Received January 2, 2013/ revised June 28, 2013/ accepted August 13, 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵ǤǤʹ͵ͻ Ǥ ǤǤ
⺺⾂#㨚⺾♪ⴖ#♿ᢾ↾ᦂ⮎#ἶ#⍆㦪㰒#㟪⟖ኂ⟖㬦⟖#♮ⷓ
ઽজ
Song, Young-Suk*
Estimation on Unsaturated Hydraulic Conductivity Function of Jumoonjin Sand for Various Relative Densities
ABSTRACT
The Soil-Water Characteristics Curve (SWCC) is affected by the initial density of soil under unsaturated condition. Also, the characteristic of hydraulic conductivity is changed by the initial density of soil. To study the effect of initial density of unsaturated soil, SWCC and the Hydraulic Conductivity Function (HCF) of Jumoonjin sand with various relative densities, 40%, 60% and 75% were measured in both drying and wetting processes. As the results of SWCC estimated by van Genuchten (1980) model, the parameter related to Air Entry Value(AEV), 쩀 in the wetting process is larger than that in drying process, but the parameters related to the SWCC slope, n and the residual water content, m are larger than those in wetting process. The AEV is increased or Water Entry Value (WEV) is decreased with increasing the relative density of sand. The AEV is larger than the WEV at the same relative density of sand. As the results of HCF estimated by van Genuchten (1980) model which is one of the parameter estimation methods, the unsaturated hydraulic conductivity maintained at a saturated one in the low level of matric suctions and then suddenly decreased just before the AEV or the WEV. The saturated hydraulic conductivity in drying process is larger than that in wetting process. The saturated hydraulic conductivity is decreased with increasing the relative density of sand in both drying and wetting processes. Also, the hysteresis in unsaturated HCFs between drying and wetting process was occurred like the hysteresis in SWCCs.
According to the test results, the AEV on SWCC is decreased and the saturated hydraulic conductivity is increased with increasing the initial density. It means that SWCC and HCF are affected by the initial density in the unsaturated soil.
Key words : Unsaturated hydraulic conductivity function, Parameter estimation method, Jumoonjun sand, Relative density, Initial void ratio
Ⅹಾ
ᇩ⡍⪵᳑Õᨱᕽ⮺᮹Ⅹʑၡࠥᨱ⮺-⧉ᙹ✚ᖒłᖁᯕᄡ⪵┅íࡹ໑, ᯕಽᯙ⦹ᩍᇩ⡍⪵᳑Õᨱᕽ⚍ᙹ✚ᖒࠥᄡ⪵⦹íࡽ݅. ᯕᨱݡ
⦽ᩢ⨆ᮥŁₑ⦹ʑ᭥⦹ᩍᔢݡၡࠥ40%, 60% ၰ75%᮹ᵝྙḥ⢽ᵡᔍᨱݡ⦽Õ᳑ၰᮅŝᱶᨱᕽ᮹⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ŝᇩ⡍⪵
⚍ᙹĥᙹ⧉ᙹෝᔑᱶ⦹ᩡ݅. van Genuchten (1980)᮹ႊჶᮥᯕᬊ⦹ᩍ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥᔑᱶ⦽đŝŖʑᮁ᯦sŝšĥࡽĥᙹ쩀 ۵ᮅŝᱶᨱᕽⓑsᮥaḡ໑, ᄡłᱱ᮹Ğᔍᨱšĥࡽĥᙹnŝඹ⧉ᙹእᨱšĥࡽĥᙹmᮡÕ᳑ŝᱶᨱᕽⓑsᮥw۵݅. əญŁ
ᔢݡၡࠥa᷾a⧁ᙹಾŖʑ⧉᯦⊹۵᷾a⦹ḡอᙹᇥ⧉᯦⊹۵qᗭ⦹໑, ࠺ᯝ⦽ᔢݡၡࠥᨱᕽŖʑ⧉᯦⊹۵ᙹᇥ⧉᯦⊹ᅕ݅Ⓧíၽᔾࡽ݅.
⦽⠙, ĥᙹ⇵ᱶႊჶaᬕߑ⦹ӹᯙvan Genuchten (1980)᮹ႊჶᮥᱢᬊ⦹ᩍᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹෝᔑᱶ⦽đŝᇩ⡍⪵⚍ᙹĥᙹ۵⡍⪵
⚍ᙹĥᙹಽᯝᱶ⦹íᮁḡࡹ݅aŖʑ⧉᯦⊹⪚ᮡᙹᇥ⧉᯦⊹ḢᱥᨱɪĊ⦹íqᗭ⦹۵äᮝಽӹ┡ԍ݅. Õ᳑ŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ۵
ᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹᅕ݅Ⓧíӹ┡ӹ໑, ᔢݡၡࠥa᷾a⧉ᨱÕ᳑ၰᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ۵qᗭ⦽݅. ᝅ⨹đŝᨱ᮹
⦹໕ᵝྙḥ⢽ᵡᔍ᮹Ⅹʑeɚእᨱ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᨱᕽ᮹Ŗʑ⧉᯦⊹(AEV)۵qᗭ⦹Ł⡍⪵⚍ᙹĥᙹ۵᷾a⦹အಽ, ⮺-⧉
ᙹ✚ᖒłᖁ(SWCC)ŝᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ(HCF)۵Ⅹʑeɚእᨱᩢ⨆ᮥၼ۵äᮝಽӹ┡ԍ݅.
áᔪᨕᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ, ĥᙹ⇵ᱶႊჶ, ᯕಆ⩥ᔢ, ᵝྙḥ⢽ᵡᔍ, Ⅹʑᔢݡၡࠥ
ݓъėॡ
1. ᕽು
ᯝၹᱢᮝಽḡၹŖ⦺ᱢྙᱽᨱᕽ᪥ᱥ⡍⪵ࡽḡၹ᮹Ğᬑᮁℕ ᮹⮱ᮡྜྷ᮹⮱อᮝಽ⦽ᱶࡹ໑, ᯕ్⦽ྜྷ᮹⮱ᮡDarcy᮹
ჶ⊺ᮥ۵äᮝಽಅᲙᯩ݅. ə్ӹᇩ⡍⪵☁ԕᨱᕽ⮱᮹
Ğᬑྜྷ, ŖʑəญŁ⮺᯦ᯱ᮹3ᔢǍ᳑ᯕအಽྜྷŝŖʑ᮹⮱ᮥ
࠺ᨱ Łಅ⦹ᩍ ⦽݅.
ᇩ⡍⪵☁ᨱᕽྜྷ᮹⮱ᮥᯕ⧕⦹۵ߑaᰆᵲ⦽ᔢššĥ۵
⮺-⧉ᙹ✚ᖒłᖁ(Soil Water Characteristic Curve, SWCC)ᯕ݅.
⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮡeɚ᮹Ⓧʑၰ༉᧲᮹ᇥ⡍, እ⢽໕ ᱢ, ᯦ࠥᇥ⡍, ྜྷญ⪵⦺ᱢ✚ᖒ, ၡࠥᝍḡᨕ᪉ࠥᨱᩢ⨆ᮥၼ۵݅.
✚⯩⮺᮹ၡࠥ⪚ᮡeɚእ۵⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᨱᩢ⨆ᮥ
ၙ⊹۵ๅᬑᵲ⦽ᗭaᬕߑ⦹ӹᯕ݅. ⮺᮹ၡࠥ⪚ᮡeɚእ۵
⩥ᰍ᮲ಆၰ⯂ᙹಆ(suction) ᳑ÕᐱอᦥܩŝÑ᮹᮲ಆၰ
⯂ᙹಆᯕಆᨱ᮹⧕ Ⓧíᄡ⪵ࢁᙹᯩ݅. Assouline (2006)ᨱ
᮹⦹໕⮺᮹ၡࠥᄡ⪵۵⮺-⧉ᙹ✚ᖒłᖁ(SWCC)᮹ᄡ⪵ᨱᯕ
í⦹໑, ᯕ్⦽⮺᮹ၡࠥᄡ⪵۵ᯱᩑ☁᮹ᯝၹᱢᯙ✚Ḷᯕ݅.
⮺᮹ ၡࠥᨱ ෙ ⮺᮹ ⚍ᙹ✚ᖒ ᄡ⪵ᨱ ݡ⦽ ᩑǍ۵ Croney and Coleman (1954)ᨱ᮹⧕ᮭ᯲ࡹᨩᮝ໑, ᯕ⬥Laliberte et al. (1966)ᨱ᮹⧕ḡᗮࡹᨩ݅. ↽ɝᨱ۵⮺᮹ၡࠥᨱෙᇩ⡍⪵
☁᮹⚍ᙹ✚ᖒᨱݡ⦽ᩑǍaฯᯕᙹ⧪ࡹᨕḡŁᯩ݅. ᩩෝॅ໕, Gallipoli et al. (2003)ᮡvan Genuchten (1980)ᨱ᮹⧕ᱽᦩࡽ
⮺-⧉ᙹ✚ᖒłᖁ⧉ᙹᨱእℕᱢ(specific volume)᮹⧎ᮥ⡍⧉⦹
ᩍᱽᦩ⦹ᩡ݅. Sun et al. (2008)ᮡ⮺᮹ℕᱢᄡ⪵⪚ᮡ༉š⯂ᙹಆ ᮹ᄡ⪵ᨱ᮹⧕ʑࢁᙹᯩ۵⡍⪵ࠥ᮹ᄡ⪵ᨱݡ⦽⚍ᙹ༉ߙᮥ
ᱽᦩ⦹ᩡ݅. Masin (2010)ᮡᮁ⬉᮲ಆ᮹ᬱญෝᯕᬊ⦹ᩍeɚእ ᨱݡ⦽⡍⪵ࠥ᮹᮹᳕ᖒᮥᩩ⊂⧁ᙹᯩ۵⚍ᙹ༉ߙᮥᱽᦩ⦹ᩡ݅.
Tarantino (2009)۵ᙹᇥእ(water ratio)ᨱݡ⦽Ğ⨹ᱢŖᮥ
☁ݡಽᄡ⩶ࢁᙹᯩ۵⮺ᨱݡ⦽⮺-⧉ᙹ✚ᖒłᖁ⧉ᙹෝᱽᦩ⦹ᩡ
݅. ᯕ༉ߙᮡGallipoli et al. (2003)ᨱ᮹⧕ᱽᦩࡽ༉ߙŝๅᬑ
ᮁᔍ⦹ḡอ, Gallipoli et al. (2003)᮹༉ߙᅕ݅1}᮹❭ີ┡a
᯲݅. Sheng and Zhou (2011)۵ᯝᱶ⦽ℕᱢᄡ⪵ݡᝁᯝᱶ⦽
᮲ಆ⦹ᨱᕽᔑᱶࡽ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥᯕᬊ⦹ᩍ⡍⪵ࠥ
᪡eɚእᔍᯕ᮹᷾ᇥšĥෝᱽ⦹ᩡ݅. əญŁZhou et al. (2012)
ᮡ⡍⪵ࠥ᪡Ⅹʑ eɚእᔍᯕ᮹᷾ᇥšĥෝ ☁ݡಽᇩ⡍⪵☁᮹
⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᨱݡ⦽⮺᮹Ⅹʑၡࠥᨱݡ⦽ᩢ⨆ᮥ
ᱶపᱢᮝಽᇥᕾ⦹ᩡ݅. ᯕᔢᨱᕽᅕ۵ၵ᪡zᯕᇩ⡍⪵᳑Õᨱᕽ
⮺᮹Ⅹʑၡࠥ⪚ᮡeɚእ۵⮺-⧉ᙹ✚ᖒłᖁᮥᄡ⪵┅íࡹ໑, ᯕಽᯙ⦹ᩍᇩ⡍⪵᳑Õᨱᕽ⚍ᙹ✚ᖒࠥᄡ⪵⦹íࡽ݅. ə్ӹ
ǎԕ᮹⮺ᮥݡᔢᮝಽᔢݡၡࠥᨱෙ⮺-⧉ᙹ✚ᖒłᖁ(SWCC) ᔑᱶၰᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ(Hydraulic Conductivity Function, HCF)᮹ ᄡ⪵ᨱ ݡ⦽ ᩑǍ۵ ๅᬑ ၙ⯂⦹݅.
ᇩ⡍⪵☁᮹⚍ᙹĥᙹ⧉ᙹෝđᱶ⦹۵ႊჶᮝಽ۵ᝅ⨹ᱢᯙႊ
ჶŝᯕುᱢᯙႊჶᮝಽǍᇥ⧁ᙹᯩ݅. ə్ӹᝅ⨹ᱢᯙႊჶᮡ
⨹ᰆ⊹aŁaᯕŁ, eŝיಆᯕฯᯕ⦥⦹໑ᱶ⪶⦽sᮥ
⊂ᱶ⦹۵äᯕๅᬑᨕಖʑভྙᨱᯕುᱢᯙႊჶᯕᵝಽᔍᬊࡹŁ
ᯩ݅.
ຝᱡ, ᝅ⨹ᱢᯙႊჶᮝಽ۵ᱶᔢඹᔢ┽ᨱᕽ⊂ᱶჶŝእᱶᔢඹ
ᔢ┽ᨱᕽ⊂ᱶჶᮝಽǍᇥ⧁ᙹᯩ݅(Masrouri et al., 2008). ᱶᔢᔢ
┽ ᝅ⨹ჶᮝಽ۵ ᯝၹᱢᯙ ᯝᱶᙹࢱჶ(conventional constant head), ᯝᱶ⮱ჶ⪚ᮡ⥭ಽᬑ⟭⥥ʑჶ(constant flow), ᬱᝍ༉⩶
⨹ჶ(centrifuge)ᮝಽǍᇥ⧁ᙹᯩᮝ໑, እᱶᔢᔢ┽ᝅ⨹ჶᮝಽ ۵ᮁ⇽ᮁ᯦(outflow-inflow), ᷪᕾ⥥ಽ❭ᯝჶ(instantaneous profile), a᪉ჶ(thermal method)ಽ Ǎᇥ⧁ ᙹ ᯩ݅.
⦽⠙, ᯕುᱢᯙႊჶᮡĥᙹ⇵ᱶႊჶŝᩎ⧕ᕾʑჶᮝಽǍᇥ⧁
ᙹᯩ݅. ĥᙹ⇵ᱶჶᮡᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹෝḢᱲ⊂ᱶ⦹۵ᨕಅ ᬡᮥɚᅖ⦹ʑ᭥⦹ᩍ⮺⧉ᙹ✚ᖒłᖁŝᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ᮹
šĥᨱɝÑ⦽ᇩ⡍⪵☁ḡ႑ႊᱶᮥ⣡ᨕᕽǍ⦽ᙹ⊹⧕ᕾđŝ
᪡ᇩ⡍⪵☁᮹༉š⯂ᙹಆᮥእƱ⦹ᩍǍ⦹۵ႊჶᯕ݅. ✚⯩ĥᙹ
⇵ᱶႊჶᮡĞ⨹ᱢᯙŖၰ☖ĥᱢᯙŖᮝಽǍᇥ⧁ᙹᯩ݅.
Ğ⨹ᱢᯙŖᮡ⮺⧉ᙹ✚ᖒłᖁ(Soil-Water Characteristics Curve, SWCC)᮹ᇩ⡍⪵šಉĥᙹෝᯕᬊ⦹ᩍᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹෝ
ᔑᱶ⦹۵ႊჶᯕ݅(Wind, 1955; Gardner, 1958; Rijtema, 1965).
əญŁ☖ĥᱢᯙŖᮡ⮺⧉ᙹ✚ᖒłᖁ(SWCC)᮹ᇩ⡍⪵šಉĥ ᙹෝᱢᬊ⦹ᩍᔢݡ⚍ᙹĥᙹ⧉ᙹෝᩩ⊂⦹۵äᯕ݅. Campbell (1974)ŝFredlund and Xing (1994)ᮡChilds and Collis-Georges (1950)᮹⚍ᙹ༉ߙᮥ᯦ࠥ⦹ᩍᔢݡ⚍ᙹĥᙹ⧉ᙹෝᱽᦩ⦹ᩡŁ, Brooks and Corey (1964)۵Burdine (1953)᮹⚍ᙹ༉ߙᮥᱢᬊ
⦹ᩍᔢݡ⚍ᙹĥᙹ⧉ᙹෝᱽᦩ⦹ᩡᮝ໑, van Genuchten (1980)
ᮡBurndine (1953) ၰMualem (1976)᮹⚍ᙹ༉ߙᮥᱢᬊ⦹ᩍ
bb᮹ ᔢݡ ⚍ᙹĥᙹ⧉ᙹෝ ᱽᦩ⦹ᩡ݅.
ǎԕᨱᕽ۵ ʑ᳕ᨱ }ၽࡽ ⨹ᰆ⊹ෝ ᯕᬊ⦹ᩍ ᇩ⡍⪵☁᮹
⚍ᙹĥᙹෝ⊂ᱶ⦽ᝅ⨹ᱢᯙᩑǍ(Jeong and Song, 1993; Lim and Lyu, 2008)᪡ᇩ⡍⪵☁᮹⮺⧉ᙹ✚ᖒłᖁ(SWCC)ᮥᔑᱶ⦹
ᩍᯕෝ☁ݡಽᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹෝ ᔑᱶ⦹۵ĥᙹ⇵ᱶႊჶ (Hwang and Kim, 2004; Kim et al., 2005)ᮥ ᱢᬊ⦽ ᩑǍa
ᙹ⧪ࡹᨕ᪵݅. ə్ӹᯕ్⦽ᩑǍᨱᕽ۵ᵝಽᇩ⡍⪵☁᮹⚍ᙹĥ ᙹ⧉ᙹ(HCF)ෝᔑᱶ⦹۵ႊჶᨱݡ⦹ᩍᗭ}⦹Łᯩᮝ໑, ⮺᮹
ᔢݡၡࠥᨱෙᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ(HCF)᮹ᄡ⪵ᨱݡ⦽ԕᬊ
ᮥ ᨙɪ⦹ḡ ᦫŁ ᯩ݅.
ᕽᅙᩑǍᨱᕽ۵ǎԕݡ⢽ᱢᯙ༉௹ᯙᵝྙḥ⢽ᵡᔍෝ
ݡᔢᮝಽⅩʑᔢݡၡࠥᨱෙ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥᝅ⨹
ᱢᮝಽ ᔑᱶ⦹Ł ᯕෝ ☁ݡಽ, ᇩ⡍⪵ ⚍ᙹĥᙹ⧉ᙹ(Hydraulic Conductivity Function, HCF)᮹ᄡ⪵ෝŁₑ⦹Łᯱ⦽݅. ᯕෝ
Fig. 1. Grain Size Distribution Curves of Jumoonjin Sand
Table 1. Physical Soil Properties of Jumoonjin Sand
Description Symbol Property
Specific gravity Ƒ 2.621
Max. void ratio ƃ 0.919 Min. void ratio ƃ 0.625 Max. dry density ĹƂ 15.824kN/m3 Min. dry density ĹƂ 13.387kN/m3 Effective particle size Î× 0.42mm
Ð× particle size Ð× 0.51mm
Ó× particle size Ó× 0.63mm Uniformity coefficient Ɠ 1.5 Coefficient of curvature Ɓ 1.0
(a) Forming Soil Sample
(b) Saturation of Soil Sample
Fig. 2. Forming Method and Saturation of the Soil Sample
᭥⦹ᩍຝᱡᯱ࠺⮺-⧉ᙹ✚ᖒłᖁ⊂ᱶᰆ⊹ෝᯕᬊ⦹ᩍᔢݡၡࠥ
40%, 60% ၰ75%᮹ᵝྙḥ⢽ᵡᔍᨱݡ⦽Õ᳑ၰᮅŝᱶ᮹
⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥ ᔑᱶ⦽݅. əญŁ van Geunchten (1980)᮹ᱽᦩᮥᱢᬊ⦹ᩍᵝྙḥ⢽ᵡᔍ᮹ᔢݡၡࠥᨱෙ
ᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹෝᔑᱶ⦽݅. ᯕෝ☁ݡಽᔢݡၡࠥ᪡Õ᳑
ၰᮅŝᱶᨱෙᵝྙḥ⢽ᵡᔍ᮹ᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ᮹✚ᖒ
ᮥ Łₑ⦹Łᯱ ⦽݅.
2. ᰍഭၰ⨹ᰆ⊹
2.1 ਏ୍߹
ᅙᩑǍᨱᕽ۵ᵝྙḥ⢽ᵡᔍෝᯕᬊ⦹ᩍ⨹ᮥᙹ⧪⦹ᩡ݅.
ASTM D 4253-83 ၰASTM D 4254-83 ⨹ჶᨱ᮹Ñ⦹ᩍᵝྙḥ
⢽ᵡᔍ᮹↽ݡၰ↽ᗭÕ᳑݉᭥ᵲపᮥ⊂ᱶ⦹Łᔢݡၡࠥ40%, 60% ၰ75%᮹᳑Õᮝಽഭෝᖒ⩶⦹ᩡ݅. ᯕ᪡zᯕᖒ⩶ࡽ
ഭ۵⡍⪵ෝ┉⬥ᯱ࠺⮺-⧉ᙹ✚ᖒłᖁ⨹ᰆ⊹ෝᯕᬊ⦹ᩍ
༉š⯂ᙹಆŝℕᱢ⧉ᙹእෝ⊂ᱶ⦹ᩡ݅. Fig. 1ᮡᵝྙḥ⢽ᵡᔍ᮹
᯦ࠥᇥ⡍łᖁᮥӹ┡ԙäᯕ໑, Table 1ᮡᵝྙḥ⢽ᵡᔍ᮹ʑᅙᱢ ᯙ ྜྷญᱢ ✚ᖒᮥ ӹ┡ԙ äᯕ݅.
ᅙ⨹ᨱᕽ۵ຝᱡഭෝ⡍⪵┉⬥Ŗʑᦶᮥa⦹ᩍeɚᙹ
ෝ ႑⇽⦹۵ Õ᳑ŝᱶᮥ ᝅ⦹í ࡽ݅. ⥭ᜅ❒ ༑ऽ(ḢĞ
5.05cm, ׳ᯕ 3.89cm)᪡ ⥭ᜅ❒ ᅪᮥ ᯕᬊ⦹ᩍ 3⊖ ݅ḱᮥ
ᝅ⦹ᩡ݅. Fig. 2(a)۵⥭ᜅ❒༑ऽᨱഭෝᖒ⩶⦹۵༉ᮥ
ӹ┡ԙäᯕ݅. əฝᨱᕽᅕ۵ၵ᪡zᯕ⥭ᜅ❒ᅪᮝಽഭෝ
݅Კᔢݡၡࠥ40%, 60% ၰ75%᮹ഭෝᖒ⩶⦹ᩡ݅. əญŁ
ഭᔢ⦹ᇡᨱ݅Ŗᕾᮥࢱᨕ⡍⪵ഭԕᇡᨱྜྷᯕᬱ⪽⦹í
⮱ෝᙹᯩࠥಾ⦹ᩡ݅. ഭෝ⡍⪵┅ʑ᭥⦹ᩍߑ⍡ᯕ░᪡
ḥŖ⟭⥥ෝ⪽ᬊ⦹ᩡ݅. ᷪߑ⍡ᯕ░ԕᨱᱶᱽࡽ᷾ඹᙹෝ₥ᬑ Ł, ᖒ⩶ࡽഭෝ᧞2/3ᱶࠥྜྷᨱᰁʑࠥಾ⦽݅ᮭḥŖ⟭⥥ෝ
ᯕᬊ⦹ᩍߑ⍡ᯕ░ԕᇡෝḥŖᔢ┽ಽอु݅. ᯕভഭ۵׳ᮡ
႑ᦶᮥ ၼí ࡹ໑, ྜྷᯕ ഭ᮹ ⦹ᇡಽᇡ░ ⡍⪵ࡹ໕ᕽ ᔢᇡಽ
Fig. 3. Automated SWCC Apparatus (Song et al., 2012)
⮹్aʑ ভྙᨱ eɚԕ ԉᦥ ᯩ۵ Ŗʑෝ ᱽÑ⦹໕ᕽ ⡍⪵a
ḥ⧪ࡽ݅. ༉௹᮹Ğᬑ᧞1eᯕᔢᮥࢱ໕ഭa⡍⪵ࡽ݅.
Fig. 2(b)۵ߑ⍡ᯕ░ԕᇡᨱᖒ⩶ࡽഭෝ᭥⊹⦽༉ᯕ݅.
2.2 ਏୋ౿
2.2.1 แ-নմট౸୨
ᅙ ᩑǍᨱᕽ۵ ᵝྙḥ ⢽ᵡᔍ᮹ ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥ
ᔑᱶ⦹ʑ ᭥⦹ᩍ ᯱ࠺ ⮺-⧉ᙹ✚ᖒłᖁ ⨹ᰆ⊹ෝ ⪽ᬊ⦹ᩡ݅
(Song et al., 2012). ᅙ⨹ᰆ⊹۵⊂ᱶᬱญae݉⦹Łᩑᗮᱢᯙ
⊂ᱶᯕa܆⦹໑, ⨹ᯱᨱ᮹⧕ၽᔾࢁᙹᯩ۵᪅₉ෝ↽ᗭ⪵⦹ᩍ
ᱶ⪶⦽ᇩ⡍⪵☁᮹⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥᔑᱶ⧁ᙹᯩ݅.
əญŁ⇶ᄡ⪹ʑჶ(Hilf, 1956)ᮥ᯦ࠥ⦹ᩍᦶಆᮥ0-300kPaჵ᭥
ʭḡ ᱢᬊ⧁ ᙹ ᯩ݅.
ᅙ⨹ᰆ⊹۵ᦶಆ᳑ᱩᰆ⊹(pressure panel), ⥭ಽᬑᖡ(flow cell), ྜྷᱡᰆᗭၰŖʑႊᬙ✙ఊ(water reservoir and air bubble trap), ᱡᬙ(balance), ᖁၹၰᱡᰆᔢᯱ(shelf and storage box),
ഭᵡእᰆ⊹(sample preparation accessories), ⊂ᱶᜅ▽॒ᮝ ಽǍᖒࡹᨕᯩ݅. Figure 3ᮡbbᨱݡ⦽Ǎᖒᗭॅᮥᩑđ⦹ᩍ
ᖅ⊹ࡽᯱ࠺⮺-⧉ᙹ✚ᖒłᖁ⨹ᰆ⊹᮹ᱥℕᱢᯙ༉ᮥӹ┡ԙ
äᯕ݅.
ᅙ⨹ᰆ⊹ᨱᕽ۵ഭᨱŖʑᦶᮥa⦹ᩍ⡍⪵ࡽഭෝᇩ⡍
⪵ᔢ┽ಽอऽ۵Õ᳑ŝᱶ(drying process)ŝᇩ⡍⪵ഭᨱྜྷᮥ
ᵝ᯦⦹ᩍ⡍⪵ᔢ┽ಽอऽ۵ᮅŝᱶ(wetting process)ᮥᰍ⩥⧁
ᙹᯩᮝ໑, Õ᳑ၰᮅŝᱶᨱෙഭԕ⧉ᙹᄡ⪵✚ᖒᮥ❭ᦦ⧁
ᙹ ᯩ݅.
ຝᱡᦶಆ᳑ᱩᰆ⊹ᨱ᮹⧕᳑ᱩၰĥ⫮ࡽŖʑᦶᮥ⮺ഭᨱ
a⧕ḡíࡽ݅. Ŗʑᦶᨱ᮹⧕⡍⪵ࡽഭԕeɚᙹaᲙӹaí
ࡹ໑, ᯕ్⦽eɚᙹ۵HAE (High Air Entry) ॵᜅⓍ᪡Ŗʑႊᬙ
✙ఊᮥÑℱᱡᬙᮥ☖⦹ᩍ⊂ᱶࡽ݅. HAE ॵᜅⓍ۵Ŗʑ᪡⮺᯦
ᯱॅᯕᯕ࠺⦹۵äᮡᱽ⦽⦹ḡอྜྷ᮹⮱ᮥᱽ⦽⦹ḡᦫ۵݅.
ᯕভŖʑᦶᮡ⮺ഭ᮹༉š⯂ᙹಆᮝಽ᯲ᬊ⦹íࡹ໑, ⮺ഭa
aḡ۵ᯝᱶ⦽Ŗʑ⧉᯦⊹ෝչᨕᕽíࡹ໕⮺ഭԕᇡᨱᯩ۵
eɚᙹaᲙӹ᪅ʑ᯲⦽݅. ᅙᝅ⨹ᨱᕽ۵ᵝྙḥ⢽ᵡᔍෝ
ᔍᬊ⦹အಽ 1 bar᮹ HAE ॵᜅⓍෝ ᯕᬊ⦹ᩡ݅.
ᯕভŖʑᦶᮡ⮺ഭ᮹༉š⯂ᙹಆᮝಽ᯲ᬊ⦹íࡹ໑, ⮺ഭ a aḡ۵ ᯝᱶ⦽ Ŗʑ⧉᯦⊹ෝ չᨕᕽí ࡹ໕ ⮺ഭ ԕᇡᨱ
ᯩ۵eɚᙹaᲙӹ᪅ʑ᯲⦽݅. ᱡᬙᮡ⍕⥉░᪡ᩑđࡹᨕᯩ
ᮝ໑a⧕ḥŖʑᦶŝ⊂ᱶࡽeɚᙹ᮹ྕí۵ᯱ࠺⊂ᱶ⥥ಽəఉ
ᮥ☖⧕ᝅeᮝಽ⪶ᯙၰᱡᰆᯕa܆⦹݅. ᅙ⥥ಽəఉᨱᕽ۵
ᝅeᮝಽeɚᙹ᮹ᮁ⇽᯦ᔢ┽ෝəฝᮝಽᅕᩍᵭᮝಽ៉݅ᮭ
݉ĥ᮹Ŗʑᦶᮥa⦹۵ᱱᮥᱶ⪶⦹íᙹᯩ݅. ᕽŖʑᦶ
ᮥ݉ĥᄥಽ᷾a⍽⮺ഭԕeɚᙹෝ႑⇽┕ᮝಽᕽÕ᳑ŝ ᱶᨱݡ⦽⧉ᙹ✚ᖒᮥӹ┡ԝᙹᯩᮝ໑, ၹݡಽŖʑᦶᮥ݉ĥᄥಽ
qᗭ⍽⮺ഭԕeɚᙹෝᮁ᯦┕ᮝಽᕽᮅŝᱶ᮹ݡ⦽⧉
ᙹ✚ᖒᮥӹ┡ԝᙹᯩ݅. ᯕ్⦽đŝෝᯕᬊ⦹ᩍÕ᳑ၰᮅŝᱶ ᨱᕽ᮹⮺-⧉ᙹ✚ᖒłᖁᮥᩩ⊂⧁ᙹᯩᮝ໑, ᇩ⡍⪵☁᮹✚ᖒ⊹ෝ
ᔑᱶ⧁ ᙹ ᯩ݅.
2.2.2 එฃറծ౸୨
ᅙᩑǍᨱᕽ۵ᔢݡၡࠥᨱෙᵝྙḥ⢽ᵡᔍ᮹⡍⪵⚍ᙹĥᙹ
ෝᔑᱶ⦹ʑ᭥⦹ᩍᔝ⇶⚍ᙹ⨹ᮥᙹ⧪⦹ᩡ݅. ݡᔢഭᨱݡ⦹
ᩍᄡᙹ᭥⨹ᮥᙹ⧪⦹ᩍ⚍ᙹĥᙹෝ⊂ᱶ⧁ Ğᬑᔢݡᱢᮝಽ
ฯᮡeᯕᗭࡽ݅. ᕽᅙᩑǍᨱᕽ۵ASTM-D5084 ⨹
ჶᨱෙᔝ⇶ᦶ⇶⨹ᰆ⊹ෝᯕᬊ⦽vᱽ⚍ᙹႊᮥᱢᬊ⦹ᩡ
݅. ⨹ႊჶᮡഭෝᖒ⩶⦹ᩍ⡍⪵┉⬥ഭ᮹ԕᇡᨱᯝᱶ⦽
ᙹᦶᮥ a⦹ᩍ ႑⇽ࡹ۵ ᮁపŝ eᮥ ⊂ᱶ⦹۵ äᯕ݅.
Fig. 4. Mass of Water Outflow for Various Matric Suctions (Ɛ
=60%)
Table 2. Fitting Parameters of Jumoonjin Sand for Various Relative Densities
Delative density ſ (kPa-1) ƌ Ƌ «Ï
Ɛ=40% Drying 0.415 8.724 0.855 0.997 Wetting 0.524 5.625 0.822 0.993
Ɛ=60% Drying 0.399 8.586 0.884 0.995 Wetting 0.548 5.625 0.822 0.991
Ɛ=75% Drying 0.393 8.553 0.883 0.995 Wetting 0.593 5.561 0.820 0.984
3. ⨹đŝၰᇥᕾ
3.1 ࡦւใߚրԩּ߆౸୨էր
Figure 4۵ᯱ࠺⮺-⧉ᙹ✚ᖒłᖁ⨹ᰆ⊹ෝᯕᬊ⦹ᩍᔢݡၡ
ࠥ60%ᯙᵝྙḥ⢽ᵡᔍ᮹༉š⯂ᙹಆᰍ⦹ၰᱽ⦹eᨱ
ෙeɚᙹ᮹⊂ᱶపᮥӹ┡ԙäᯕ݅. ᷪ, ഭᨱ༉š⯂ᙹಆᮥ
ᰍ⦹⍽eɚᙹෝ႑⇽┅۵Õ᳑ŝᱶŝ, ၹݡಽ༉š⯂ᙹಆᮥ
ᱽ⦹⍽eɚᙹෝᮁ᯦┅۵ᮅŝᱶᮥᰍ⩥⦹ᩡ݅. əฝᨱᕽ
ᅕ۵ၵ᪡zᯕÕ᳑ŝᱶᨱᕽ۵༉š⯂ᙹಆᯕ᷾a⧉ᨱeɚ ᙹ᮹⊂ᱶపᮡ᷾a⦹Ł, ᮅŝᱶᨱᕽ۵༉š⯂ᙹಆᯕqᗭ⧉ᨱ
eɚᙹ᮹⊂ᱶపᯕqᗭ⦹۵äᮝಽӹ┡ԍ݅. ݉ĥᄥ༉š⯂
ᙹಆ᮹᳑ᱩಽᯙ⦹ᩍeɚᙹ᮹ᄡ⪵۵ⅩʑᨱɪĊ⦹íᄡ⪵⦹݅
aeᯕḡԉᨱᙹಕ⦹íࡽ݅. əญŁᯝᱶ݉ĥ᮹༉š⯂ᙹ ಆ ᙹᵡᨱᕽ eɚᙹ ႑⇽ ၰ ᮁ᯦ᯕ ᙹಕࡽ ᯕ⬥ ݅ᮭ ݉ĥ᮹
༉š⯂ᙹಆᮥᰍ⦹⪚ᮡᱽ⦹⦹ᩡ݅. ᕽᔢݡၡࠥᨱෙᵝྙ
ḥ⢽ᵡᔍ᮹ᇩ⡍⪵ᔢ┽ᨱݡ⦽Õ᳑ၰᮅŝᱶᮥᰍ⩥⦹ᩡ݅.
⦽⠙, əฝᨱᕽᅕ۵ၵ᪡zᯕᮅŝᱶ᮹⨹eᯕÕ᳑ŝᱶ ᮹⨹eᅕ݅ᔢݡᱢᮝಽʕäᮝಽӹ┡ԍ݅. ᯕ్⦽ᬱᯙᮡ
Õ᳑ၰᮅŝᱶᨱᕽeɚᨱh⯭ࠦพࡽŖʑᨱ᮹⦽⮱ᱡ⧎ᨱ
᮹⦽äᮝಽ❱݉ࡽ݅. ੱ⦽࠺ᯝ⦽Ŗʑᦶ᳑Õᨱᕽഭԕℕᱢ⧉
ᙹእ۵ Õ᳑ŝᱶᨱᕽ ⓑ äᮝಽ ӹ┡ԍ݅.
3.2 แ-নմট(SWCC) ુ౸
⊂ᱶࡽ༉š⯂ᙹಆŝeɚᙹపᮥ☁ݡಽvan Genuchten (1980) ᮹ ᱽᦩᮥ ᯕᬊ⦹ᩍ ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥ ᩩ⊂⦹ᩡ݅.
van Genuchten (1980)ᮡMualem (1976)᮹༉ߙᮥ☁ݡಽᮁ⬉⡍
⪵ࠥ(¬ƃ)᪡ᦶಆᙹࢱ(Ɔ)᮹ᔢššĥෝᯕᬊ⦹ᩍ⮺-⧉ᙹ✚ᖒłᖁ (SWCC)ᮥᩩ⊂⦹ᩡ݅. Eq. (1)ᮡvan Genuchten (1980)ᨱ᮹⧕
ᱽᦩࡽ ⮺-⧉ᙹ✚ᖒłᖁ(SWCC) ᔑᱶᮥ ӹ┡ԙ äᯕ݅.
¬ƃá ćÎ à ¬Ɛ
¬ à ¬Ɛ
á ćľƑà ľƐ ľ à ľƐ
á ƙƜƚćÎ âãķÞƓſà Ɠƕßƌä
Î ƛ
ƝƞƋ (1)
ᩍʑᕽ, ¬ƃ۵ᮁ⬉⡍⪵ࠥ, ¬Ɛᮡඹ⡍⪵ࠥ, ľƑ۵⡍⪵ℕᱢ⧉ᙹ እ,ľƐᮡඹℕᱢ⧉ᙹእ, Ɠſ۵eɚŖʑᦶ, Ɠƕ۵eɚᙹᦶ,ķ۵
Ŗʑᮁ᯦sŝ šĥࡽ ĥᙹ, ƌᮡ ᄡłᱱ᮹ Ğᔍᨱ šĥࡽ ĥᙹ, əญŁƋᮡ ඹ⧉ᙹእᨱ šĥࡽ ĥᙹᯕ݅.
⊂ᱶࡽ༉š⯂ᙹಆŝℕᱢ⧉ᙹእෝ☁ݡಽእᖁ⩶↽ᗭᱽŒჶ
(nonlinear least squares analysis)ᮥᱢᬊ⦹ᩍvan Genuchten (1980) ᱽᦩ᮹ᇩ⡍⪵ĥᙹᯙķ,ƌ ၰƋᮥᔑᱶ⦹ᩡ݅. ↽ᗭᱽ Œჶ᮹ᝁࠥෝӹ┡ԕ۵đᱶĥᙹ(coefficient of determination,
«Ï)۵Õ᳑ŝᱶ᮹Ğᬑ0.995-0.997, ᮅŝᱶ᮹Ğᬑ0.984-0.993 ᮝಽ ๅᬑ ׳í ӹ┡ԍ݅.
Table 2۵Õ᳑ၰᮅŝᱶᨱݡ⦽ᵝྙḥ⢽ᵡᔍ᮹ᔢݡၡࠥᨱ
ෙᇩ⡍⪵ĥᙹෝӹ┡ԙäᯕ݅. ⢽ᨱᕽᅕ۵ၵ᪡zᯕŖʑᮁ᯦
sŝšĥࡽĥᙹķ۵ᮅŝᱶᨱᕽⓑsᮥaḡ໑, ᄡłᱱ᮹
Ğᔍᨱšĥࡽĥᙹƌŝඹ⧉ᙹእᨱšĥࡽĥᙹƋᮡÕ᳑ŝᱶ ᨱᕽⓑsᮥw۵݅. ⦽⠙, Õ᳑ŝᱶ᮹Ğᬑᔢݡၡࠥa᷾a⧉
ᨱŖʑᮁ᯦sŝšĥࡽĥᙹķ᪡ᄡłᱱ᮹Ğᔍᨱšĥࡽ
ĥᙹƌᮡ qᗭ⦹໑, ඹ⧉ᙹእᨱ šĥࡽ ĥᙹƋᮡ ᷾a⦹۵
Ğ⨆ᮥᅕᯙ݅. ə్ӹᮅŝᱶ᮹Ğᬑᔢݡၡࠥa᷾a⧉ᨱ
Ŗʑᮁ᯦sŝšĥࡽĥᙹķ۵᷾a⦹ӹ, ᄡłᱱ᮹Ğᔍᨱšĥࡽ
ĥᙹƌŝඹ⧉ᙹእᨱšĥࡽĥᙹƋᮡᄡ⪵aๅᬑᱢᮡäᮝಽ
ӹ┡ԍ݅.
Table 2ᨱ ᱽࡽᇩ⡍⪵ ĥᙹෝ ᯕᬊ⦹ᩍᵝྙḥ ⢽ᵡᔍ᮹
ᔢݡၡࠥᨱෙÕ᳑ၰᮅŝᱶᨱᕽ᮹⮺-⧉ᙹ✚ᖒłᖁ(SWCC)
ᮥ ӹ┡ԝᙹᯩ݅. Fig. 7ᨱᕽFig. 9۵ᔢݡၡࠥᨱෙᵝྙḥ
⢽ᵡᔍ᮹⮺-⧉ᙹ✚ᖒłᖁᮥӹ┡ԙäᯕ݅. əฝᨱᕽᅕ۵ၵ᪡
zᯕ⮺-⧉ᙹ✚ᖒłᖁᮡᯝၹᱢᯙᔍḩ☁ᨱᕽӹ┡ӹ۵Sᯱ༉᧲
᮹እᖁ⩶ᱢᯙšĥෝᅕᯕ۵äᮝಽӹ┡ԍ݅. əญŁÕ᳑ŝᱶ᮹
༉š⯂ᙹಆᯕᮅŝᱶ᮹༉š⯂ᙹಆᅕ݅ᔢݡᱢᮝಽⓑsᮥӹ
(a) Drying Path (b) Wetting Path Fig. 5. Estimation of Volumetric Water Contents and AEV or WEV (Ɛ=40%)
(a) Drying Path (b) Wetting Path
Fig. 6. Estimation of Volumetric Water Contents and AEV or WEV (Ɛ=60%)
(a) Drying Path (b) Wetting Path
Fig. 7. Estimation of Volumetric Water Contents and AEV or WEV (Ɛ=75%)
Table 3. Saturated and Residual Volumetric Water Contents, and AEV or WEV of Jumoonjin Sand for Various Relative Densities
Relative densities ľƑ ľƐ AEV/WEV (kPa)
Ɛ=40% Drying 0.44 0.03 1.94
Wetting 0.42 0.03 1.24
Ɛ=60% Drying 0.43 0.03 2.01
Wetting 0.40 0.03 1.19
Ɛ=75% Drying 0.41 0.03 2.10
Wetting 0.39 0.03 1.10
(a)Ɛ=40% (b) Ɛ=60% (c) Ɛ=75%
Fig. 8. SWCCs Estimated by the Van Genuchten Model
┡ԕ໑, łᖁ᮹ ʑᬙʑࠥ ₉ᯕa ᯩ۵ äᮝಽ ӹ┡ԍ݅.
Fig. 5ᇡ░ Fig. 7ᨱᕽ ᅕ۵ ၵ᪡ zᯕ Õ᳑ ၰ ᮅŝᱶ᮹
⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥ☁ݡಽ Õ᳑ŝᱶᨱᕽ᮹Ŗʑ⧉᯦⊹
(AEV)᪡⡍⪵(ľƑƂ)ၰඹℕᱢ⧉ᙹእ(ľƐƂ)᪡ᮅŝᱶᨱᕽ᮹ᙹᇥ
⧉᯦⊹(Water Entry Value, WEV)᪡⡍⪵(ľƑƕ)ၰඹℕᱢ⧉ᙹ እ(ľƐƕ)ෝᔑᱶ⦹ᩡ݅. əญŁᯕෝᱶญ⦹໕Table 3ŝzᯕӹ┡ԝ
ᙹ ᯩ݅. ⢽ᨱᕽ ᅕ۵ ၵ᪡ zᯕ ⡍⪵ℕᱢ⧉ᙹእ۵ Õ᳑ŝᱶᯕ
ᮅŝᱶᨱᕽᅕ݅Ⓧíӹ┡ӹ໑, ඹℕᱢ⧉ᙹእ۵Õ᳑ၰᮅ ŝᱶᨱᕽ࠺ᯝ⦽äᮝಽӹ┡ԍ݅. ੱ⦽ᔢݡၡࠥa᷾a⧉ᨱ
Õ᳑ၰ⡍⪵ℕᱢ⧉ᙹእ۵qᗭ⦹۵Ğ⨆ᮥᅕᯕ۵äᮝಽӹ┡ԍ
݅. ⦽⠙࠺ᯝ⦽ᔢݡၡࠥᨱᕽŖʑ⧉᯦⊹۵ᙹᇥ⧉᯦⊹ᅕ݅Ⓧí
ӹ┡ӹ໑, ᔢݡၡࠥa᷾a⧁ᙹಾŖʑ⧉᯦⊹۵᷾a⦹ḡอᙹᇥ
⧉᯦⊹۵ qᗭ⦹۵ äᮝಽ ӹ┡ԍ݅.
Fig. 8ᮡᔢݡၡࠥᨱෙᵝྙḥ⢽ᵡᔍ᮹Õ᳑ၰᮅŝᱶᨱ
ෙ⊂ᱶđŝ᪡van Genuchten (1980) ႊჶᮝಽᩩ⊂⦽⮺-⧉ᙹ
✚ᖒłᖁ(SWCC)ᮥ⧉̹ࠥ⦽äᯕ݅. əฝᨱᕽᅕ۵ၵ᪡zᯕ
࠺ᯝ⦽༉š⯂ᙹಆᨱᕽÕ᳑ŝᱶ᮹ℕᱢ⧉ᙹእaᮅŝᱶ᮹ℕᱢ
⧉ᙹእ⪚ᮡᮁ⬉⡍⪵ࠥᅕ݅Ⓧíӹ┡ԍ݅. ✚⯩, Õ᳑ၰ
ᮅŝᱶᮥ Ñ⊹۵ ࠺ᦩ ⮺᯦ᯱ ᔍᯕ᮹ eɚᯕ ၡ⠱ࡹᨕ eɚ
ԕŖʑah⯩íࡹ໑, h⯭Ŗʑ᮹ᩢ⨆ᮝಽᯙ⦹ᩍÕ᳑ŝᱶ᮹
⡍⪵ℕᱢ⧉ᙹእ(ľƑƂ)᪡ᮅŝᱶ᮹⡍⪵ℕᱢ⧉ᙹእ(ľƑƕ)a݅í
ӹ┡ӽ݅. ᷪ Õ᳑ ၰ ᮅŝᱶ᮹ ⮺-⧉ᙹ✚ᖒłᖁᯕ ᯝ⊹⦹ḡ
ᦫ۵ ᯕಆ⩥ᔢᯕ ၽᔾࢉᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.
Õ᳑ၰᮅŝᱶᨱᕽၽᔾࡹ۵⮺-⧉ᙹ✚ᖒłᖁ᮹ᯕಆ⩥ᔢᨱ
ݡ⦽ᵝᬱᯙᮝಽ۵ᯪⓍᄲ⬉ŝ, ᱲⅪbᩢ⨆॒ᮥॅᙹᯩ݅.
ᯪⓍᄲ⬉ŝ۵⮺᮹Ǎ᳑ᱢ✚Ḷ(eɚ᮹Ⓧʑ, ⩶ᔢၰᇥ⡍)ᯕ
እɁḩ⦹ʑভྙᨱၽᔾ⦹໑, እɁḩ⦽eɚᨱᕽ᮹༉ᖙšᮥŁಅ
⧉ᮝಽ៉ᙹᯩ݅. ᷪྜྷᮥ⯂ᙹ⦹۵ᮅŝᱶᨱᕽ۵ⓑeɚ᮹
ᩢ⨆ᯕᱩݡᱢᯕŁ, ྜྷᮥ႑ᙹ⦹۵Õ᳑ŝᱶᨱᕽ۵᯲ᮡeɚ᮹
ᩢ⨆ᯕᵝ⦹ʑভྙᯕ݅(Lu and Likos, 2004; Park et al., 2006;
Shin and Park, 2006; Lee et al., 2008; Song and Choi, 2012;
Oh et al., 2012).
3.3 ऄඑฃറծ(HCF) ુ౸ࢺ࣑ࢫէր ᇩ⡍⪵☁᮹⚍ᙹĥᙹ⧉ᙹෝđᱶ⦹۵ႊჶᮝಽ۵ᝅ⨹ᱢᯙႊ
ჶŝᯕುᱢᯙႊჶᮝಽӹ٭ᙹᯩ݅. ᬑᖁᝅ⨹ᱢᮝಽᇩ⡍⪵☁᮹
⚍ᙹĥᙹෝ⊂ᱶ⦹۵ႊჶᮝಽ۵ᙹḢʑࣆᮥᯕᬊ⦽ᱶᔢᔢ┽⧕
ᕾ(Richards, 1931), ၹᩢǍᱢᯙቭ౩ᯙᮥᯕᬊ⦽ᱶᔢᔢ┽⧕ᕾ
(Hassler and Brunner, 1945), əญŁእᱶᔢᔢ┽⧕ᕾ(Welge, 1952)ᯕaᰆฯᯕᔍᬊࡹŁᯩ݅. ၹ໕, ᯕುᱢᮝಽᇩ⡍⪵☁᮹
⚍ᙹĥᙹෝđᱶ⦹۵ႊჶᮝಽ۵ĥᙹ⇵ᱶႊჶŝᩎ⧕ᕾʑჶᯕ
aᰆฯᯕᔍᬊࡹŁᯩᮝ໑ฯᮡᩑǍᯱॅᨱ᮹⧕ᱽᦩࡹᨕ᪵݅
(Zachman et al., 1981; Dane and Hruska, 1983; Abu-Hejleh et al., 1993; Wildenschild et al., 1997).
ᅕ☖ᝅ⨹ᱢᯙႊჶᮝಽᇩ⡍⪵☁᮹⚍ᙹĥᙹ⧉ᙹෝđᱶ⦹ʑ
ᨕಖʑভྙᨱᯕುᱢᯙႊჶᮥᖁ⪙⦹Łᯩ݅. əaᬕߑ⮺-⧉ᙹ
✚ᖒłᖁ᮹ᇩ⡍⪵ĥᙹෝᯕᬊ⦹ᩍ⚍ᙹĥᙹ⧉ᙹෝ⇵ᱶ⦹۵ĥ
(a)Ɛ=40% (b) Ɛ=60% (c) Ɛ=75%
Fig. 9. Unsaturated Hydraulic Conductivity Function of Jumoonjin Sand for Various Relative Densities Table 4. Saturated Hydraulic Conductivity of Jumoonjin Sand for
Various Relative Densities
Relative density Saturated hydraulic conductivity, ƉƑ (cm/sec)
Drying Wetting
Ɛ = 40% 2.080 Z 10-3 1.583 Z 10-3
Ɛ = 60% 1.998 Z 10-3 1.539 Z 10-3
Ɛ = 75% 1.887 Z 10-3 1.482 Z 10-3 ᙹ⇵ᱶႊჶᯕᵝಽᔍᬊࡹŁᯩ݅. ✚⯩Mualem (1976)᮹༉ߙᮥ
ʑⅩಽ⦽van Genuchten (1980)᮹⚍ᙹĥᙹ⧉ᙹ༉ߙᯕĥᙹ⇵
ᱶႊჶᮝಽaᰆฯᯕᯕᬊࡹŁᯩ݅. Eq. (2)۵van Genuchten (1980)ᯕ ᱽᦩ⦽ ᇩ⡍⪵☁᮹ ⚍ᙹĥᙹ⧉ᙹෝ ӹ┡ԙ äᯕ݅.
Ɖ á ƉƑZ ¬ƃÎîÏãÎ à ÞÎ à ¬ƃÎîƋßƋäÏ (2)
ᩍʑᕽ, Ɖ=ᇩ⡍⪵⚍ᙹĥᙹ, ƉƑ=⡍⪵⚍ᙹĥᙹ,¬ƃ=ᮁ⬉⡍⪵ࠥ
Ƌ=Î à Îîƌ Þ× ï Ƌ ï Îß
Table 4۵ ᔢݡၡࠥᨱ ෙ ᵝྙḥ ⢽ᵡᔍᨱ ݡ⦽ Õ᳑ ၰ
ᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹෝӹ┡ԙäᯕ݅. ᯕෝ᭥⦹ᩍຝᱡ
ᔢݡၡࠥᨱෙᵝྙḥ⢽ᵡᔍ᮹⡍⪵⚍ᙹĥᙹෝ⊂ᱶ⦹ᩡ݅.
ᯕsᮥ☁ݡಽvan Genuchten (1980)ᯕᱽ⦽ᇩ⡍⪵☁᮹⚍ᙹ ĥᙹ⧉ᙹᔑᱶᮥᯕᬊ⦹ᩍÕ᳑ၰᮅŝᱶᨱᕽ⡍⪵ᮁ⬉⡍
⪵ࠥෝ⚍ᙹĥᙹ⧉ᙹᔑᱶᨱ᯦ಆ⦹ᩍĥᔑ⦽äᯕ݅. ⢽ᨱᕽ
ᅕ۵ၵ᪡zᯕÕ᳑ŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ۵ᮅŝᱶᨱᕽ᮹
⡍⪵⚍ᙹĥᙹᅕ݅Ⓧíӹ┡ԉᮥᙹᯩ݅. əญŁᔢݡၡࠥa
᷾a⧉ᨱÕ᳑ၰᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ۵qᗭ⦹۵
äᮝಽ ӹ┡ԍ݅.
Fig. 9۵ᔢݡၡࠥᨱෙᵝྙḥ⢽ᵡᔍ᮹༉š⯂ᙹಆŝᇩ⡍⪵
⚍ᙹĥᙹ᮹šĥෝӹ┡ԙäᯕ݅. ੱ⦽Õ᳑ŝᱶ᮹Ŗʑ⧉᯦⊹᪡
ᮅŝᱶ᮹ᙹᇥ⧉᯦⊹ෝ⧉̹ࠥ⦹ᩡ݅. əฝᨱᕽᅕ۵ၵ᪡
༉š⯂ᙹಆᯕ᷾a⧉ᨱᇩ⡍⪵⚍ᙹĥᙹ۵ᯝᱶ⦹íᮁḡࡹ
݅aɪĊ⦹íqᗭ⦹۵äᮝಽӹ┡ԍ݅. ᷪÕ᳑ၰᮅŝᱶᨱᕽ
ᇩ⡍⪵⚍ᙹĥᙹ۵⡍⪵⚍ᙹĥᙹಽᯝᱶ⦹íᮁḡࡹ݅aŖʑ
⧉᯦⊹⪚ᮡᙹᇥ⧉᯦⊹ḢᱥᨱɪĊ⦹íqᗭ⦹۵äᮝಽӹ┡ԍ
݅. ⦽⠙, Õ᳑ၰᮅŝᱶᨱᕽ᮹ᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ۵⮺-⧉ᙹ
✚ᖒłᖁᨱᕽ᪡࠺ᯝ⦹íᯕಆ⩥ᔢᯕၽᔾ⦹۵äᮝಽӹ┡ԍ݅.
əฝᨱᕽᅕ۵ၵ᪡zᯕÕ᳑ŝᱶ᮹⚍ᙹĥᙹ⧉ᙹaᮅŝᱶ᮹
⚍ᙹĥᙹ⧉ᙹᅕ݅ⓑsᮥw۵äᮝಽӹ┡ԍ݅. ✚⯩Õ᳑ŝᱶ᮹
Ğᬑᮅŝᱶᨱእ⧕እƱᱢⓑ༉š⯂ᙹಆᨱᕽ⚍ᙹĥᙹ᮹qᗭ a ᯲ࡹ۵ äᮝಽ ӹ┡ԍ݅.
3.4 ొ׆ঃ۩ࢤܑݗࠛऄඑฃറনճఝ
༉௹᮹ Ⅹʑ ᔢݡၡࠥ ⪚ᮡ Ⅹʑ eɚእ۵ ⮺-⧉ᙹ✚ᖒłᖁ (SWCC)ᨱᩢ⨆ᮥၙ⊹۵ๅᬑᵲ⦽ᗭᯕ݅. ᷪ, ᇩ⡍⪵᳑Õᨱ ᕽ ⮺᮹ Ⅹʑ ᔢݡၡࠥ ⪚ᮡ Ⅹʑ eɚእ۵ ⮺-⧉ᙹ✚ᖒłᖁᮥ
ᄡ⪵┅íࡹ໑, ᯕಽᯙ⦹ᩍᇩ⡍⪵⚍ᙹ✚ᖒࠥᄡ⪵⦹íࡽ݅
(Zhou et al., 2012). ᯕ్⦽ ᩢ⨆ᮥ Łₑ⦹ʑ ᭥⦹ᩍ Romero et al. (1999)۵⮺ԕᇡ᮹eɚᮥࢱaḡಽⓍíᇥඹ⦹ᩡ݅. ᷪ,
༉š⩥ᔢᨱḡ႑ࡹ۵Ñᱢᯙšᱱᨱᕽ᮹eɚŝྜྷญ⪵⦺ᱢᯙ
⯹ᨱ᮹⧕ḡ႑ࡹ۵ၙᱢᯙšᱱᨱᕽ᮹eɚᮝಽᇥඹ⦹ᩡ݅.
Alonso et al. (2010)ᮡၙᱢᯙšᱱᨱᕽ⡍⪵ࠥ۵ಆ(⯂ᙹಆ
⪚ᮡ ʑĥᱢᯙ ⦹ᵲ)ᨱ ྕš⦹í ᯝᱶ⦹໑, ᯕ۵ ඹ⡍⪵ࠥ᪡
࠺ᯝ⦹݅Ł ⦹ᩡ݅. ᕽ Ⅹʑ ᔢݡၡࠥ ⪚ᮡ Ⅹʑ eɚእ᮹
ᄡ⪵۵᪅ಽḡÑᱢᯙšᱱᨱᕽ᮹⡍⪵ࠥ ⪚ᮡ༉š⯂ᙹಆᨱ
᮹⧕ᕽอᩢ⨆ᮥၙ⊹໑, ၙᱢᯙəญŁඹ⡍⪵ࠥ۵Ⅹʑᔢݡ ၡࠥ ၰ Ⅹʑ eɚእᨱ ྕš⦹݅Ł aᱶ⧁ ᙹ ᯩ݅.
༉௹᮹Ⅹʑᔢݡၡࠥᨱෙᇩ⡍⪵⚍ᙹ✚ᖒᄡ⪵ෝŁₑ⦹ʑ
Fig. 10. AEVs on SWCCs of Jumoonjin Sand for Various Initial Void Ratios
Fig. 11. Saturated Hydraulic Conductivities of Jumoonjin Sand for Various Initial Void Ratios
᭥⦹ᩍ༉௹᮹Ⅹʑeɚእ᪡Ŗʑ⧉᯦⊹᮹šĥෝӹ┡ԕᨩ݅.
Fig. 10ᮡᅙᝅ⨹ᨱᕽᔍᬊࡽᵝྙḥ⢽ᵡᔍ᮹ᔢݡၡࠥᨱෙ
Ⅹʑeɚእ᪡Õ᳑ŝᱶᨱᕽ᮹Ŗʑ⧉᯦⊹(AEV)ෝࠥ⦽äᯕ
݅. əฝᨱᕽᅕ۵ၵ᪡zᯕ࠺ᯝ⦽᯦ࠥ᳑ᖒᮥaḥ༉௹ᨱᕽ
Ⅹʑeɚእa᷾a⧉ᨱŖʑ⧉᯦⊹۵qᗭ⦹۵äᮝಽӹ┡
ԍ݅. əญŁ ༉௹᮹ Ŗʑ⧉᯦⊹(AEV)᪡ Ⅹʑeɚእ᮹ šĥෝ
ᔢšᮝಽ ӹ┡ԕ໕ Eq. (3)ŝ zᯕ ӹ┡ԝ ᙹ ᯩ݅.
¯ÞƉ©ſß áà ÎíÒÔÞƃƇß âÐíÎÖ (3)
ᩍʑᕽ, ƃƇ۵ Ⅹʑeɚእᯕ݅.
⦽⠙, ༉௹᮹Ⅹʑeɚእ᪡⡍⪵⚍ᙹĥᙹ᮹ᔢššĥෝŁₑ⦹
ʑ᭥⦹ᩍÕ᳑ၰᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ᪡༉௹᮹Ⅹʑe
ɚእෝ ⧉̹ ࠥ⦹ᩡ݅. Fig. 11ᮡ ༉௹᮹ Ⅹʑeɚእ᪡ Õ᳑
ၰᮅŝᱶ᮹⡍⪵⚍ᙹĥᙹෝӹ┡ԙäᯕ݅. əฝᨱᕽᅕ۵ၵ᪡
zᯕÕ᳑ၰᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ۵Ⅹʑeɚእa᷾a
⧉ᨱ᷾a⦹۵Ğ⨆ᮥᅕᯙ݅. əญŁ༉௹᮹Ⅹʑeɚእ᪡
Õ᳑ၰᮅŝᱶ᮹⡍⪵⚍ᙹĥᙹ᮹ᔢššĥෝᮝಽӹ┡ԕ໕
Eq. (4)ಽӹ┡ԝᙹᯩ݅. ᯕෝᔕ⠕ᅕ໕Ⅹʑeɚእᨱෙ⡍⪵⚍
ᙹĥᙹ᮹ ᷾aᮉᮡ Õ᳑ŝᱶᯕ ᮅŝᱶ᮹ ᧞ 2႑ᨱ ⧕ݚ⧉ᮥ
ᙹᯩ݅. ᯕᔢᨱᕽᅕ۵ၵ᪡zᯕ༉௹᮹Ⅹʑeɚእᨱ
⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ŝᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ(HCF)aᄡ⪵
⦹í ࢉᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.
ƉƑÞƁƋîß á ×í××ÎÖÞƃƇß â×í×××Ó (Õ᳑ŝᱶ) (4a) ƉƑÞƁƋîß á ×í××Î×ÞƃƇß â×í×××Õ (ᮅŝᱶ) (4b)
ᩍʑᕽ, ƉƑ۵ ⡍⪵⚍ᙹĥᙹᯕ݅.
4. đು
ᇩ⡍⪵᳑Õᨱᕽ⮺᮹Ⅹʑᔢݡၡࠥ⪚ᮡⅩʑeɚእ۵⮺-⧉
ᙹ✚ᖒłᖁᮥᄡ⪵┅íࡹ໑, ᯕಽᯙ⦹ᩍᇩ⡍⪵᳑Õᨱᕽ⚍ᙹ
✚ᖒࠥᄡ⪵⦹íࡽ݅. ᯕᨱݡ⦽ᩢ⨆ᮥŁₑ⦹ʑ᭥⦹ᩍᵝྙḥ
⢽ᵡᔍ᮹Ⅹʑᔢݡၡࠥᨱෙ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ŝᇩ⡍
⪵⚍ᙹĥᙹ⧉ᙹ(HCF)ෝᔑᱶ⦹ᩡ݅. ຝᱡᯱ࠺⮺-⧉ᙹ✚ᖒłᖁ
⊂ᱶᰆ⊹ෝᯕᬊ⦹ᩍᔢݡၡࠥ40%, 60% ၰ75%᮹ᵝྙḥ⢽ᵡᔍ ᨱݡ⦽Õ᳑ၰᮅŝᱶᨱᕽ᮹⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮥᔑᱶ⦹
ᩡ݅. ᔢݡၡࠥᨱෙᵝྙḥ⢽ᵡᔍ᮹⮺-⧉ᙹ✚ᖒłᖁ(SWCC) ᮝಽᇡ░ bbᇩ⡍⪵ĥᙹෝđᱶ⦹Ł, ᯕෝvan Geunchten (1980) ᮹ ᱽᦩᨱᱢᬊ⦹ᩍᵝྙḥ⢽ᵡᔍ᮹ᔢݡၡࠥᨱෙᇩ⡍⪵
⚍ᙹĥᙹ⧉ᙹෝᔑᱶ⦹ᩡ݅. ᯕॅđŝෝᱶญ⦹໕݅ᮭŝz݅.
(1) van Genuchten(1980)᮹ႊჶᮥᯕᬊ⦹ᩍᵝྙḥ⢽ᵡᔍ᮹
ᔢݡၡࠥᨱ ෙ ⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ᮝಽᇡ░ ᇩ⡍⪵
ĥᙹෝᔑᱶ⦽đŝŖʑᮁ᯦sŝšĥࡽĥᙹķ۵ᮅŝᱶ ᨱᕽⓑsᮥaḡ໑, ᄡłᱱ᮹Ğᔍᨱšĥࡽĥᙹƌŝ
ඹ⧉ᙹእᨱ šĥࡽ ĥᙹƋᮡ Õ᳑ŝᱶᨱᕽ ⓑ sᮥ
w۵݅.
(2) ᵝྙḥ⢽ᵡᔍ᮹ᔢݡၡࠥa᷾a⧉ᨱ⮺-⧉ᙹ✚ᖒłᖁ (SWCC)ᔢ᮹Õ᳑ၰ⡍⪵ℕᱢ⧉ᙹእ۵qᗭ⦹۵Ğ⨆ᮥᅕᯙ
݅. əญŁᔢݡၡࠥa᷾a⧁ᙹಾŖʑ⧉᯦⊹۵᷾a⦹ḡอ
ᙹᇥ⧉᯦⊹۵qᗭ⦹໑, ࠺ᯝ⦽ᔢݡၡࠥᨱᕽŖʑ⧉᯦⊹۵
ᙹᇥ⧉᯦⊹ᅕ݅ Ⓧí ၽᔾࡽ݅.
(3) ĥᙹ⇵ᱶႊჶaᬕߑ⦹ӹᯙvan Genuchten (1980)᮹ᇩ⡍⪵
⚍ᙹĥᙹ⧉ᙹෝ ᔑᱶ⦽ đŝ Õ᳑ŝᱶᨱᕽ᮹ ⡍⪵⚍ᙹĥᙹ۵
ᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹᅕ݅Ⓧíӹ┡ӹ໑, ᔢݡၡࠥa
᷾a⧉ᨱÕ᳑ၰᮅŝᱶᨱᕽ᮹⡍⪵⚍ᙹĥᙹ۵qᗭ⦽݅.
(4) Õ᳑ၰᮅŝᱶᨱᕽᇩ⡍⪵⚍ᙹĥᙹ۵⡍⪵⚍ᙹĥᙹಽ
ᯝᱶ⦹íᮁḡࡹ݅aŖʑ⧉᯦⊹⪚ᮡᙹᇥ⧉᯦⊹ḢᱥᨱɪĊ
⦹íqᗭ⦹໑, Õ᳑ŝᱶ᮹Ğᬑᮅŝᱶᨱእ⧕እƱᱢⓑ
༉š⯂ᙹಆᨱᕽ ⚍ᙹĥᙹ᮹ qᗭa ᯲ࡽ݅.
(5) ᵝྙḥ⢽ᵡᔍ᮹Ⅹʑᔢݡၡࠥ⪚ᮡⅩʑeɚእᨱ⮺-⧉
ᙹ✚ᖒłᖁ(SWCC)ᨱᕽ᮹Ŗʑ⧉᯦⊹(AEV)۵qᗭ⦹Ł⡍
⪵⚍ᙹĥᙹ۵᷾a⦹အಽ, ᵝྙḥ⢽ᵡᔍ᮹Ⅹʑeɚእᨱ
⮺-⧉ᙹ✚ᖒłᖁ(SWCC)ŝᇩ⡍⪵⚍ᙹĥᙹ⧉ᙹ(HCF)a
ᄡ⪵ࢉᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.
qᔍ᮹ɡ
ᅙᩑǍ۵⦽ǎḡḩᯱᬱᩑǍᬱᵝᔍᨦᯙ‘Ųᔑ}ၽᨱෙḡ ḩ⪹Ğᰍ⧕⪶ᔑᱽᨕʑᚁ}ၽ’ ŝᱽ᮹ᯝ⪹ᮝಽᙹ⧪ࡹᨩܩ݅.
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