Ulangan I Matematika Terapan (TA 600)

Project 2 Numerical Analysis (TA5011)

Graduate Program in Mining EngineeringTopic:

Permeable zone in underground mining (water pocket)

Objective:Modeling using system of linear equations (SLE)

Modeling using system of non linear equations (SNE)

Modeling using system of ordinary difference equations (SODE)

Numerical method for SLE, SNE and SODE

Water balance

System dynamic

Application in mining engineering

Schedule:14 daysData:At PTFI mining, some of karstic caverns or low RQD rock zones may present as water pockets. They are hydraulically interconnected by fractures or permeable zones, while some of others are not. When these water pockets are broken through by drilling, big and sudden flowrate of water blows out from the drill hole and was called by PTFI as rock burst. Some of water pockets that are hydraulically connected with surface flow or water will supply unlimited GW recharge and have to be given an attention. Following is a model of hydraulically interconnected water pockets.

Figure. 1: Model of Hydraulic Connection between Stream, Water Pocket, Fractures and Subsurface Drainage Gallery Fractures can be modeled as or like pipes with following position of two end points:

PointXYZPointXYZ

(msl)(msl)

A1003103748E4344023745

B1252803718F3763923675

C1552503645G3803933660

D1804103578H3953943573

Case 1: steady state flow storativity is disregarded Stream water depth at point A and E

: 2 m & 3 m

Fracture aperture (eh)

: 0.1 cm

Analog model diameter of fractures (D)

: 4 cm

Head loss factor of velocity within fractures: 0.02 Kinematic viscousity of stream water ()

: 10-6 m2/sec

Gravity acceleration (g)

: 9.8 m/sec2 Unit mass of stream water ()

: 1010 Kg/m3 Head at D and H were assumed similar to the top of subsurface gallery

Assignment for case 11. Compute length of fractures !

2. Determine estimated hydraulic conductivity of fractures !

3. Compute hydrostatic pressure at point A, B, C, E, F and G !

4. Compute flow velocity at point A, B, C, E, F and G !

5. Compute head at point A, B, C, E, F and G !

6. Compute flowrate at point D and H and total flowrate in subsurface drainage gallery !Case 2: unsteady state flow storativity is considered Estimated area of water pocket 1, 2, 3 dan 4: 0.5; 0.75; 0.6 dan 0.8 Ha

Temporal river water depth at point A and E : 2 e-0.3t m dan 3 e-0.2t m

Initial head at each water pocket

: 3750, 3700, 3725, 3695 msl

Datum of each water pocket is roughly estimated at its respective level Head at D and H were assumed similar to the top of subsurface galleryAssignment for case 21. Compute temporal hydrostatic pressure at point B, C, F and G !

2. Compute temporal velocity at point A, B, C, E, F and G !

3. Compute temporal head at point B, C, F and G !

4. Compute temporal flowrate at point D and H dan temporal total flowrate in gallery !Headnya = lewat numerik metode ITERASI,, setelah dapat headx kemudian menggunakan runge kutta.. (ini untuk tiap2 head)A

Stream bed

Subsurface drainage gallery

BA

C

E

F

DE

G

H

WP 1

WP 2

WP 3

WP 4