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  1. ν•œκ΅­κ±΄μ„€κΈ°μˆ μ—°κ΅¬μ› μˆ˜μžμ›Β·ν•˜μ²œμ—°κ΅¬μ†Œ, μˆ˜μ„μ—°κ΅¬μ› (Korea Institute of Civil engineering and building Technology)
  2. ν•œκ΅­κ±΄μ„€κΈ°μˆ μ—°κ΅¬μ› μˆ˜μžμ›Β·ν•˜μ²œμ—°κ΅¬μ†Œ, μ—°κ΅¬μœ„μ› (Korea Institute of Civil Engineering and Building Technology)
  3. ν•œκ΅­κ±΄μ„€κΈ°μˆ μ—°κ΅¬μ› μˆ˜μžμ›Β·ν•˜μ²œμ—°κ΅¬μ†Œ, μ„ μž„μ—°κ΅¬μœ„μ› (Korea Institute of Civil Engineering and Building Technology)


ν•˜μ²œμˆ˜ κ°μ†Œμœ¨, μ§€ν•˜μˆ˜ μ–‘μˆ˜, λˆ„μˆ˜λŒ€μˆ˜μΈ΅, Zlotnik and Tartakovsky 해석해, Hunt 해석해
Stream depletion rate, Groundwater pumping, Leaky aquifer, Zlotnik and Tartakovsky’s analytical solution, Hunt’s analytical solution

  • 1. μ„œ λ‘ 

  • 2. 이둠적 λ°°κ²½ 및 뢄석 방법

  •   2.1 Zlotnik and Tartakovsky 해석해

  •   2.2 뢄석 방법

  • 3. κ²°κ³Ό 및 κ³ μ°°

  •   3.1 λŒ€μˆ˜μΈ΅κ³Ό ν•˜μ²œ μˆ˜λ¦¬νŠΉμ„±μ— λ”°λ₯Έ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨ μ‚°μ •

  •   3.2 Zlotnik and Tartavasky (2008) 해석해와 Hunt 해석해 (2009) 적용 결과의 비ꡐ

  • 4. κ²° λ‘ 

1. μ„œ λ‘ 

졜근 μ „ μ„Έκ³„μ μœΌλ‘œ ν•˜μ²œ μ£Όλ³€μ˜ μ§€ν•˜μˆ˜ μ΄μš©λŸ‰μ΄ λ§Žμ•„μ§μ— 따라 μ–‘μˆ˜μ— μ˜ν•΄ μ€„μ–΄λ“œλŠ” ν•˜μ²œμˆ˜ μ†μ‹€λŸ‰μ— λŒ€ν•œ μ •ν™•ν•œ 예츑이 μ€‘μš”ν•œ μ—°κ΅¬μ£Όμ œλ‘œ λŒ€λ‘λ˜κ³  μžˆλ‹€. μ§€ν•˜μˆ˜ μ–‘μˆ˜μ— μ˜ν•΄ κ°μ†Œλ˜λŠ” ν•˜μ²œμˆ˜λŸ‰μ„ μ˜ˆμΈ‘ν•˜κΈ° μœ„ν•΄μ„œλŠ” μ‹€μ œ μˆ˜λ¦¬μ§€μ§ˆν•™μ μΈ 쑰건을 λͺ¨ν˜•ν™”ν•˜μ—¬ κ°€μš©ν•œ λ§€κ°œλ³€μˆ˜μ˜ μ •ν™•ν•œ 좔정을 기반으둜 ν•œ 수치λͺ¨λΈλ§μ„ μˆ˜ν–‰ν•˜κ±°λ‚˜ κ°„λ‹¨ν•œ 해석적 λͺ¨ν˜•μ„ μ΄μš©ν•  수 μžˆλ‹€. ν•˜μ²œμˆ˜ κ°μ†Œλ₯Ό λͺ¨μ˜ν•˜λŠ”데 μžˆμ–΄μ„œ μ‹œκ°„μ , λΉ„μš©μ  μΈ‘λ©΄μ—μ„œλŠ” ν›„μžμ˜ 방법이 νš¨κ³Όμ μ΄λ‹€.

ν•˜μ²œμˆ˜ κ°μ†Œμ˜ μ‹œκ°„μ  거동을 λͺ¨μ˜ν•  수 μžˆλŠ” 고전적인 해석적 λͺ¨ν˜•μœΌλ‘œ Theis (1941), Hantush (1965), Jenkins (1968) 등을 λ“€ 수 μžˆλ‹€. 이듀 ν•΄μ„ν•΄λŠ” ν•˜μ²œκ³Ό μ–‘μˆ˜μ •μ΄ 단일 λŒ€μˆ˜μΈ΅μ„ μ™„μ „κ΄€ν†΅ν•œ κ²½μš°μ— λŒ€ν•΄ μœ λ„λ˜μ—ˆλŠ”λ°, μ΄λŸ¬ν•œ 쑰건이 μ‹€μ œ ν™˜κ²½μ—μ„œλŠ” λ“œλ¬Όκ²Œ μ‘΄μž¬ν•œλ‹€. λ”°λΌμ„œ 보닀 ν˜„μ‹€μ μΈ 해석적 λͺ¨ν˜•μ„ κ°œλ°œν•˜λŠ” 연ꡬ가 μ§„ν–‰λ˜μ–΄ ν•˜μ²œμ΄ λŒ€μˆ˜μΈ΅μ„ μ–•κ²Œ κ΄€ν†΅ν•œ 쑰건에 λŒ€ν•œ 해석해(Hunt, 1999; Zlotnik and Huang, 1999; Butler et al., 2001), λ°˜ν”Όμ•• λŒ€μˆ˜μΈ΅(Hunt, 2003) 및 μœ ν•œν­μ„ 가진 ν•˜μ²œκ³Ό λŒ€μˆ˜μΈ΅μ— κ΄€ν•œ 해석해(Hunt, 2008), μœ ν•œ λŒ€μˆ˜μΈ΅ν­μ— κ΄€ν•œ 해석해(Butler et al., 2001) 등이 κ°œλ°œλ˜μ—ˆλ‹€.

μ–‘μˆ˜λŸ‰μ˜ 일뢀뢄은 ν•˜μ²œμˆ˜μ˜ μ†μ‹€λŸ‰μΌ 수 있고 λ‚˜λ¨Έμ§€ 뢀뢄은 더 κΉŠμ€ λŒ€μˆ˜μΈ΅μœΌλ‘œλΆ€ν„° λ°˜λŒ€μˆ˜μΈ΅(aquitard)을 거쳐 곡급될 수 μžˆλ‹€. ν•˜μ²œ 인근 λˆ„μˆ˜λŒ€μˆ˜μΈ΅μœΌλ‘œλΆ€ν„° μ–‘μˆ˜κ°€ μ§„ν–‰λ˜λŠ” 경우 이와 같은 ν˜„μƒμ΄ μΌμ–΄λ‚œλ‹€λŠ” 것이 규λͺ…λœ λ°” μžˆλ‹€(Hantush, 1964; Zlotnik, 2004, Butler et al., 2007). 특히 Zlotnik and Tartakovsky (2008)λŠ” μ–‘μˆ˜μ‹œ ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ€ μˆ˜λ‘κ°•ν•˜κ°€ λ°œμƒν•˜μ§€ μ•ŠλŠ”λ‹€λŠ” κ°€μ •ν•˜μ— 2μΈ΅ λˆ„μˆ˜λŒ€μˆ˜μΈ΅(leaky two-aquifer)κ³„μ—μ„œ 이와 같은 ν˜„μƒμ„ κ΅¬ν˜„ν•˜λŠ” 해석해λ₯Ό κ°œλ°œν–ˆλ‹€. 이 ν•΄μ„ν•΄λŠ” ν•˜μ²œ-μƒλΆ€λŒ€μˆ˜μΈ΅μ˜ μ—°κ²°μ„±κ³Ό μƒλΆ€λŒ€μˆ˜μΈ΅-ν•˜λΆ€κ³΅κΈ‰μ›(source bed)의 연결성에 따라 μ–‘μˆ˜λŸ‰ μ€‘μ—μ„œ ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰μ— κΈ°μ—¬ν•˜λŠ” λΉ„μœ¨μΈ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨(stream depletion rate, SDR)을 κ²°μ •ν•  수 μžˆλ‹€. 이와 같은 ν•΄μ„ν•΄λŠ” Hunt (2003) ν•΄μ„ν•΄μ—μ„œ κ³΅κΈ‰μ›μ˜ μ €λ₯˜κ³„μˆ˜κ°€ λ¬΄ν•œνžˆ 큰 κ²½μš°μ— ν•΄λ‹Ήν•˜μ—¬ μ–‘μˆ˜μ— λ”°λ₯Έ κ³΅κΈ‰μ›λ‚΄μ˜ μˆ˜λ‘κ°•ν•˜κ°€ μΌμ–΄λ‚˜μ§€ μ•ŠλŠ” κ²½μš°μ— ν•΄λ‹Ήν•œλ‹€(Christensen et al., 2009). Hunt (2009)λŠ” 2μΈ΅ λˆ„μˆ˜λŒ€μˆ˜μΈ΅λ‚΄μ— μœ„μΉ˜ν•œ ν•˜μ²œμΈκ·Όμ˜ μƒλΆ€λŒ€μˆ˜μΈ΅ μ–‘μˆ˜μ— μ˜ν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ κ²°μ •ν•˜κΈ° μœ„ν•΄ 상뢀와 ν•˜λΆ€μ˜ μ§€ν•˜μˆ˜μœ„ λ³€ν™”λ₯Ό λ™μ‹œμ— κ³ λ €ν•œ 해석해λ₯Ό μ œμ‹œν•œ λ°” μžˆλ‹€. Ward and Lough (2011)λŠ” Hunt (2009)와 μœ μ‚¬ν•œ λ°©λ²•μœΌλ‘œ λˆ„μˆ˜λŒ€μˆ˜μΈ΅-ν•˜μ²œ-μ–‘μˆ˜μ • μ‹œμŠ€ν…œμ— κ΄€ν•œ 해석해λ₯Ό μœ λ„ν•˜μ—¬ ν•˜λΆ€λŒ€μˆ˜μΈ΅ μ–‘μˆ˜λ‘œ μΈν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ‚°μ •ν•˜λŠ” 식을 μ œμ‹œν•˜μ˜€λ‹€.

ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ˜ 좔정을 μœ„ν•΄μ„œλŠ” ν•˜μƒμ˜ μˆ˜λ¦¬μ „λ„λ„μ™€ λŒ€μˆ˜μΈ΅μ˜ 측별 νˆ¬μˆ˜κ³„μˆ˜μ™€ μ €λ₯˜κ³„μˆ˜μ˜ 정보가 ν•„μš”ν•˜λ‹€. 이 μ€‘μ—μ„œ ν•˜μƒμ˜ μˆ˜λ¦¬μ „λ„λ„λŠ” λŒ€μˆ˜μΈ΅κ³Ό ν•˜μ²œμ˜ 연결도λ₯Ό κ²°μ •ν•˜λŠ” λ³€μˆ˜λ‘œμ„œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ 산정함에 μžˆμ–΄ μ€‘μš”ν•œ 영ν–₯μΈμžμ΄λ‹€. λ˜ν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ κ²°μ •ν•˜λŠ”λ° μžˆμ–΄μ„œ ν•˜μ²œκ³Ό λŒ€μˆ˜μΈ΅μ΄ λ™μΌν•œ 좩적측에 μ‘΄μž¬ν•œλ‹€λŠ” λ‹¨μˆœν•œ 쑰건이 μ•„λ‹ˆλΌ μƒν•˜λΆ€ λŒ€μˆ˜μΈ΅μ΄ μ—°κ²°λœ λˆ„μˆ˜λŒ€μˆ˜μΈ΅μ˜ 쑰건을 κ³ λ €ν•˜μ—¬ 보닀 μ‹€μ œμ μΈ λŒ€μˆ˜μΈ΅ ꡬ쑰λ₯Ό λ°˜μ˜ν•΄μ•Ό ν•œλ‹€(Zlotnik, 2004). λ”°λΌμ„œ ν•˜μ²œκ³Ό λŒ€μˆ˜μΈ΅κ°„μ˜ 수리적 μ—°κ²°μ„±κ³Ό λˆ„μˆ˜λŒ€μˆ˜μΈ΅μ˜ 수리적 쑰건에 λ”°λ₯Έ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨ 거동 뢄석이 ν•„μš”ν•˜λ‹€. 이에 Lee et al. (2016a)은 Hunt (2009)의 해석해λ₯Ό μ΄μš©ν•˜μ—¬ λŒ€μˆ˜μΈ΅ 및 ν•˜μƒμ˜ λ‹€μ–‘ν•œ μˆ˜λ¦¬νŠΉμ„± 쑰건에 λ”°λ₯Έ μ§€ν•˜μˆ˜ μ–‘μˆ˜ 영ν–₯을 μ •λŸ‰μ μœΌλ‘œ λΆ„μ„ν•˜μ˜€κ³ , μΆ©μ£Όμ‹œμ— μœ„μΉ˜ν•œ μž„μ˜ μ§€ν•˜μˆ˜ 관정에 λŒ€ν•΄ ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰μ˜ μ‹œκ°„μ  거동 νŠΉμ„±μ„ λΆ„μ„ν•œ λ°” μžˆλ‹€. Lee et al. (2016b)은 Ward and Lough (2011)의 해석해λ₯Ό μ΄μš©ν•˜μ—¬ κΉŠμ€ λŒ€μˆ˜μΈ΅ μ–‘μˆ˜λ‘œ μΈν•œ ν•˜μ²œμˆ˜ κ°μ†Œ 양상을 λΆ„μ„ν•˜μ˜€λ‹€.

λ³Έ μ—°κ΅¬μ—μ„œλŠ” 상뢀와 ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ³€ν™”λ₯Ό ν•¨κ»˜ κ³ λ €ν•œ Hunt (2009)방법에 λΉ„ν•΄ 보닀 더 κ°„λ‹¨ν•œ 방법인 Zlotnik and Tartakovsky (2008) 해석해λ₯Ό μ΄μš©ν•˜μ—¬ μƒλΆ€λŒ€μˆ˜μΈ΅κ³Ό ν•˜λΆ€μ˜ 곡급원 사이에 λ°˜λŒ€μˆ˜μΈ΅(aquitard)이 μœ„μΉ˜ν•˜λŠ” κ΅¬μ‘°μ—μ„œ μ–‘μˆ˜μ— λ”°λ₯Έ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ‚°μ •ν•˜κΈ° μœ„ν•œ μˆ˜μΉ˜μ‹€ν—˜μ„ μˆ˜ν–‰ν•˜κ³  κ·Έ 거동 νŠΉμ„±κ³Ό μ μš©μ„±μ„ ν‰κ°€ν•˜μ˜€λ‹€.

2. 이둠적 λ°°κ²½ 및 뢄석 방법

2.1 Zlotnik and Tartakovsky 해석해

Zlotnikand Tartakovsky (2008)λŠ” Fig. 1κ³Ό 같이 ν•˜μ²œ(stream)- λŒ€μˆ˜μΈ΅(aquifer)-λ°˜λŒ€μˆ˜μΈ΅(aquitard) μ‹œμŠ€ν…œμ— λŒ€ν•΄ ν•˜μ²œμ—μ„œ PIC52A2.gif 만큼 떨어진 κ±°λ¦¬μ—μ„œ μ§€ν•˜μˆ˜ μ–‘μˆ˜ PIC52C2.gif둜 μΈν•œ μ§€ν•˜μˆ˜μœ„ κ°•ν•˜λŸ‰κ³Ό ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰μ„ κ³„μ‚°ν•˜λŠ” 해석해λ₯Ό μœ λ„ν•˜μ˜€λ‹€.

Fig. 1.

Definition Sketch for Stream-Aquifer-Auitard System (Zlotnik and Tartakovsky, 2008)

Figure_KSCE_37_06_06_F1.jpg

해석해 μœ λ„λ₯Ό μœ„ν•΄μ„œ μˆ˜ν‰λ°©ν–₯(PIC52C3.gif)으둜 λ¬΄ν•œν•œ λŒ€μˆ˜μΈ΅μ€ λ“±λ°©, κ· μ§ˆν•˜κ³ , μ’…λ°©ν–₯(PIC52C4.gif)으둜 λ¬΄ν•œν•œ ν•˜μ²œμ˜ νš‘λ‹¨λ©΄ ν¬κΈ°λŠ” λŒ€μˆ˜μΈ΅ λ‘κ»˜μ— λΉ„ν•΄ λ¬΄μ‹œν•  μ •λ„λ‘œ μž‘μœΌλ©°, Dupuit 근사가 μœ νš¨ν•˜λ„λ‘ μ§€ν•˜μˆ˜μœ„ κ°•ν•˜λŸ‰μ΄ λŒ€μˆ˜μΈ΅ λ‘κ»˜μ— λΉ„ν•΄ μž‘λ‹€κ³  κ°€μ •ν•˜μ˜€λ‹€. λ˜ν•œ λŒ€μˆ˜μΈ΅μ€ λΉ„μ••μΆ•μ„± λ°˜λŒ€μˆ˜μΈ΅μ„ 사이에 두고 μˆ˜λ‘κ°€ PIC52D5.gif둜 μΌμ •ν•œ ν•˜λΆ€ 곡급원(source bed)κ³Ό 수리적으둜 μ—°κ²°λ˜μ—ˆμœΌλ©°, λŒ€μˆ˜μΈ΅κ³Ό κ³΅κΈ‰μΈ΅κ°„μ˜ κ΅ν™˜λŸ‰μ€ 두 측의 μˆ˜λ‘μ°¨μ΄μ— λΉ„λ‘€ν•œλ‹€. ν•˜μƒν‡΄μ μΈ΅(streambed)을 ν†΅κ³Όν•˜λŠ” ν•˜μ²œκ³Ό λŒ€μˆ˜μΈ΅κ°„μ˜ μΉ¨μœ€νλ¦„(seepage flow) μ—­μ‹œ μˆ˜λ‘μ°¨μ΄μ— λΉ„λ‘€ν•˜λ©°, 이 λ•Œ ν•˜μ²œμˆ˜μœ„λŠ” μΌμ •ν•˜λ‹€κ³  κ°€μ •ν•˜μ˜€λ‹€. 이와 같은 κ°€μ •ν•˜μ— μ§€ν•˜μˆ˜ 흐름은 Eq. (1)κ³Ό 같은 λ°©μ •μ‹μœΌλ‘œ λ‚˜νƒ€λ‚Ό 수 μžˆλ‹€.

PIC52D6.gif (1)

PIC52E7.gif                

μ—¬κΈ°μ„œ, PIC52E8.gifλŠ” νˆ¬μˆ˜λŸ‰κ³„μˆ˜, PIC52F8.gifλŠ” μ €λ₯˜κ³„μˆ˜, PIC52F9.gifλŠ” μ§€ν•˜μˆ˜λ‘, PIC52FA.gifλŠ” μ–‘μˆ˜λŸ‰, PIC530B.gifλŠ” Dirac delta ν•¨μˆ˜, PIC530C.gif은 ν•˜μ²œκ³Ό μ–‘μˆ˜μ •κ°„ 거리, PIC530D.gifλŠ” ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±(streambed hydraulic conductance)으둜 ν•˜μƒμˆ˜λ¦¬μ „λ„λ„(streambed hydraulic conductivity) PIC532D.gif와 ν•˜ν­PIC532E.gif의 곱을 ν•˜μ²œλ°”λ‹₯μΈ΅ λ‘κ»˜PIC532F.gif으둜 λ‚˜λˆˆ 값이며, PIC534F.gifλŠ” λ°˜λŒ€μˆ˜μΈ΅μ˜ μˆ˜λ¦¬μ „λ„λ„, PIC5350.gifλŠ” λ°˜λŒ€μˆ˜μΈ΅ λ‘κ»˜μ΄λ‹€. 초기 및 경계쑰건은 Eqs. (2) and (3)κ³Ό κ°™λ‹€.

PIC5351.gif (2)

PIC5372.gif (3)

μ–‘μˆ˜λ‘œ μΈν•œ ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰ PIC5382.gifλŠ” ν•˜μ²œμ΄ μœ„μΉ˜ν•œ PIC5383.gifμ—μ„œμ˜ μ§€ν•˜μˆ˜μœ„ κ°•ν•˜λŸ‰μ„ ν•˜μ²œκΈΈμ΄ PIC5394.gifλ°©ν–₯으둜 μ λΆ„ν•˜κ³  여기에 ν•˜μƒμˆ˜λ¦¬μ „λ„μ„± PIC5395.gifλ₯Ό κ³±ν•΄ Eq.(4)와 κ°™λ‹€.

PIC53A5.gif (4)

μ—¬κΈ°μ„œ, PIC53A6.gifλŠ” μˆ˜μœ„κ°•ν•˜λŸ‰μ΄λ‹€.

Zlotnikand Tartakovsky (2008)λŠ” Eq. (5)와 같은 무차원 λ³€μˆ˜λ₯Ό μ‚¬μš©ν•˜μ—¬ 지배방정식 Eq. (1)을 λ¬΄μ°¨μ›ν™”ν•˜κ³ , 이λ₯Ό Laplace- Fourier λ³€ν™˜μ„ 톡해 상미뢄 방정식 ν˜•νƒœλ‘œ λ‚˜νƒ€λ‚΄μ–΄ ν•΄λ₯Ό κ΅¬ν•˜μ˜€λ‹€. 그리고 λ‹€μ‹œ Laplace-Fourier μ—­λ³€ν™˜ 과정을 톡해 Eq. (6)κ³Ό 같이 μˆ˜μœ„κ°•ν•˜λŸ‰ PIC53B7.gif에 λŒ€ν•œ ν•΄λ₯Ό μœ λ„ν•˜μ˜€λ‹€.

(PIC53B8.gif,PIC53B9.gif,PIC53CA.gif,PIC53CB.gif,PIC53DB.gif,PIC53DC.gif)=(PIC53DD.gif,PIC53EE.gif,PIC53FF.gif,PIC540F.gif,PIC5410.gif,PIC5411.gif) (5)

PIC5422.gif

(6)

μ—¬κΈ°μ„œ, PIC5423.gifλŠ” μš°λ¬Όν•¨μˆ˜(well function), PIC5433.gif, PIC5434.gif

PIC5445.gif, PIC5446.gif이닀.

ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰μ— κ΄€ν•œ 해석해λ₯Ό μœ λ„ν•˜κΈ° μœ„ν•΄μ„œ λ¨Όμ € Eq. (5)λ₯Ό μ΄μš©ν•˜μ—¬ Eq. (4)λ₯Ό λ¬΄μ°¨μ›ν•˜κ³  이λ₯Ό Laplace λ³€ν™˜μ‹œν‚€κ³ , 여기에 무차원 μˆ˜μœ„κ°•ν•˜λŸ‰ PIC5447.gif의 Laplace-Fourier λ³€ν™˜μΉ˜λ₯Ό λŒ€μž…ν•˜μ—¬ ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰μ˜ Laplace imageλ₯Ό μ–»λŠ”λ‹€. λ‹€μ‹œ Laplace μ—­λ³€ν™˜ 과정을 톡해 μ΅œμ’…μ μœΌλ‘œ Eq. (7)κ³Ό 같은 μ–‘μˆ˜λŸ‰ λŒ€λΉ„ ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰(μ΄ν•˜ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨)에 κ΄€ν•œ 해석해λ₯Ό μœ λ„ν•˜μ˜€λ‹€.

PIC5467.gif (7)

μ—¬κΈ°μ„œ, PIC5468.gifκ³Ό PIC5469.gifλŠ” Eq. (8)κ³Ό κ°™λ‹€.

PIC547A.gif, PIC547B.gif     (8)

2.2 뢄석 방법

λŒ€μˆ˜μΈ΅ 및 ν•˜μƒμ˜ μˆ˜λ¦¬νŠΉμ„±μΉ˜ λ“± μž…λ ₯ λ³€μˆ˜μ˜ λ‹€μ–‘ν•œ 쑰합에 따라 Zlotnikand Tartakovsky (2008) ν•΄μ„ν•΄λ‘œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ κ³„μ‚°ν•˜κ³  κ·Έ νŠΉμ„±μ„ λΆ„μ„ν•˜μ˜€λ‹€. νˆ¬μˆ˜λŸ‰κ³„μˆ˜ PIC547C.gifλŠ” 1, 10, 100m2/d, μ €λ₯˜κ³„μˆ˜ PIC548D.gifλŠ” 0.1, 0.2, 0.3, ν•˜μƒμˆ˜λ¦¬μ „λ„μ„± PIC548E.gifλŠ” PIC549E.gif,PIC549F.gif,PIC54B0.gifm/s, 1μΈ΅κ³Ό 2μΈ΅ μ‚¬μ΄μ˜ λˆ„μˆ˜κ³„μˆ˜ PIC54B1.gifPIC54B2.gifλŠ” PIC54C2.gif,PIC54C3.gif,PIC54D4.gif1/s, 그리고 ν•˜μ²œκ³Ό κ΄€μ •κ°„μ˜ 이격거리 PIC54D5.gif은 100, 300, 500m둜 ν•˜μ—¬ 총 35=243가지 κ²½μš°μ— λŒ€ν•΄ λͺ¨μ˜λ₯Ό μˆ˜ν–‰ν•˜μ˜€λ‹€.

Zlotnikand Tartakovsky (2008) ν•΄μ„ν•΄λŠ” λˆ„μˆ˜μΈ΅ ν•˜λΆ€μ˜ μ§€ν•˜μˆ˜λ‘κ°€ λ³€ν•˜μ§€ μ•ŠλŠ” κ³ μ •μˆ˜λ‘ 경계쑰건에 λŒ€ν•΄ μœ λ„λœ κ²ƒμœΌλ‘œ 2μΈ΅ ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μ§€ν•˜μˆ˜λ‘ λ³€ν™”λ₯Ό ν•¨κ»˜ κ³ λ €ν•˜μ—¬ μœ λ„ν•œ Hunt (2009) 해석해에 λΉ„ν•΄ λ‹¨μˆœν™”λœ 쑰건에 λŒ€ν•΄ μœ λ„λœ 것이닀. λ”°λΌμ„œ λ³Έ μ—°κ΅¬μ—μ„œλŠ” 두 ν•΄μ„ν•΄μ˜ 적용 κ²°κ³Όλ₯Ό μƒλŒ€ λΉ„κ΅ν•˜μ—¬ Zlotnik and Tartakovsky (2008) ν•΄μ„ν•΄μ˜ μ μš©μ„±μ„ κ²€ν† ν•˜μ˜€λ‹€. Hunt (2009) 해석해 μ μš©μ„ μœ„ν•΄μ„œ μ•žμ„  μž…λ ₯ λ³€μˆ˜ 쑰건에 2μΈ΅ νˆ¬μˆ˜λŸ‰κ³„μˆ˜ PIC54D6.gif = 1, 10, 100m2/d, 2μΈ΅ μ €λ₯˜κ³„μˆ˜ PIC54E7.gif=0.01, 0.001, 0.0001의 쑰건을 μΆ”κ°€ν•˜μ—¬ 총 37=2,187 가지 κ²½μš°μ— λŒ€ν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ λͺ¨μ˜ν•˜μ˜€λ‹€. Hunt (2009) ν•΄μ„ν•΄μ˜ νŠΉμ§•μ€ Lee et al. (2016)의 논문을 μ°Έμ‘°ν•  수 μžˆλ‹€.

3. 결과 및 고찰

3.1 λŒ€μˆ˜μΈ΅κ³Ό ν•˜μ²œ μˆ˜λ¦¬νŠΉμ„±μ— λ”°λ₯Έ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨ μ‚°μ •

Zlotnikand Tartakovsky (2008) 해석해λ₯Ό μ΄μš©ν•˜μ—¬ λŒ€μˆ˜μΈ΅μ˜ νˆ¬μˆ˜λŸ‰κ³„μˆ˜, μ €λ₯˜κ³„μˆ˜, λˆ„μˆ˜κ³„μˆ˜, ν•˜μ²œμ˜ ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±, ν•˜μ²œ-κ΄€μ • 이격거리 λ“± 2.2μ ˆμ—μ„œ μ œμ‹œν•œ λŒ€μˆ˜μΈ΅ 및 ν•˜μƒμ˜ μˆ˜λ¦¬νŠΉμ„±μΉ˜ 쑰합에 λ”°λ₯Έ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ‚°μ •ν•˜μ˜€λ‹€. 각 μ‘°κ±΄λ³„λ‘œ μ–‘μˆ˜ 5λ…„ κ²½κ³Ό ν›„ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ‚°μ •ν•˜κ³ , κ·Έ κ²°κ³Όλ₯Ό ν•˜μ²œκ³ κ°ˆμΈμž SDF(Stream Depletion Factor, PIC54E8.gif), ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±(PIC54F8.gif), λˆ„μˆ˜κ³„μˆ˜(PIC54F9.gif) 등에 따라 Fig. 2에 λ‚˜νƒ€λ‚΄μ—ˆλ‹€. SDFκ°€ 증가함에 따라 ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ μ€„μ–΄λ“œλŠ” 양상을 보이고 μžˆλ‹€. SDFκ°€ ν¬λ‹€λŠ” 것은 νˆ¬μˆ˜λŸ‰κ³„μˆ˜λ₯Ό μ €λ₯˜κ³„μˆ˜λ‘œ λ‚˜λˆˆ μˆ˜λ¦¬ν™•μ‚°κ³„μˆ˜κ°€ μž‘κ±°λ‚˜ ν•˜μ²œκ³Ό κ΄€μ •κ°„μ˜ 이격거리가 κΈ΄ 것을 μ˜λ―Έν•˜λŠ” κ²ƒμœΌλ‘œ 이둜 인해 μ–‘μˆ˜ 영ν–₯이 ν•˜μ²œμ— λ„λ‹¬ν•˜λŠ” μ‹œκ°„μ  지체가 μ»€μ„œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ μž‘κ²Œ λ°œμƒν•œλ‹€. Fig. 2(a)μ—μ„œ Fig. 2(c)μ—μ„œ λ³΄μ΄λŠ” 바와 같이 ν•˜μ²œκ³Ό λŒ€μˆ˜μΈ΅κ°„μ˜ μ—°κ²°ν†΅λ‘œμΈ ν•˜μ²œλ°”λ‹₯측의 μˆ˜λ¦¬μ „λ„μ„±μ˜ 크기에 따라 ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ˜ λ³€ν™”κ°€ 큰 것을 μ•Œ 수 μžˆλ‹€. Fig. 2(a)μ—μ„œμ™€ 같이 ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±μ΄ 큰 경우(PIC54FA.gifm/s) μ΅œλŒ€μ™€ μ΅œμ†ŒμΉ˜μ˜ 변동폭이 80%으둜 맀우 μ»ΈμœΌλ‚˜, Figs. 2(b) and (c)둜 ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±μ΄ PIC550B.gifm/s, PIC550C.gifm/s둜 쀄어듦에 따라 변동폭이 각각 52%와 15%둜 크게 κ°μ†Œν•˜μ˜€λ‹€. λˆ„μˆ˜κ³„μˆ˜ PIC550D.gifκ°€ 증가함에 따라 ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ 쀄어든 것을 확인할 수 있으며 μ΄λŠ” ν•˜λΆ€ λŒ€μˆ˜μΈ΅ κ³΅κΈ‰μ›μœΌλ‘œλΆ€ν„° μƒλΆ€λŒ€μˆ˜μΈ΅μœΌλ‘œμ˜ μ§€ν•˜μˆ˜ μœ μž…λŸ‰ 증가에 λ”°λ₯Έ 것이닀. λˆ„μˆ˜κ³„μˆ˜κ°€ 10λ°°μ”© μž‘μ•„μ§μ— 따라 ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ μ¦κ°€ν•˜κ³  μžˆμœΌλ‚˜ κ·Έ 증가뢄은 λˆ„μˆ˜κ³„μˆ˜μ— μ„ ν˜•μ μ΄μ§€ μ•Šκ³  점차 λ‘”ν™”λ˜μ–΄ μ¦κ°€ν•˜κ³  μžˆλ‹€. Figs. 2(b) and (c)의 κ²½μš°μ—λŠ” λˆ„μˆ˜κ³„μˆ˜κ°’μ΄ μž‘μ„μˆ˜λ‘ ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±μ΄ 큰 Fig. 2(a)에 λΉ„ν•΄ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ 보닀 μ‚°ν¬λ˜μ–΄ λ‚˜νƒ€λ‚˜κ³  μžˆλ‹€. μ΄λŠ” ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±κ³Ό λˆ„μˆ˜κ³„μˆ˜κ°€ μž‘μ€ 경우 λ‹€λ₯Έ μΈμžλ“€μ΄ 영ν–₯을 크게 미쳐 ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ˜ 변동폭이 μ¦κ°€ν•œ 것을 μ˜λ―Έν•œλ‹€. λ˜ν•œ λˆ„μˆ˜κ³„μˆ˜κ°€ PIC551E.gif1/s 인 경우 λ™μΌν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨ 값에 λŒ€ν•΄ 3개의 PIC551F.gif값이 μ‘΄μž¬ν•˜λŠ” κ²ƒμ²˜λŸΌ λ‚˜λ‚˜νƒ€λ‚¬λŠ”λ° μ΄λŠ” λ°˜λŒ€μˆ˜μΈ΅μ˜ λˆ„μˆ˜κ³„μˆ˜κ°€ 큰 경우 PIC5520.gifκ°’ λ³΄λ‹€λŠ” λ‹€λ₯Έ 영ν–₯μΈμžκ°€ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ— 지배적인 영ν–₯을 λ―ΈμΉ˜λŠ” κ²ƒμœΌλ‘œ 보인닀.

Fig. 2.

Streamflow Depletion Rates According to Stream Depletion Factor (SDF), Streambed Hydraulic Conductance (PIC5530.gif), and Leakance(PIC5550.gif) After 5-Year Pumping

Figure_KSCE_37_06_06_F2.jpg

3.2 Zlotnik and Tartavasky (2008) 해석해와 Hunt 해석해 (2009) 적용 결과의 비ꡐ

2.2μ ˆμ— μ œμ‹œν•œ λŒ€μˆ˜μΈ΅ 및 ν•˜μ²œ 쑰건에 λŒ€ν•΄ ν•˜λΆ€ κ²½κ³„μ‘°κ±΄μœΌλ‘œ μ΄ˆκΈ°μˆ˜λ‘κ°’μœΌλ‘œ κ³ μ •μˆ˜λ‘κ°’μ„ λΆ€μ—¬ν•œ Zlotnik and Tartakovsky (2008) 해석해(μ΄ν•˜ Z-T 해석해)와 μƒν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ₯Ό μ—°λ¦½ν•˜μ—¬ λ™μ‹œμ— κ³„μ‚°ν•˜λŠ” Hunt(2009) 해석해(μ΄ν•˜ H 해석해)의 적용 κ²°κ³Όλ₯Ό λΉ„κ΅ν•˜μ˜€λ‹€. Fig. 3은 Z-T 해석해와 H ν•΄μ„ν•΄λ‘œ μ‚°μ •ν•œ μ–‘μˆ˜ 1λ…„ 및 5λ…„ ν›„μ˜ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ 1:1둜 λ„μ‹œν•œ κ²ƒμœΌλ‘œ Z-T 해석해가 μƒλŒ€μ μœΌλ‘œ κ³Όμ†Œ μ‚°μ •λœ κ²½μš°κ°€ λ§Žμ€ 것을 μ•Œ 수 μžˆλ‹€. μ΄λŠ” ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ 경계쑰건을 κ³ μ •κ°’μœΌλ‘œ κ°€μ •ν•˜λŠλƒ λ³€λ™κ°’μœΌλ‘œ κ³ λ €ν•˜λŠλƒμ˜ μ°¨μ΄μ—μ„œ κΈ°μΈν•œ κ²ƒμœΌλ‘œ Z-T 해석해가 ν•˜λΆ€ κ³΅κΈ‰μ›μœΌλ‘œλΆ€ν„°μ˜ μ§€ν•˜μˆ˜ μœ μž…μœΌλ‘œ 인해 ν•˜μ²œμˆ˜ κ°μ†ŒλŸ‰μ΄ 항상 μ€„μ–΄λ“€κ²Œ λͺ¨μ˜λœ λ°˜λ©΄μ— H ν•΄μ„ν•΄λŠ” μƒν•˜λΆ€ λŒ€μˆ˜μΈ΅ 및 λˆ„μˆ˜μΈ΅μ˜ 쑰건에 따라 μƒλΆ€μ—μ„œ ν•˜λΆ€λ‘œ λ˜λŠ” ν•˜λΆ€μ—μ„œ μƒλΆ€λ‘œμ˜ μ§€ν•˜μˆ˜ μœ λ™μ„ λͺ¨μ˜ν•˜κΈ°μ— ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ΄ 항상 곡급원이 λ˜λŠ” 것은 μ•„λ‹ˆκΈ° λ•Œλ¬Έμ΄λ©°, 곡급원이 된 경우라 할지라도 ν•˜λΆ€λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„μ €ν•˜λŸ‰μ΄ ν•¨κ»˜ 고렀되기 λ•Œλ¬Έμ— λˆ„μˆ˜μΈ΅μ„ ν†΅κ³Όν•˜λŠ” μœ λ™λŸ‰μ—λ„ Z-T 해석해 적용 결과와 차이가 λ°œμƒν•œλ‹€. 즉, μ €λ₯˜κ³„μˆ˜κ°€ 큰 κ²½μš°μ™€ 같이 ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„ λ³€ν™”λ₯Ό λ¬΄μ‹œν•  수 μžˆλŠ” κ²½μš°μ—λŠ” 두 해석해가 μœ μ‚¬ν•œ κ²°κ³Όλ₯Ό λ„μΆœν•˜κΈ°μ— μƒλŒ€μ μœΌλ‘œ κ°„λ‹¨ν•œ Z-T 해석해λ₯Ό μ΄μš©ν•  수 μžˆμ§€λ§Œ, ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ³€ν™”κ°€ 큰 κ²½μš°μ—λŠ” Z-T 해석해 λ³΄λ‹€λŠ” H 해석해λ₯Ό μ΄μš©ν•΄μ•Ό ν•œλ‹€. μ–‘μˆ˜ 5λ…„ 후에 λŒ€ν•œ 결과인 Fig. 3(b)이 μ–‘μˆ˜ 1λ…„ 후에 λŒ€ν•œ 결과인 Fig. 3(a)보닀 더 큰 차이λ₯Ό 보이고 μžˆμ–΄ μ–‘μˆ˜ 기간이 κΈΈμ–΄μ§ˆμˆ˜λ‘ 두 ν•΄μ„ν•΄κ°„μ˜ νŽΈμ°¨κ°€ 증가함을 μ•Œ 수 μžˆλ‹€. μ–‘μˆ˜ 1λ…„ ν›„μ˜ 경우 H 해석해가 Z-T 해석해에 λΉ„ν•΄ 평균값이 μ•½ 2% 크게 μ‚°μ •λ˜μ—ˆκ³ , μ–‘μˆ˜ 5λ…„ ν›„μ—λŠ” μ•½ 7% 만큼 크게 μ‚°μ •λ˜μ—ˆμœΌλ©°, μ΅œλŒ€ νŽΈμ°¨κ°€ 60%λ₯Ό λ„˜λŠ” κ²½μš°λ„ λ°œμƒν•˜μ˜€λ‹€.

Fig. 3.

Comparison of Streamflow Depletion Rates Calculated using Zlotnik and Tartakovsky (2008) and Hunt (2009) Solutions after 1-year (a) and 5-year (b) Groundwater Pumping

Figure_KSCE_37_06_06_F3.jpg

Fig. 4λŠ” Table 1에 λ‚˜νƒ€λ‚Έ λŒ€μˆ˜μΈ΅κ³Ό ν•˜μ²œ 쑰건 2κ°€μ§€μ˜ κ²½μš°μ— λŒ€ν•΄ 두 ν•΄μ„ν•΄λ‘œ μ‚°μ •ν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ λΉ„κ΅ν•œ μ˜ˆμ‹œμ΄λ‹€. Fig. 4(a)와 같이 Case 1 μ‘°κ±΄μ—μ„œλŠ” Z-T 해석해 적용 κ²°κ³ΌλŠ” μ–‘μˆ˜ 4λ…„ κ²½κ³Ό ν›„μ—λŠ” 거의 μ •μƒμƒνƒœμ— λ„λ‹¬ν•˜κ³  μžˆμœΌλ‚˜, H 해석해 적용 κ²°κ³ΌλŠ” ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ μ‹œκ°„μ— 따라 μ§€μ†μ μœΌλ‘œ μ¦κ°€ν•˜κ³  μžˆλ‹€. μ–‘μˆ˜κΈ°κ°„μ΄ 증가함에 따라 두 해석해 결과의 차이가 μ¦κ°€ν•˜κ³  μžˆμ–΄ 이와 같은 μ‘°κ±΄μ—μ„œλŠ” ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„μ €ν•˜ 영ν–₯을 λ¬΄μ‹œν•  수 μ—†μŒμ„ 보여주고 μžˆλ‹€. λ°˜λ©΄μ— Fig. 4(b)와 같이 Case 2의 κ²½μš°μ—λŠ” ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μ €λ₯˜κ³„μˆ˜κ°€ μ»€μ„œ ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„μ €ν•˜λŸ‰μ΄ μž‘κΈ° λ•Œλ¬Έμ— 두 ν•΄μ„ν•΄κ°„μ˜ 차이가 μž‘κ²Œ λ‚˜νƒ€λ‚¬λ‹€.

Fig. 4.

Comparison of Streamflow Depletion Rates Calculated using Zlotnik and Tartakovsky (2008) and Hunt (2009) Solutions for Example Two Conditions

Figure_KSCE_37_06_06_F4.jpg
Table 1. Hydraulic Properties for Example Cases Table_KSCE_37_06_06_T1.jpg

H ν•΄μ„ν•΄λŠ” ν•˜λΆ€λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ³€ν™”λ„ ν•¨κ»˜ κ³ λ €ν•˜κΈ° λ•Œλ¬Έμ— 보닀 μ‹€μ œμ μΈ 방법이고 μ •ν™•ν•œ κ²°κ³Όλ₯Ό 얻을 수 μžˆλŠ” μž₯점이 μžˆμœΌλ‚˜, Laplace μ—­λ³€ν™˜μ΄λ‚˜ μˆ˜μΉ˜μ λΆ„ 과정을 거쳐야 ν•˜κΈ° λ•Œλ¬Έμ— 계산 과정이 λ³΅μž‘ν•˜κ³ , 해석해 μ μš©μ„ μœ„ν•΄ ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ νˆ¬μˆ˜λŸ‰κ³„μˆ˜μ™€ μ €λ₯˜κ³„μˆ˜ λ“± 좔가적인 μž…λ ₯μžλ£Œκ°€ ν•„μš”ν•˜λ‹€. λ°˜λ©΄μ— Z-T ν•΄μ„ν•΄λŠ” 이와 같은 과정이 ν•„μš” μ—†κ³  μƒλŒ€μ μœΌλ‘œ μž…λ ₯μžλ£Œλ„ κ°„λ‹¨ν•˜κΈ° λ•Œλ¬Έμ— μ‚¬μš©ν•˜κΈ°μ— νŽΈλ¦¬ν•˜μ§€λ§Œ, Fig. 3κ³Ό Fig. 4μ—μ„œμ™€ 같이 λŒ€μˆ˜μΈ΅ 및 ν•˜μ²œμ˜ 쑰건에 따라 ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„ λ³€ν™” 영ν–₯을 λ¬΄μ‹œν•  수 μ—†λŠ” κ²½μš°κ°€ μ‘΄μž¬ν•˜κΈ° λ•Œλ¬Έμ— H 해석해에 μ€€ν•˜λŠ” 정확성을 λ‹΄λ³΄ν•˜κΈ° μœ„ν•΄μ„œλŠ” μ œν•œμ μΈ μ‘°κ±΄μ—μ„œ μ‚¬μš©λ˜μ–΄μ•Ό ν•œλ‹€. Fig. 5λŠ” Z-T ν•΄μ„ν•΄λ‘œ μ‚°μ •ν•œ μ–‘μˆ˜ 1λ…„ 및 5λ…„ ν›„ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ—μ„œ H ν•΄μ„ν•΄λ‘œ μ‚°μ •ν•œ κ²°κ³Όλ₯Ό κ°ν•œ 값을 λˆ„μˆ˜κ³„μˆ˜μ™€ ν•˜μ²œ-κ΄€μ • 이격거리λ₯Ό κ³±ν•œ κ°’κ³Ό ν•˜μ²œκ³ κ°ˆμΈμžμ˜ μ œκ³±κ·Όμ— 따라 λ„μ‹œν•œ 것이닀. H 해석해 적용 κ²°κ³Όλ₯Ό μ°Έκ°’μœΌλ‘œ κ°„μ£Όν•˜λ©΄, Z-T ν•΄μ„ν•΄λŠ” Fig. 5(a)와 같이 μ–‘μˆ˜ 1λ…„ ν›„μ˜ 경우 PIC5551.gifκ°€ 50일 보닀 크면 즉, PIC5552.gifκ°€ 2,500일 보닀 크면 였차λ₯Ό 10% μ΄λ‚΄λ‘œ 쀄일 수 있고, PIC5563.gifκ°€ 10cm/s 미만이면 PIC5574.gifκ°€ 맀우 μž‘λ”λΌλ„ Hunt (2009) ν•΄μ„ν•΄μ™€μ˜ 차이λ₯Ό 쀄일 수 μžˆλ‹€. Fig. 5(b)λŠ” μ–‘μˆ˜ 5λ…„ ν›„ 였차λ₯Ό λ‚˜νƒ€λ‚Έ κ²ƒμœΌλ‘œ μš°ν•˜λ‹¨ μ˜μ—­κ³Ό 같이PIC5575.gifκ°€ 크고 PIC5585.gifκ°€ μž‘μ•„μ§μ— 따라 μ˜€μ°¨κ°€ 쀄어듀고 μžˆμœΌλ‚˜, μ˜€μ°¨κ°€ 큰 λ²”μœ„κ°€ μ§€λ°°μ μœΌλ‘œ μ°¨μ§€ν•˜κ³  μžˆμ–΄ μž₯κΈ°κ°„ μ–‘μˆ˜ 영ν–₯을 λΆ„μ„ν•˜λŠ”λ°μ—λŠ” ν•œκ³„κ°€ μžˆμŒμ„ μ•Œ 수 μžˆλ‹€. λ”°λΌμ„œ Z-T 해석해λ₯Ό μ‚¬μš©ν•  λ•Œμ—λŠ” Fig. 5와 같이 ν•˜μ²œκ³ κ°ˆμΈμžμ™€ λˆ„μˆ˜κ³„μˆ˜κ°’μ˜ 적정 λ²”μœ„λ₯Ό κ³ λ €ν•΄μ•Ό ν•˜λ©°, 가급적 1λ…„ μ΄ν•˜μ˜ 단기간 μ–‘μˆ˜μ˜ν–₯ μ˜ˆμΈ‘λ§Œμ— μ‚¬μš©ν•˜λŠ” 것이 λ°”λžŒμ§ν•  κ²ƒμœΌλ‘œ νŒλ‹¨λœλ‹€.

Fig. 5.

Differences of Streamflow Depletion Rates between Zlotnik and Tartakovsky (2008) and Hunt (2009) Solutions after 1-year (a) and 5-year (b) Groundwater Pumping

Figure_KSCE_37_06_06_F5.jpg

4. κ²° λ‘ 

λ³Έ μ—°κ΅¬μ—μ„œλŠ” λˆ„μˆ˜λŒ€μˆ˜μΈ΅-ν•˜μ²œ-μ–‘μˆ˜μ • κ²½κ³„μΉ˜ λ¬Έμ œμ— κ΄€ν•œ Zlotnik and Tartakovsky (2008) 해석해λ₯Ό μ΄μš©ν•˜μ—¬ ν•˜μ²œ-κ΄€μ • 이격거리, λŒ€μˆ˜μΈ΅μ˜ νˆ¬μˆ˜λŸ‰κ³„μˆ˜ 및 μ €λ₯˜κ³„μˆ˜, λˆ„μˆ˜μΈ΅μ˜ λˆ„μˆ˜κ³„μˆ˜, ν•˜μƒμ˜ μˆ˜λ¦¬μ „λ„μ„± 등을 λ³€ν™”μ‹œμΌœκ°€λ©΄μ„œ μ–‘μˆ˜λ‘œ μΈν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ‚°μ •ν•˜κ³  κ·Έ 거동 νŠΉμ„±μ„ λΆ„μ„ν•˜μ˜€μœΌλ©°, κ·Έ κ²°κ³Ό λ‹€μŒκ³Ό 같은 결둠을 얻을 수 μžˆμ—ˆλ‹€.

(1)ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±μ΄ PIC5586.gifm/s인 κ²½μš°μ— ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ˜ 변화폭이 80%으둜 맀우 크게 λ‚˜νƒ€λ‚¬κ³ , 이 값이 PIC5597.gifPIC5598.gifm/s, PIC55A9.gifm/s둜 쀄어듦에 따라 변동폭이 각각 52%와 15%둜 크게 κ°μ†Œν•˜μ—¬ Zlotnik and Tartakovsky (2008) ν•΄μ„ν•΄μ—μ„œλŠ” ν•˜μƒμˆ˜λ¦¬μ „λ„μ„±μ΄ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ‚°μ •ν•˜λŠ”λ° μžˆμ–΄μ„œ 지배적인 인자둜 μž‘μš©ν•˜μ˜€λ‹€.

(2)λ°˜λŒ€μˆ˜μΈ΅μ˜ λˆ„μˆ˜κ³„μˆ˜κ°€ 컀짐에 따라 ν•˜λΆ€ λŒ€μˆ˜μΈ΅ κ³΅κΈ‰μ›μœΌλ‘œλΆ€ν„° μƒλΆ€λŒ€μˆ˜μΈ΅μœΌλ‘œμ˜ μ§€ν•˜μˆ˜ μœ μž…λŸ‰ μ¦κ°€ν•˜μ—¬ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ μ€„μ–΄λ“œλŠ” 양상이 λͺ…ν™•ν•˜κ²Œ λ‚˜νƒ€λ‚˜λŠ” λ“± λˆ„μˆ˜κ³„μˆ˜ μ—­μ‹œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ— λ―ΈμΉ˜λŠ” 영ν–₯이 큰 κ²ƒμœΌλ‘œ ν‰κ°€λ˜μ—ˆμœΌλ©°, λˆ„μˆ˜κ³„μˆ˜ 변화에 λ”°λ₯Έ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ˜ λ³€ν™”λŠ” μ„ ν˜•μ„±μ΄ 크지 μ•Šμ€ κ²ƒμœΌλ‘œ λΆ„μ„λ˜μ—ˆλ‹€.

(3)ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ³€ν™”λ₯Ό κ³ λ €ν•˜μ§€ μ•Šμ€ Zlotnik and Tartakovsky (2008) 해석해와 μƒν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ³€ν™”λ₯Ό ν•¨κ»˜ κ³ λ €ν•œ Hunt (2009) 해석해λ₯Ό 주어진 쑰건에 각각 μ μš©ν•˜μ—¬ λΉ„κ΅ν•œ κ²°κ³Ό μ „μžκ°€ μ–‘μˆ˜ 1λ…„ ν›„μ—λŠ” ν‰κ· μ μœΌλ‘œ μ•½ 2%, 5λ…„ ν›„μ—λŠ” μ•½ 7% 만큼 μž‘κ²Œ μ‚°μ •λ˜μ—ˆκ³  μ–‘μˆ˜ 기간이 길어짐에 따라 두 ν•΄μ„ν•΄κ°„μ˜ νŽΈμ°¨κ°€ μ¦κ°€ν•˜μ—¬ μ΅œλŒ€ 60%λ₯Ό λ„˜μ€ 차이λ₯Ό λ‚˜νƒ€λ‚΄λŠ” κ²½μš°λ„ λ°œμƒν•˜μ˜€λ‹€.

(4)Zlotnik and Tartakovsky (2008) ν•΄μ„ν•΄λ‘œ μ‚°μ •ν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ΄ 보닀 μ‹€μ œμ μΈ 쑰건에 λŒ€ν•œ 해석해인 Hunt (2009) 해석해에 μ€€ν•˜λŠ” 정확성을 λ‹΄λ³΄ν•˜κΈ° μœ„ν•œ μž…λ ₯ 쑰건의 적정 λ²”μœ„λ₯Ό μ œμ‹œν•˜μ˜€λ‹€. λ³Έ μ—°κ΅¬μ—μ„œ μ μš©ν•œ 쑰건에 λŒ€ν•΄μ„œ μ „μžκ°€ μ–‘μˆ˜ 1λ…„ ν›„μ—λŠ” ν•˜μ²œκ³ κ°ˆμΈμžκ°€ 2,500일보닀 ν¬κ±°λ‚˜ λˆ„μˆ˜κ³„μˆ˜μ™€ ν•˜μ²œ-κ΄€μ • 이격거리λ₯Ό κ³±ν•œ 값이 10cm/s 미만인 쑰건이 μ μ ˆν•œ λ²”μœ„μΈ κ²ƒμœΌλ‘œ λΆ„μ„λ˜μ—ˆλ‹€.

(5)Zlotnik and Tartakovsky (2008) ν•΄μ„ν•΄λŠ” λ³΅μž‘ν•œ μˆ˜μΉ˜μ λΆ„κ³Ό μˆ˜μΉ˜λ³€ν™˜κ³Όμ •μ„ κ±°μΉ˜μ§€ μ•Šκ³  ν•˜λΆ€ λŒ€μˆ˜μΈ΅ μˆ˜λ¦¬νŠΉμ„±μΈμž 값을 ν•„μš”λ‘œ ν•˜μ§€ μ•ŠκΈ°μ— μ§€ν•˜μˆ˜ μ–‘μˆ˜λ‘œ μΈν•œ ν•˜μ²œμˆ˜ κ°μ†Œμœ¨μ„ μ˜ˆμΈ‘ν•˜λŠ”λ° κ°„νŽΈν•˜κ³  μœ μš©ν•œ 방법이닀. ν•˜μ§€λ§Œ, ν•˜λΆ€ λŒ€μˆ˜μΈ΅μ˜ μˆ˜μœ„λ³€ν™”λ₯Ό κ³ λ €ν•˜μ§€ μ•ŠκΈ° λ•Œλ¬Έμ— μˆ˜μœ„λ³€ν™”κ°€ 큰 μ§€μ—­μ΄λ‚˜ μž₯κΈ°κ°„ μ–‘μˆ˜ 영ν–₯ λΆ„μ„μ—λŠ” ν•œκ³„κ°€ 있으며 1λ…„ μ΄ν•˜μ˜ 단기간 영ν–₯ 뢄석에 ν™œμš©ν•˜λŠ” 것이 λ°”λžŒμ§ν•˜λ‹€.

Acknowledgements

λ³Έ μ—°κ΅¬λŠ” ꡭ토ꡐ톡뢀 ν•œκ°•ν™μˆ˜ν†΅μ œμ†Œ β€œν•˜μ²œμˆ˜ 영ν–₯을 κ³ λ €ν•œ ν•˜μ²œλ³€ μ§€ν•˜μˆ˜ κ΄€λ¦¬λ°©μ•ˆ 연ꡬ” 과제의 지원에 μ˜ν•΄ μˆ˜ν–‰λ˜μ—ˆμŠ΅λ‹ˆλ‹€.

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