Theory and Application of Flow Box Test Result to ...

9'1, Indonesian Geotechnica/ Conference and I 5th Annual Scientific Meeting Jakarta, 7 - 8 December 201 I

Theory and Application of Flow Box Test Result to Explain Initiation of Mudflow Shannon Hsien Heng Lee National Taiwan University ofScience and Technology

Budijanto Widjaja National Taiwan University ofScience and Technology

ABSTRACT: Mudflow is one of the most dangerous types of mass movement, which always occurs in Indonesia. Its behavior is characterized by high water content equal to or higher than its liquid limit. The main soil type is fine-grained soil. This material is initiated during the plastic state when water content is lower than the liquid limit. However, when the water content reaches its liquid limit, the material will behave as viscous liquid. To explain this behavior, well-known rheology models, such as the Bingham and Herschel- Bulkley models, are introduced. The parameters are yield shear stress and viscosity, which can be derived using a viscometer. However, this conventional test gives only the viscous liquid state parameters; thus, some difficulty arises in obtaining the viscosity lower than or equal to the liquid limit.

The current study aims to give a reliable test both on the plastic and viscous liquid states. The authors developed a new method, called the flow box test, to determine the viscosity in a laboratory test to explain the initiation of mudflow. The governing equation was derived using soil-column equilibrium coupled with the Bingham model. This mathematical model was developed, and interpretation of the result was conducted using the curve-matching procedure. This procedure is similar to the Herschel- Bulkley model. The result showed that the viscosity has a shear-thinning behavior where the viscosity reduces following the increase in time. The laboratory test results of the analytical model showed that the viscosity was within the range when compared with other scholars' previous research. A real mudflow event in the Maokong area was simulated using Flo2d software. The simulation result showed that when the liquidity index was equal to or higher than one, the material behavior conforms to the laboratory results and is classified as mudflow. Hence, the theory and the application of the flow box test succeed in demonstrating the mudflow behavior.

Keywords: mudflow, plastic state, viscous liquid state, viscosity, rheology

I INTRODUCTION Mudflow is a kind of mass movement that occurs in the viscous liquid state (Hungr et al., 2001). The viscous liquid state takes place when the water content is equal to or higher than the liquid limit (LL). Hence, mudflow exhibits flow behavior for fine-grained soils (i.e., silt or clay). Flow velocity occurs during the flow, implying that velocity (v) or displacement (d) data can be used to model the mudflow during movement. The flow velocity itself can be higher than 5 mis, showing how dangerous mudflow can be because of the suddenness of their occurrence. Research

on mudflow is generally divided into three areas: source (i.e., initiation), transportation, and depositional areas. To describe the behavior of mudflow, a laboratory test was developed using the flow box test (FBT). The current paper aims to elucidate how the FBT result (i.e., displacement profile) is interpreted. The final result is viscosity ( 77), which is a key parameter for explaining mudflow initiation. Rheology models, such as the Bingham and HerschelBulkley models, are also introduced.

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9'" Indonesian Geotechnical Conference and I 5'" Annual Scienlijic .'v/eeting Jakarta, 7 - 8 December 20 II

2 BACKGROUND The Bingham model is typically used to model mudtlow behavior (Franzi, 2000). This mechanical model has a viscous dashpot (i.e., reflects viscosity 17) and a friction plate (i.e., reflects yield shear stress -z;.) in a parallel connection. The model can be expressed as (1) where r is the shear stress, -z;.s denotes the Bingham yield stress, and y represents the shear strain rate. Equation (l) indicates that when r is lower than -z;.8 , the material is in a plastic state. However, when r is higher than -z;.8 , the material flows (Krizek, 2004). Many researchers believe that mudflow occurs when its water content (w) reaches its LL. The Herschel-Bulkley model is a purely empirical curve-matching representation, applicable only to viscometer test results (Lorenzini and Mazza, 2004; Takahashi, 2007) with the equation

- c(2+ H/(BC2))+q - L+ pie c, 2 v(t 2 ) = , ) + V( I ,., H /(s-c 2

) 1

(3)

where c is the cohesion, q pertains to the loading, y denotes the unit weight, H is the sample height, B is the trap door width, v(t1) represents the velocity at time t1, and v(ti) is the velocity at time t2 • Constants C1 and C3 are related to the dimension of the FBT. They are expressed as follows:

p

C=-K I A a C~, =

6-e-c,-H) .

(4)

(5)

where P is the perimeter, A pertains to the area, Ka denotes the lateral active earth pressure. The velocity should decrease during testing. This requirement modifies Eq. 3, resulting in the minimum cohesion

(2)

where K (consistent coefficient) and n (flow index) are the constant fitting parameters. Similar to the Bingham model, the HerschelBulkley model is characterized by dominance for relatively high-viscosity fluids with laminar flow (Huang and Garcia, 1988). Chen (1987) recommended the use of this model for studying fine soil.

3 MATERIALS AND METHODS The FBT was developed using the trap door concept developed by Terzaghi (1943). Initially, this concept was applied to sand materials, and then subsequently extended to clay soil and rock (Lee et al, 2006). Thus, the FBT is intended for fine-grained soils. A detail mathematical model derivation could refer to Widjaja and Lee (2011). The equilibrium of soil column was coupled with the Bingham model. The velocity at time t [v(t)] is expressed as follows:

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cmin

=

(2+H/ (BC 2 ))

(6)

From Eq. 6, c is related to a certain geometry and the loading of the FBT, not viscosity. In obtaining the displacement profile (i.e., displacement and time relationship), the integration of the velocity profile is possible. Analogous to the Herschel-Bulkley model, the calculated displacement profile is calibrated and curve-fitted to the experiment data using (7) t=0;ford