Sunjoto Shape Factor under Full Penetration Slug Test

Sunjoto developed shape factor equations in order to determine the drawdown and hydraulic conductivity value. Many researchers had conducted research using these equations under the pump test. Moreover, most of the research used Sunjoto equations as the comparison with the other pump test equations. Since 1951, shape factor equations have been developed to determine hydraulic conductivity value under slug test which mainly focus on the dimension of well. Afterwards, many scientists and researchers developed shape factor equations including Sunjoto, Bouwer and Rice. Therefore, this research intends to use Sunjoto equation under the slug test. The comparison of hydraulic conductivity by constant head test and slug test has been conducted in this research. The comparison value is acceptable although there are difference values that were caused by disturb and Un-disturb sample.


I. INTRODUCTION
The aquifer parameters K, which is known as hydraulic conductivity value, can be determined by many kinds of methods in the field of groundwater engineering [1], [2]. Hydraulic conductivity test can be conducted not only in the filed area, but also in the laboratory. The field methods can be divided into two types, pump test and slug test. Pump test is a well-known method to determine aquifer parameters in the hydrogeology. A slug test is different from standard aquifer tests, which typically involves well pumping at a constant flow rate, and monitoring the response of aquifer in monitoring wells nearby. The slug tests are preferably to be performed instead of constant rate test, because the slug tests do not require pumping and there is no need to take too much time for test [3], [4]. The equations for slug test are mainly focused on the well dimension than geomorphology of aquifer. Many equations were developed and mainly focused on well dimension, i.e. shape factor. Sunjoto also developed shape factor with various well dimension in the groundwater engineering field based on Hvorslev (1951) equations [5], [6]. These equations have been used in many previous researches. Most of the researcher used Sunjoto equations under groundwater pumping test [7]

II. MATERIALS AND METHODS
The main objective of this research is to prove the Sunjoto shape factor for determination of hydraulic conductivity value under slug test. The methods can be divided into two types, i.e. constant head test and slug test. These two tests have been conducted in the laboratory. The hydraulic conductivity value from constant head test has been taken as reference for comparison to prove Sunjoto equation.

A. Constant Head Test
Constant head permeameter can be used to measure hydraulic conductivities of consolidated or unconsolidated formations under low heads. Water enters the cylinder medium from the bottom and it is collected as overflow once it pass upward through the material. According to Darcy's law, hydraulic conductivity can be obtained using the constant head test equation [8].

B. Slug Test
Researcher has conducted the test in the laboratory in order to have slug test with various well dimensions even though slug test can be easily conducted at any field area. The experiment design was built in Laboratory of Hydraulic, Department of Civil and Environmental Engineering, Universitas Gadjah Mada. The 50 cm dimension of glass tank has been used to demonstrate aquifer and the 2.6 cm diameter and 70 cm length of PVC pipe has been used for groundwater well demonstration. The 114.20 g container was used to slug into the well as transducer (Fig. 1). The Progo river sand has been used as the groundwater aquifer.

III. CONSTANT HEAD TEST
The soil test, including grain size analysis and constant head test of this soil sample, was conducted in Laboratory of Soil Mechanics, Department of Civil and Environmental Engineering, Universitas Gadjah Mada, to find out the soil characteristics. According to grain size result analysis, the Sunjoto Shape Factor under Full Penetration Slug Test Thinzar Aye, S. Sunjoto, and Djoko Luknanto soil sample can be determined as fine sand. The disturbed soil sample must undergo constant head test in the laboratory to determine its soil characteristics. This test method covers the determination of permeability coefficient with a constant-head method for the water laminar flow through soils.
The diameter of specimen is 7.5 cm, area is 44.18 cm 2 and volume is 618.5 cm 3 . The data measurement was taken as the constant head test (Table 1) was performed. The average discharge q is 2.176 cm 3 /sec, hydraulic gradient I value is 2 and the Correction factor, Rt is 0.838. The hydraulic conductivity K value gets 2.1E-0.4 m/sec, based on the determination of constant head test at the laboratory. In a slug test, a small volume of water is suddenly removed from a well once the rise rate of water level in the well is measured. Alternatively, a small slug of water is poured into the well and the rise and subsequent fall of water level are measured. The aquifers transmissivity or hydraulic conductivity can be determined based on the measurements. The slug test has advantages, i.e. there is no pumping required, no piezometers are needed, and the test can be completed within a few minutes, or in a few hours at the most [3], [4]. The slug test method has been used in this research by using the transducer (Fig. 2). (2) where K is the Coefficient Permeability value (m/sec), Q is the constant recharged rate (m 3 /sec), S is the drawdown value (m), and F is the shape factor (Geometry of Well) in (m) [5]- [7]. First, the dimension of well, i.e. shape factor, was proposed by Hvorslev (1951) [12]. Later, many researchers have studied and developed many well shape factor equations including Sunjoto. Shape factor is a representation of circumference and cross section of the area, hydraulic gradient, soil layers condition, and position of the well. Shape Factor is a value that function as diameter of casing, length of perforated casing, base condition of casing (pervious or impervious), the tip of casing position to the aquifer layer position, and confined or unconfined aquifer [13], [14]. Research on shape factor of the Well has been conducted by many researchers, e.g. Shape factor (F) for various condition in graphic form by Luthian J.N., Kirkham D. (1949) etc.
[15]- [17]. Sunjoto also developed the shape factors under confined and an unconfined aquifer with full and partial penetration [6]. Sunjoto shape factor under full and partial test, and other shape factor equations that were not practically proved yet, as it is described in Table II.  VII. DATA MEASUREMENT Different from pump test, the slug test only requires the measurements for around the well dimension. The slug test has been conducted using experiment tank in the laboratory of hydraulic, Department of Civil and Environmental Engineering, Universitas Gadjah Mada. This research only uses full penetration of well under unconfined aquifer. The static water level is 12.05 cm and aquifer thickness is 20 cm during the slug test, and the data measurement has been taken for (7) hours from 1:50 to 9:00 pm. The 114.0 g transducer was put in the well according to the procedure of slug test. The researcher conducted water level measurement in the well with tape ruler that was put around the tank boundary.  Many researchers have used this equation under pump test  and there also many researches have used this equation by  doing the comparison with other pump test equations for example with the Cooper-Jacob method. In 1951, Hvorslev firstly introduced the equations for well shape factor and these equations developed for slug test [12]. Therefore, the researcher has tried to use this equation under slug test yet some of the previous research used this equation under pump test. Data analysis was conducted using Sunjoto equations (Equation. 2) and shape factor equations for full penetration test, and shape factor for unconfined aquifer by Hvorslev (1951), Taylor (1948) and Harza (1935) (from Table II). In this research, the trial and error method were used to determine hydraulic conductivity value without graphic method.  (Fig. 3). It is important to use shape factor with appropriate well conditions.

CONFLICT OF INTEREST
The authors declare no conflict of interest.

AUTHOR CONTRIBUTIONS
Thinzar Aye has conducted the data analysis and wrote the research. S. Sunjoto and Djoko Luknanto supervised this research. All authors had approved the final version.