.l. of the .urf.c •• lop. or of mat. rial .olubility. Th. Cro.l
I.ction of the rill and it ..... oci.t.d pa~ in .traiaht form .J.gna
the cr •• t .uaaa.t th.t it repre.ant. a .uifac. appro.china a me.t
69,
efficient energy disaipating' configuration under conditions of sustained
rainfall. As bypothe.ie', surfaces that induce the' gr~ate.t turbu
lence are those removed by solution thefaat~st, (the r~te of solution
is proportional to the rate at.which water is exchanged at the solid
surfaca).
The parabolic ch&Dn~ or rill cros.-secti6n ia regarded AI a
respons. to the sU~f~ce turb~ence pres.nt 4~ 'li~uid-so]j,d inter- " , ' . " <:.f
face, this turbulence baing graatly reduced in are .. carrying a thickar
film. ,The develo.pment of the rill results in the reduction of turbu-,
lent ensrgy over the :rilll partition, which resulta in a slowing of the .,.
rate at wh:l.ch material is removed thare and the per,istence of the
rill partition .. an :eroaional form •. i
412 The R1llenkar:ren Surface, what it Repre •• nts.
The ,eeminaly enomaloul developme~t o~ R:l.lleDkarren .. a
drainage or micro-flow featUre on exposad and inclined rock surface. -
is explained by the experimental :r .. ultl. Rillankarren do not rep:re .. nt
conventional lurfaca flow channell dalcribed by R.B. Horton.' Although "
the rilll repre.ent a,very .fficient aurface form for the direction of ,
.urface flow they ara, not initiated or maiDtainedby this type of flow
regime. The "a.hina out of tha r1~1 at a point on the .lope lupportl
. ~hi. bypoth .. il. ,
In the craltaraa,water il conltantly be:tna driven aaainit
the lurf.ce by droplet impact. In the lowar lurface region the e.tab1:l.-, :"
Ihment of a 'tI\1n,aurface, flow inta:rm:l.ttantly moving down-dope 11
\
\
effective in cuahioning the droplet impact"; It ia hypothesised that
the effect of auch hydraulic cuahionin8 ia ~n it~elf'inBi8Dificant'
with,reapect to the rate'of surface aolution.' If it were important , ./
a difference in the aurface lowering would be ,aa\ociated with the
" tilled and un-rilled porUana of the aurface. Such conditione were
not obaerved at any time during the experimllltal work on plaater, or
salt.
The behaviour of the water on the aurtace and the aelective
aoluticrial removal of material in the croat lIone to form rilla 18
tundamental to any explanation ot proc,.a regarding Rillenkarren. ,J
Two altemative explanationa exiat regarding the above, depmding ,~ ,
, I -,
on the degree to which the lolutionel capacity of vater ia Ittected \
by mechanical turbulence. Either the rate of lolution of the
aurface il not directly related to the volume,ot water and the
variation in mechanical tlow from tha cre.t dOWQllope accounta for
the differmce in aurface confiauration. Under thaae conditionl
lufficiant watarfor tha meaaurad rate of lolution il adlquate OVer the
aurtace. Or, the volume of water 18 critical in detarm1nina tha
lolutional rata of the lurtaca. 'Obaervation ot Rillmkarren davelopment,
however, ~ndicatal that the ri~lad cralt il eradiUS flltar and r
/
undergoins'com=enluratl lurface reduction. Under luch conditionl
the 101ut1on rate per litre il araater in the rilled craat lone, 10
effective~ tha weter iri the cralt 'lone 18 workad harder. The Ihape
of the rill partition etlectivI~, deflectl turbulent aneray end hanca
caacllltratal lolution in tM rill trouah.'
I 1
, \
;-"
\
70
.'
71 .. , ,."
. . Ooodcll11d, and rON.'1 lXpu11H1lti ihCll!ed'that thl dlwlopment-,1 • • • ~ .' •
of a paok.d pattern of .rodonal~.callop. 11 ·,the . at.bl •• urrace dew loped . . .'" "
in tn. p~.enc. of tU1:blllant chenne1 flovof aUHldVl vltn OVl1:
loluble eU1:fac.e; In the .ama way the p1:el.nt .xpe1:1~t. have oon- .
~ U1:alld that th.· pack.d1:111 IU1:faO. 11 It.bl. uridll: cond1t1oue of . . . ~
. 0
, I ' . I
.u.ta1n.d t:a1nfall. A. v~th the Goodch11d and rON lXpu1a11nt.1t ~. o • . •
luppo~.d th.t th11 et.ble f01:m,v111 b. eb.ent on tho •• 01 ..... of '. /' . .
.olubb rock wholl fHqu.ncy. of 11:0 ••• u1:f.ce 1nhOmolen1U .. aH. a. . .
den.e ••. ; 01: den.e1:thm, the 1:111 rHquency, ~1: paclUnl pal:t101ll.~ to . '_. I
,t~t ~ta1:1al. Koat -co1:l1.i HpH.ent .Iooda.ampla. of .uch rock.
~' . , .
o
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f..,; ~'~,: . "'\
<t
. ~.
J .• \
~ -~ ..
,.
, :
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'. <i'f " ',- .
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.:. . ......
, .
'1IOi11. ,11. •• US!. '~b'lUlI d.~xauenb:l.1dlllll" "oaQ"Moa He.l11e'b-toa. , ' , H. 3. U:51. 'Ul-204. ,,',' C', " , I
'10111. A.. U60. Kelk10l\llli "lI1\d JCauenbUdunl' ' 8." lui ~h i ,Supp. ~'. ·4;.;z1. " ,,' ' , '
110111. A~. 1961. Karrentilchl. dn IIdtral .ur KaratlllOrPholol11. . ", Z.,ftho~, ,lid ~. Hlft 3. ~as-U3. , '
" IIryen. 1.11 •• 1970. Itn 1mpreved ~a1ufa11 dlllulltor for Ull in lredon 'rel .. rch. Ca.tt.'tl. of A'al'th 801.'. Vol.7. 1552-1561.'
ev1J1c;J •• U24. Thl lvOlution of lap1all. I Itud;, in karlt ph1dolrlph;,. GlQg. tl. 141.26-49. '. '.
~I1or~ N.J. IIld J.R. Olav. 1974. Thl Trent pattlm rlit\fall dlllulltor. , "", ~tUl11v.n1t;, Ocaldonel 'aplr No.3, )(aUUHllllnt in
", phflical Iiolraph;, - laborator;, IIld fi11d 1~u1p~nt built at \ ' Trent Univenit.1. 27-40., " " ' ';
",;' " " ....., .• ~",!. .-,. . . . ,
Ickll't.K •• U02. ,Dal Oottllachl",lltlali..' I1n: Kll'renfe1din 11.1111« , Warenl 11'11111 a.dew~~ alt.n. ~'lMn~nl. 33. 3-71. :l
, ' ,
,,', lrH, 0.1.., 1960. I~don charaotlriltica of rainfall. ~g. !'nitntt1"tng. 41. 7, 447~49. ," '" I,
. ". . . . , ,::'." ,: "', J
Gabriala. l).end Ddoodt. K •• U75. A rainfall. l:lIIIulator for 10:1.1 ',' Ircaion Itudi .. in thllaboratory'; h40~ •• 25. 2. 80-86.,
Ooodch:l.14. H.'., li69. Thl lenll'at101lo~'l1IIail-lciall HUlt 'flaturel , of lredld l1"l~onl t ,. ItuQ of Ircai!1lial Icallopl. lIDpub. ,
'h. D.,~ .. il. KaKutll' UniV1nit1. I , , :
, , " OoqdchUd. ,H. end Ford. D.C •• Un,., Itn ltnalYI1a of BCllloP 'at,tlml. , tl. 0.°1 •• 71(lt I 51-62.. " .....
" . .' " . ' , aura R. IIldK:lD,lr., 0~1949. ~l'III1nal velocity ofwatlr drepllu in , 'atlanent lifO', tl. 18 •• O. !4)., , ' , '
•
• s " ,'W, , .
, '
..
I
.. - .
'f
~)
y'
. ,-Honcm,' •• 1., '1945. lrollonel.,. dlwloPMllt of ItHIIIII and thl:Ll" draine,1
h .. :I.IlI, ~dropb7lioa1'RP~ach to quant'li:etlvtl .l1rpboio8y. -0.01. ~oo. -Am. awn. 5'; 275-3.70. ' ' , _ ' -
, '
Hortcm, 1.1., 1948.8tet~.tloal di.tdhutloll of drop da •• 11141 thl OOOUfHlIol of dOllllllllt drop Ila •• :I.Il rlln. ' J'rczna. AIIIQI. 0." .. lIn~on, ,U' 6Z4-6l7. " - , , .
. ", ...' Hudtcm, N., 1971. -son Cortt~~Otl. B~T. Betdord Ltd. Londoni 3Upp.
bIai, 1., 1950. OIl thl fiu ,"looity of railldrop..J. 'N.tI'Ol' Soo • .rapczn, 28-113. "
JOII"i D.H.A., 1959. Thl .hapl of raindrop'" J. of N.tIIoJ'Ologlla Vol. 16. 504-310. ' '
-loaudlmllk, J.D. " Woodford. A.o~. lin'. COllolmba Ullln.tlini. Am. J. Soi, Sir. 5. Zl. 135-54.
, , " '.. ' . LaMI.J.O •• 1941.KI"uumlAt of:fall~loolty 'of watlr-drop. :.nd
• ,raindrop..!NnI. Ame1o; Oeo~ •• 1In~, 22.; 709-715.
'Q
LIhIIIIIn. 0 •• ~927. D .. 'rotl,Gehlioal al. HOahkIHt.Nt.tltI. -cfn POiI' 0. .. Will. " '-,-- ._ .. -- - '
lCuou. J.H.-~.1940. nutinlllld floltina of rook fr .... llt •• J. 0.01. , Vol. 48, 711-781.
-,
K:Lharl, Y •• lU9.', lailldrOpi 11141 .011 1~llolI. awu of NatlZ,lt'id • • of Ag. 80("'01. Serll. AI. 7-35.
-.-"
\
Klotkl. '.D •• 1948. hHtIIOrpholoallobl Stuclllll iII.dlr Illllel-Wlldorat.1I , -, Hohu.tlat. der "PlcO. dl I\mIPI". NoflS.plIIlllI • Jahrb. o.ogl'.
Ge •• Hannowr. Sondlthln. 4. 1-161.
Hut-ohler, C,I. 1114 KoldlllMuer. W.C •• 1963. Applicltor for lIhorltory rainfall Il.ulltor. Trllli. AW. Vol. e.3. ,220-Ua.
, OUlll', C.D". 1ie9.t.'.atl1l.~. ,Oliver ~410Jd, Idlnb~lh, 304 p.
'urctr, I.O.,197~;' a.lf C01lfllurltlon. ICIU.I aDd Ifflct.in I • ./ lldl in tiM ,In4 SpICI., L.r. Liportl14. B.I.P.H., ~74.
lathjllll. C., lU9. Qaoaoipl:\ololllOhl 1hltl~UchU1l1111 in 41~ alUeral. , und. ,1. LI~tlll'lbirl.' ",.tI cIIl' geo,f'. 'a' •• Hunoh.lI.
alllltlr:,. r.o •• 1936. Condition. lnflulllclni .ro.1on on thl 10:1.11 river , ,Wltlnh.d. UGA. Tlch Bull. 528. , ,
, i I ,
• , .
73
/
loha1dt,' W~. 1905. I1n.'lIIlId.tt.lbara 'ut~1 d.r ,.11-I.lchwind4lk.1t VOtI. .lIl1ltroptlll •. se'ba. AW. W •• W~ Xl .... 118U. 71-84. '
llIi.th)J., •• ad .Ubritton. a.a •• 1941. 101~t1on Ift.otl' on U"lton. , , .', u • tunot1on ot elop.. o.ol. 800. Am. Bun. ',,"01., 5a. U-78,'"
IpUh.lII. A., .. 1548. .Iindrop d ... ihlp" Ip.ld. .r.Nd., 5. 108-110.
av •• tina. M.H., usa, Thl ItaHtiandl ot J ... oa. o.09l' • .r. 124, I, '" _":-_,_184~55.
, Tlchahl, H., UU, Th. pI.udoul'l'an aDd axtoUat1on tOI'llll ot Iran1t. on Pulau ~ll1n, S1naapOH, I fIao 0.0lIl • . NJ' lIand ,5, 30a-311.
Wall. J ••• D. and mUord, 0.1. ,1966. A ooillpli-hon ot lmall 10al. , .. tunl , OD lli.oro-lranod1or1t. and ltMlton.in V'lt Barwalt, Halll1dl.
8. ~. N.'. 10, 412-468. " . ," . ~ '.
W.t'1/IMn". 1.1;, , '" 1I .. ~a~
W111. P.X., 1558. 163-176.
S1l11ullt1on ot Conduit N.twork Davalopllllllt on Planll. Hlo. thldi. KoICut.r'~1var.1ty.
, , . Thl lolutton k1n.tiOl at oaloit.. .rOIll'. o.ol.
l I
Vol. 66,,'
W1ltord, 0.1., .. Wall. J' ••• D •• 15115 • .r. fl'op. o.op. U, 44-70.
ItaH t topolraphy in I'malt., I
YaUn. K., 1971. .2'haol'V 01 ~bctw,,,o No.' •. Londollo K1cmi11an, 2e6p. . ...., . ,Zotov, V .D., 1941. , 'othoUnl ot'l:f.llllitonu by the d.velopmant ot lolu-
t10n 0upl. .r. o/~. , 4. 71-73. ' , /
./
\
74
..
APPINDIX It
IQUIPKINT
jI'b. McHt!StE l'Ufell aillu1it;or .Th. di.1In of th.XcMt.t.r r,inf,ll ,
.imul.tor v,. bll.d on th. lan.r.l .p.cific.tion. of two ot~r .i911.r
Hcbin .. , th. 14monton and THnt typ .. , Bryan (1970) and Cro,itr IIld
OllY (11174).. Both th ... IIrlilE. !tchin .. v.H built to .tudy .cU
.rodibility .tD .th. l,bor'tory' Th. MCH,.t.r .illul'tor incorpor.t ••
• ome impcrtlllt t •• turi. of th ••• t1P" but i. 1.rl.r and h,. b •• u '/
d.dan.d ·to tlltlrltt.r .ud.c •• HU ('11. 33). , ~
Th. aillu1.tor i. of th •• pr~1inatyp., the 'prl1inl no •• l ••
b.inl diHcttd upw,rd •• t • lit 11111. avl1 fEO! the '!!plEill.ut.l .
• urf.c.. 'nI. drop1tt~ .EI fom.4 by the bHik-up of the j.t U it
,
. .. ' . , " ~.
lc ••• Vtlocity !h •• 4 of th. UQ •• l •.• tth, .picll h'1Iht.of th •• prl1,
drop. thue fOEllld fill throqh th •• illul.tor •. Th. fill hdlht tc the .. '-
lurf.a, v.ri .. from 2.5 to 2.6 IIIt'f" d.pandinl·2n th. inclin.tion "L' .
of .,thl .urf.o. andth •• ,tttQa of th. 'prl1 .ro. Thi. hUlht lIl,bl ..
111 dropl't •• 1II11.r than 1.4 ... to appro.ch 'their H.p.ctiVl t.r!1nll , . D . , vtlociU ...
, Th. 1II:in .frill' of'th •• illul.tor VU· f.brio.tld fEO! '2UI
typ. D9Xion .101t.4 .t •• l.IIlI~" th •• tructur •. cOllpri.i~1 of two
p.rt •• , Th.·lev.r •• ation aou.i.t.d of •• upportinl lantry and op.r.
tinl pl.tfoEII.pannml th. bu. tank. th. ·upPIE frllll lIouHd to th.
top of th. levlE IIctioU olEri .. th. lllin pipavork •• 1Iotrioal "£violl •
....
75
i~ I
J' d~ r----d . .1
. " "
o
'"
.. , '
. " / "" 7'
. . "
- . _., ' .
•. . ,t t I .
,,'
. ; \
motor aDd r.duotion unit and .pr&1 b.r .upport. (I'll, ' 34), .. -~'. . . \" , .
''', ,All pip' work ,on t~ •• :lmul.tor WII of rilid oopp.r or AIlS. '
ucludina th.' 11mbl. lin,J oonn.otinl the oontrol .".lva. to ,the .pr&1
/ b.n, Th •• pr&1 bar ••• I11III1)' o01llpri •• d of. In alllllllnlllll alloy o.rr ... . . ,;. -
oarryinl .:f.lht rolll1' luld •• and' 'upportilll. four. half inch dllllllt.r '.' '. .
OOPPI1' .pr&1'bar. lIIOUntina Ilx nOlll.. (I'll, 35),' . ..'
....... , Th. ,xpl1':lm.ntal bloob .ra mollllted in the Ilmul.tor on a-.' oradl. PO'1t~on'd dinotly ,b~OW the .pr&1 DO~I1'" The oradl. i. ,
o.pabl. of .djuatina th..urf.o. inclin. from "1'0 d'lra.. to 75 d'lra •• . \'" I .
\ . ,
by lilian. of •• :iDll. j .ok .oraw (FlI, 36). \ ':
Th.w.tl1' .upply for the 1III0hin •• II d.Uvorad f1'Olll • Uxod .. ' 1 •
. . . \ ' . .' '
pn •• ura oontrol proyU.d by • hlldd tank nmoto frOlll tho .:lmul.tor, \ .
All\lin valvo .uppU.d \~h. Ux,d pr ... ur. &IIPPly to the lIIInU~ld. alonl
with. by-p ..... uch an~rrl\llllllant provid.d tho o.p.bility for inj.otinl
the .upply,withollt .hutti;;' oUOl' raduolnl pr ••• ura to the m~Uold. Th. by-p ••• ·lin. v •• fitt.d with. two inoh rllllo.".bl. plul ,(ril. 37).
I!p.r&!tnt.l jl09k. Pri'lIIIt~o o •• t plut.r blooka w.r. ua.d for .11
plut.r .lIrf.o •• xp.rimant.,' Th. blaek,.h.p. Pro~d'd maxllIIlIIII .urf.o •
• ra •• nd .tnnlth vith • lIIlnlllllllll valiaa. ,the 15 d'ln. tlp.r an.bl.d
.uiar o •• tinl and provid.d • widl1' ranlo 'of.110P' anll .. ' to b •• Il.ot.d
in the oradl. (lia" 7. 8 and 38). - -', 'f . ,'" .
Th. block IIIOlild 11 of thl box typ' eon.truet.ld f1'Olll 1/2. inch " "
tliiok lIIIr:t.nl pl.ry9od vith thl fomna .urfee .. llllllnetl'd,,!ith al ... . . ",.
'Ubra. A motor vibrator W •• lIIOlIntld 01\ tho back of thl box toald in , , . '. . - /'
thl ralllOval ot ail' bllllbl" vhU.t pourina thl pllltl1' (Fla- .3~).
------, .. ,
, " 78
.. r
,----,. - . _ .. - ...
, ,
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<" "
" , .... • , ,
, " '/
,
.".
~ •. w-J • ~ 0-375 1-
_I ; ! . r '---' ,·1 . . . I
f AJI dimens' oasiJ iIdJes I . '
241JHF,
GOSoll .~ -f \
~'!:I " ~, ~.~
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! ~ • If) • dI ] Ii:
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.... t---i:)(J.-1
:, 1 . ' 1 ~,t--' ,--£>(1---1
IN~
11 . f . . I ~ ..... i
..
£><1:---- I- .----, ..• ' . r·· . I'
, .
.' '
,81 '
,>, . ,', .... :J
, ,
• '8 .
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. t~~ ~ . . .
;. , •
"
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....
. ,
. I {. o ' . ....
; . i •
. ~ . ' ". . ...
. ."0 . ~ .• . , " .' .
.• . 'l
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, . " 83
. ".
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.. .. .'
. : ~
• 1'01: ,0\ ! ~
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RAINrALL SIMULATOR SPECIrlCATIONS
MotOl'l 1/4 H.P. "'111111 Ph~1 ,110 volt • •
IIduatioD Voitl 0.11' tJPlvith oil blth.
IIduction-l'ltiol' 80 I 1 . ' Outputi.p1ld (St1'Ok •• pIl'min)1 15 ~ 25.
, '
Nlllllbar. of nOllll.1 24 (in bank. of 6).
'\
:
(OVI1'l11)
wnlth 2.5 III
OpI1'Itini Tank'
, Llllith
Width
1~8 ai
2.75111
5.0 III
1.9 III
Hliaht 0.6 III
Ilook CIPI~t7 60 x <~ 0lIl
"
o
84
\
-,
• -
t
...
,
•
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-~- ... -:------:-r -------
- ", ___ ,.,_ - '. '-_0
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~,
ElCPERIMENTAL MEASlJlU!MI!!I' AND PROCEDURE
Surface Haasuremant. In ed~ition to ,the direct mechanical mealuremants' !
taken during end efter each experiment photography Val used to ,record , / ,,', the surfaee development over time end to determine the magnitude of
"
) . surface features. Twoitema facilitated the photography, one Val the
inat~llat1on of the camera mounting beam that ,loeeeed "the, camera
preciselyvith respect to the block surfaee, end enabled stereoscopic . . photographs t'o be obtained, (Fig. 40 & 41) •. The second festure, a ~ne
. / .
,projector, vas lIecured to the main-frame of the simulator. , The line
projector provided a'narrow flat li~t beam which intercepted the block
surface at 45' degrees wti,en" the experillllln.tal surface vas, tilted to,
its photographic positon, (li'ig. 42 & 43). Photographs eakin, of the surface
, in conjunction with the projector enabled surface profiles to be taken
at desired time intervals. , "
Raindrop Measuremant8 No direct calculation of the kinetic energy
generated, at the block surfaee by rainfall vas carried out in this .. /
series of 8l1periments. A check on the droplet size, and size distri-
bution vere made 8t,35 end 40 mm/hr, however" (the two main intensities
'~ used in the present series of ellperiments).
The measurement of droplet size end droplet size distribution I
'vere made using an oU bath, into.which simulated rain drOJ'lef8 verI!
, . , ,'.
, .'
•
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Number 1 ; ~."';,
; ',: ~oule select:1DIio 18(1l ; :".(see fis- n)' 6(2) . :~." ~}:, .'
~.-t. ~~ spray bar 4
~\ Set inten.s:lty
Speed l!..P.H.
Stroke
'Slope angle
Block type*
Material ** ' :--
Duration (DrS.)
40
24
75%
45
1
1
650
SD!TlT,lTQll SEl'risc Foll ElPElUHEBtS1 - 10
2
12(1) 12(2)
4
3S
25
'85%
45
1
2
800
3 4
12(1)18(1) 12(2)' 6(2)
4' 4
5 6
18(1) 118(1) ~(2) 6(2)
.4 4 • , .
7
18(1) 6(2)
4
3S /
". . .3S_..-/ 40 3S 3S I .
25 f 25 25 .. \
8S% ). 85% L_____ .
~ 3S 55
1
2
550
1
2
550
75%
30
2
2.
550
25~ 25
85% 95%
~ 1/2 45
2 1
3 . 1 -.,
550· 600
8
18(1) 6(2)
·4
3S
25
95%
45
3
4
500
9 .1ei
.1200 12(1) 12(2) . 12(2)
I
.' 4 ,40 40
22 22 "
85% 85%
50 '. 60
..
l(spec) l(spec)
"3 1
600 550
**Material 1: ~Ipl.aster . *UOc:k'type see Fia.1 &9.' .
i
2: Reagent grade IIlaster type 2ll 3: lIe.agent. c-~ 1I1x _ 4:. ~ with 10% sand
.~
J
,
y'
"
~,<P •
t
... o 01'.
~'
~.
, ,
, \ 1 : \.
, ,
al10wld to fall for a fixl tim. intlrval. Thl drOVI r.m.1nld
.... nCially 'phlric~l Whan'-imarlld in thl 01.1 and thl dltlminat1on,
of tha 4rop d1amatlr WI. mad 'Ul1nl ~-mal.ur1nl maln1f1lr of mld1um , '\ ... ' . . -
powar, (x 10) 011 by photolrapllinl tho dropllu in tha 01.1 bath on a' , ,'\' ,
lmall Hlht ·tabla. TIl. ba .. o'f thl 01.1 bath wa. of 6 II1II thick llall . . \
I
with itl lowu a1dl Itchld for', th1l purpo .. , (111. 44). / . : ,.
Aircraft Iud I 1005 Ql1(Sholl No.AC'3519) wa. u ... d in tho bath,
it wa. found dvan.t',loUi toCint thl 011 with a .mall quantity of ,
uuthanl'b~ •• d,paint 1n,·~rdar to mau tho ,,1l.mora opaqui.
roi' t1mad oxpo.ur. o!: thl a1mulatld rainfall thl\oU bath \ " "
1. locatod on I fram. in 'thl cradl0, (111.45).' TII~ oil bath framo • ~ t •
. 1. aUrDlOuatod by a 12· em .quari .Icdon tubl 25 em loril, thl'1na1dl
.urfaca. of tho tuba -·arl: covorld with cotton fabric •. TIl. purPo .. of ., '
, t, .. '
_thl tub~ i.,to an.url that th. oil bath r.~I1va. only .1mulatod rain-
drop. falling· fr'I,ly throulh thl maChinl and not .pla'h for adjacant
. T1m1n1 of thl IxpO'uro of thl'bath.1. dlUl'lll1nld by thl ,plld
at which ... hroud 45. em in d1amltu, ptvotld IboUt·th.· cradll;ox!. 1. i • •
rot,att pu.t .thl upplr an,d of thl t~be.. .. ,. ' .
. ' TIl. 'ahroud 1. drivan Illctr1cally u.1nl a ravlr.4bla D.C. motor
and tldaat1bn'un1t~ '"
. . . \..
TIll f1nal.dr1vI ut1li'l. a .procut to oporltl
,th •• chroud, .. lect1on of whl.l 1.11:., .. tt1ng 'tho' rot.at1ona! Ipeed. , TIIb IIIGchanbm op.ratcrd mora ralillbly than a friction drive in tho
wet c:ond1t1ona' 'of the. a1=ullltion bUI tank. Expolun t1ma. from one
to five. ucond. could bo mad. Ul1ng thb arrangmant:
91
..
,,'\.. -- I , /
\
i M '~: 92
\I~ ~.e '
ilDd '§-''a § U,
a.: j ._ I&J I' ' -a.: ''5 :: ~
;j , III c.J
i ii,i" ~'
.c: -.8 ,-0
.... , ,
, .
i
',e;'
. 'rrr===~~~ _.. .'~' ,
• , • ~.~ <) ,
• "
,
i : !.
! i ,
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I
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93 I j
•
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, '~ ! " ..c: C5 ..
~i ' ~ ,
Me •• urament·of·V11m·Th1ckn ••• ·on·Block·Surf.c.
Direct m ... urlllllnt of the th1ckna •• of f,low on the block
.urtac.w •• not po.dbl. dOl to ,the m1cro ... cal. d1man.1on. of the 0' .' •
flow and to the .halt.r .• ff.ct producad by plac1na machaDical ma •• ur~
~na aqu1pmant in the .r •• of'.1mul.t.d rainfall clo •• to the block
aurf.c.. An 1nd1r.ct malluring tachn1qu. WII th.r.for. adopt.d. Th1.
tochn1qu. util1zed the normal clllllr •• qu1pment and an optic.l d.vic.
to d.t.rm:l.n. the depth of the liquid flow th.t VII coloured for th.
purpo ••• of the exp.riment. Dy.d ~1quid f1ow1na in thin f11ma .how.
a marked 1ncrea .. in colour .atur.t1On for' a lIIIal1 1ncre ... in depth
within a l1m1rad rllDge.
Th. preclle d.term:l.nat1on of thl fUm th1cm •• awII mad. by
relating the ob •• rv.d colour .aturat1on of the liquid II it p •••• d
through a wedge ap.rture, to that 'flowing off the block lurfac.,
(i1a· 46 & 47). By- ob •• rving the ap.rture calibrated 'from 0.014 to 0.002
inches dmultlllt.ouaIy with the surfac. film flow,· •• t1mat •• ,of .tb.
flow th1ckn8's were po •• 1bl. within 0.002 1nCh.I. The apparatua
op.rated well .ven und.r conditions of rapidly changing dye 1ntendty
due to the fact that 'th.flow rat. th~ugh thl aperture could b •
. adjusted t~ the ,rate of flow .ov.r the block .urface.
The dye used in the exp.r1ment. vas commercial food colour I
injected into the by-pa •• lin. (iig. 37.) whU. the dmulator was
lOperat1ngsS to 10 m1 of colour was used for each mealurement.
94
95
, .... :
JII! 10 II
, , "
t
<9-< o
C' -f-
, \..! .®
-' G
Fig.47General ariYJngemenf of the' aperture gauge for measuring film flow thickness over the block surface,
\
KEY
I· Catdmeld for gc.Jge
2 EichQlst saeen
3 Gauge ptofe{fig.uJ
4 CoIiJroted gauge Ct1IIf!r
5 Vocwm line
6
7
'8
Pressure line
Pressure exhaust -, ~CfN}rlure
'" '"
• 97
, ,
• Notes on Special 'Experiments 9 & 10, (Table 3.6) ,
Iq order to test ths hypothe'ds regarding surface erosion and
flowing water characteristics at the test surface several tests ~ere 0
. ,
.carri~d ouJ:, lllIingmodified blocks. Because of the difficulty associated
with obst!rv1-ng very thin fi~1DIJ of flowing liquid over uneven, surfaces,
no direct attempt was made to measure tha thickness or the nature of
flow, instead devices we~e i~stall~d on and.adjacent 'to the test surface
to interrupt a sel'!cted part of the proceas and observe the resultant
form response on the,surface.
Two experiments wer~ carried out. The first one was designed • , ?
to reduce the effect of the flowing film and so enhance the, raindrop
action, the second reversed this conditi~ by attenuating the effect
of falling droplets and establishing a runoff film. The test utilised
a 60 x 36 cm,plaster block into 'which thin f~ow fences had been cast,
these were made of copper sheet and were positioned at right angles
e set incline at varying distance from the crest •. The flow fences
e intended to direct the flow of the run-off film around them, thereby "
providing,a zone below it with no run-off water. Over the crest of the , '
block in two positions were 1DO~ted fine wire mesh screens 6 CD square
and adjusted to be 2 cm above the test surface. The screans were poSitioned
to break up and arrest falling droplets before they reached the crest but
ensured that ,the water film developed below.
The modified test block was subject to a 600 hour test at 35 mm/hr
at an inclination of 45°. The surface developed with mature rill
,
!
r --'-'--"~-- -":'"-----_. -.---.---.. -.. --~
98
"
development at the cresi:' and below each of the flow fences. At the SSll18
time the smooth surfaces that developed predominantly at lower parts of
the incline were extended to the crest under the screened sress. ,' .
•
\
---------~----------------.-----.-,-.--,-,-
/
~ Experiment 01, 45 degrees rill length (in C1II)
15.0 14.0
9.0-·' -_.4;6
17.0 6;5
16.0 ., 16.0 5;0 5.0 8.5' 9.5 9.0 5.5 7.5 5.0
13.0 11.5 11.0 11.5 10.5 12.0 10.0 10.5
7.5 7.0
. '-.9.0 '13·;0 1Z;0 6.0
12.0 - 6.5 12.0 8.0 9.5 5.0 7.0 9.0 5.0
13.5 17.0 14.5 15.0 19.0 13.0 10.0 13.0 22.0
..
\ \
99
,.
Experiment 02, 45 degrees ri~l length (in em)
16.0 19.5 9.5 8.5
20.5 3.0
21.5 13.5 10.0 18.0 15.5 20.5 9.5
10.0 9.0
, 5.5 4.5
11.5 7.5 9.5
10.5 13.5 12.5
9.0 16.0 5.0
14.0
'/11.0 19.0
8.5 14.5 8.0
14.0 8.5 3.0 9.0
16.0 6.0 9.0 5.0 9.0
16.0 9.0 3.0
13.0 9.0
11.0 4.0 8.0
10.0 4.0
13.0 16.5
8.5 15.0 10.S
,
100
/,
f "
--'-------~----.-.-.--- - I
Experiment 03, 45 degrees rill length (in em) ~
\ . 21.0 10.0 20.5
,20.5 19.5 14.5 14.0 14.0 11.0 19.0 10.5 13.5 18.0
8.0 3.0
16.0 16.0 5.0 8.5 3.0
16.0 , 15.5
5.0 9.0 6.5 8.5 9.0 9.0 9.0
, .
.r
9'.0 8.:5 9.5
, 5.0 4.0
'; 9.0 .10.5
6.0 9.5 '
10.5 9.5
,3.0 4.0
10.0 ',11.0
7.0 14.0
4.'0 16.5 15.5 10.5
8.0 .r 13.0
9.0 - 16.0
16.0 12.5 13.5
"
;'<Q\ " .
101
;. ,
r' Exper~t 04, 55 degree. rill length (in em)
. 13.0 19.0 22.0 23.0
.25.0 28.0 30.0 33.0 27.5 25.5 25.0 22.5 22.5 22.5 23.0 24.0 20.5 23.0 24.0 19.5 19.0 18.0 II 16.5 15.0 15.5
26.0 15.0 22.5 24.0 . 20.0 26.0 26 •. 0
.26.5 26.0 30.5 33.0 27.5 25.0 25.5 23.0 24.0 17..5
.0 4.5 7.5
.. 102
/ '~
~ Experiment 05 . 30~ree8 rill length in !IIIII.
9 72 25 71 79 .~ 70 80 , 70 37 67 .41 65 60 I 68 61 68 64 65 57 67 55 . 67 17 71 49 70 47 70 49. 69 43 70 22 72 58 73 46 , 79 59 73 30 83 43 81 74 85 77 85 78 81 75 57 59
103
I -'
i
Experiment 06 22 1/2 degrees rill length in mm.
5.5 4.0 4.0 3.0 5.0 5.0 .4.5 4.5 4.0 4.5 5.0 3.0 3.0 3.0 5.5 3.5' 4.5 . 3.0 5.0
" 2.0
6.5 4.5 5.0 2.0 4.5 4.0 2. 5 4.0 ~.O' 3.5
/ 7.0 4.0 6.5 2.5 5.0 2.0 4.5 4.0 5.0 4.0 5.0 4.0 4.5 4.0 5.0
" 3.5
. 5.5 4.5 4.5 5.0
--------
,
\
105
Experiment 07, 4S degre •• rill length (in em)
22.0 19.5 20.5 ·17.0 18.0 16.5 19.0 9.0 14.0 11 •. 0 16.0 .10.0 9.0 8.0
18.0 8.0 10.0 5.S 10.0 8.0 10.5 9'.5 16.0 9.0 15.0 15.~ 12.0 1l. 16.5 13.0 .- 15.0 12.0 9.0 15.0
10.5 10.5 18.0 12.5 17.5 10.0 2':1.. 0 8.0 11.5 7.5 ' . 10.0 . 11.0
I . 106
Experiment 08, 45 degrees rill length (in em)
21.0 10.5 21.0 5.5 21.5 10.5 20.0 9.0 19.5 6.0 19.5 8.0 20.5 6.0 I 19.0 6.5 19.5 7.5 19;5 9.0 20.0 6.0 10.0 7.0 14.0 10.5 10.0 9.5 11.5 10,0 20.5 9.0 18.5 10.0
9.5 10.0 10.0 11.0 16.5 11.0 ., 15.5 7.0 10.0 15.0 9.5 " . 6.0
10.5 17.5 ,~ "
16.0 11.0 '\ 9.0 15.0 )
9.0 9.0 10.0 13.0 16.0
..I
,
I 107
"; . l"
. Experiment 09', 45 degrees rill length (in em) (
24.0 ~ 23.0 , 29.5 21.5 29,.0 17.5 , 23.5 24.5 24.5 .. 32.5 26.0 .~ 25.5 .---. -25.0 24.0 20.5 23.5 14.5 ~ 19.5 13.0 23.0 lB.O 24.0 20.0 22.5 31.0 23.5 27.5 24.0 23.0 23.0 22.5 30.0 25.5 23.0 24.5 24.0 32.0 24.0 27.0 21.5 21.0 19.0 25.0 16.0 25.0 16.0 ... 17.0 26,.0
Exp~r1ment 10, 60 ~egree. ,rill length (in em)
22.0 25'.0 22.5
I 25.5
- 20.0 I 26.0 24.0 27.5 23.0 28.5 26.0 29.6 24.5 26.5 23.0 20.0 27.0 24.0
. I 27.0 20.0 27.0 22.5 26.5 23.0
. ,
• I ,.,
108
J
"'.' ¥,
',' ... ": .' .,,' .",
.: -'>}:~'-"" ~ .',
'ii,'" • • -,
1. Surface erosion after 36 hours, scale in em.
\ 109 . " !
,':)
/ 110
/' ./
.. ,
" -~-'
..
.......... II
~---" -.;.~:~: .. ~:-:~.-.:-_ .. ...4 __ .~ -.,. __ .. _ • , " .. -: -'" ,--; .. '-'-,- ~~;;:::.~;;~*::= ... , .. ~: ,,'-' ... :'", .... :
.(~--::--:- .• _ .'.,;., r." ... .;.;.:,~ .. . ,':. -:...~-.~:.
" ,.'
' . ., . .! .:::.s., . "'-... -. ::;r;;;-~ -:.: ""':~::"J,.""-" : - ' .. ' . :_'~.""'." ~,:
...... '. ' .... ,.
2. Surface erosion after 120 hours, scale in em.
Q
III
'.,
3. Surface erosion after 240 hours, scale in em.
,112
"
-'
.~
, , . .. - ~ /.' .~.
4. Surface erosiOn after 360 hours, scale in em.
. ' u
. .. '
,113
---!.I "
\ l ':H \"i\l,!,' '\ df'::'lj;i<:l'i.ill'·llr"I\'I!·i)':~I\ t,'ll, 1,1, ' .. \ i , \ " ',' 'i! ,'! ,,' I , ,i, ' " ' ,:' ,II .' r I ' I :
'
" i:;' \ I' I ,,' I , I. \' .\ iJ.,.!' ·l' .. ·., .. Y'
. ,. i" '.~'. I . • '.. .
",
, , j
, , 'j
.. . y ", ~.. ,.
" ,
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5. Surface erosion after 444 hours, scale in en.
i ' I' '- '--';:';'==::r "-t', " "~ ~~~ , -, .
'., .
..•. ,~~~
!
)
~;~~:E',~', : \
6. Surface erosion after 516 hours, scale in em.
114
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ti Z;';
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u' ' , .. -.-"'.'\"
1 'f' ;.. ~. •
I
, ,,'f ' '/. ';
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.. , '
"
7. Close up of part of crest at 516 hours, (see photo No.6)
!.
i I
" f
I !'
115
8. Experiment No.9. Eroding surface after 416 hours, using flow fences, (for description see paies 97-98).
,116
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