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Downloaded from the Online Library of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING This paper was downloaded from the Online Library of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). The library is available here: https://www.issmge.org/publications/online-library This is an open-access database that archives thousands of papers published under the Auspices of the ISSMGE and maintained by the Innovation and Development Committee of ISSMGE. Geotechnical Aspects of Underground Construction in Soft Ground, Kastner; Emeriault, Dias, Guilloux (eds) © 2002 Spécinque, Lyon. ISBN 2-9510416-3-2 The effect of seepage forces at the tunnel face of shallow tunnels In-Mo Lee Korea University, Seoul, Korea Seok-Woo Nam Korea University, Seoul, Korea Lakshmi N. Reddi Kansas State University, Manhattan, KS, U.S.A / ABSTRACT: In this paper, seepage forces arising from the groundwater flow into a tunnel were studied. First, the quantitative study of seepage forces at the tunnel face wa_s performed. The steady-state groundwater flow equation was solved and the seepage forces acting on the tunnel face were calculated using the upper bound solution in limit analysis. Second, the effect of tunnel advance rate on the seepage forces was studied. In this part, a finite element program to analyze the groundwater flow around a tumiel with the consideration of tun­ nel advance rate was developed. 'Using the program, the effect of the tunnel advance rate on the seepage forces_ was-studied. A rational design methodology for the assessment of support pressures required for main­ taining the stability of the tumiel face was suggested for underwater tunnels. 1 INTRODUCTION may affect the tunnel support pressure or the tumiel Tunnel faces are subjected to many problems' regard­ face stability. ing stability during constmction, but there _has been The seepage force acting in a unit volume of soil little research with respect to the stability of the tun­ grains can be expressed as iy W, where y W is the unit nel support and the surrounding ground. .When a weight of water and i is the hydraulic gradient. Con­ tunnel is excavated below the groundwater level, the sequently, to calculate the seepage force, the distri­ groundwater flows into the excavated surface of the bution of hydraulic head around the tunnel should be tunnel and seepage forces act on the tunnel face. The calculated first by solving the groundwater . flow stability of tunnel face will be significantly affected equation. In order to calculate the seepage forces act­ by these seepage forces. In this study, a procedure to ing onthe tunnel face under a steady-state condition, estimate the seepage pressure acting on the tunnel PENTAGON-3D was used in this study. The face is suggested for the case when the tunnel is ex­ PENTAGON-3D is a finite element analysis _pro­ cavated with constant advance rate in the presence of gram for solving 3-dimensional "continuum .problems groundwater flow. such as tunnels, earth retaining structures,‘structural mechanics, and steady-state groundwater flow. To calculate the hydraulic gradient, the failure surfaces 2 SEEPAGE FORCES ACTING ON THE in front of the tunnel face should be pre-detennined -TUNNEL FACE or assumed. To solve this problem, the modified up­ per bound solution with the consideration of seepage 2.1 Estimation of seepage forces acting on the tunnel _face ' forces proposed by Lee et al. (2001) was adopted: The groundwater flow passing through soil grains N, (KP -1)&+1 +NY(Kp-1)LS(K,,-1)l‘-Ei-+1D _ , occurs in response to an energy gradient and a meas­ OC Oc OC ure of this gradient is provided by the difference in (1) hydraulic head (Freeze and Cherry 1979). When a where os refers to the surcharge, oc is the unconfined tunnel is excavated below the groundwater level, the compressive strength of the soil, OT is the retaining groundwater flows into the excavated surface of the pressure applied to the tunnel face, os, is the seep­ turmel and there exists a difference in hydraulic head age pressure acting on the tunnel face, KP is the around the tunnel. The force that acts on the soil Rankine’s earth pressure coefficient for passive fail­ grain due to the differential head is known as the ure, Y is the unit weight of soil, D represents the seepage force and it is exerted in the direction of tunnel diameter, and Ns and NY are weighting coeffi­ groundwater flow. In this case, the seepage force is cients. in addition to the effective stress of the ground and Table 1. Properties of the ground. Soil t e Unit weight Cohesion Friction angle _ YP <1<N/m“> (kN/me (dee) Sand 15.2 0.0 35.0 In this study, two types of tunnels were c0nsid_ ered - a drainage type tunnel and a water-proof type tunnel. In the case of a drainage type tunnel, it is a5_ sumed that groundwater flows into all of the ex¢a_ vated surfaces including the tunnel face. In the cage of a water-proof type tunnel, the groundwater flows only into the tunnel face. In both types of tunnels, the analyses to obtain seepage forces were conducted for 21 cases of ground conditions by varying 'C/1) Figure 1. Hydraulic head distribution and failure surface. from 2.0 to 4.0, and H/D from 1.0 to 4.0. The values of average seepage pressures during tunnel excavation calculated from numerical analy­ .%@,_ ses are presentedin Figure 4. In this figure, it can be ‘ p TUIIIICI F366 seen that the average seepage pressures have an al­ »' ‘f ‘. most linear relation with the H/D ratio both for the drainage -and the water-proof types although the V7/I/¢’/!}!!“ A I ­ /iff’/f¢.. 7 A , former case has lower values than the latter case. The ranges of the average seepage pressure were % Area of Failure 18.2kN/rnz to 47.6kN/m2 for the drainage type tunnel `@,,f',W ' and 21.9kN/m2 to 62.4kN/m2 for the water-proof type tunnel. As the average seepage pressure is posi­ Figure 2. Division of failure surface. tively linear to the H/D ratio, the seepage pressure ratio shows little variation. The values of seepage The major steps_ involved in calculating the seepage pressure ratio during tumiel excavation calculated pressure 'are as follows. Figure 1 shows the total from numerical analyses are presented in Figure 5. head distribution around_ the tunnel face determined As shown in Figure 5, the values of the SPR were by seepage analysis and failure surface determined about 22% for the drainage type and about 28% for by limit analysis. From this figure the seepage pres­ the water-proof type and this value does not show sure could be calculated. First, divide the failure area much change with the variation of H/D ratios. into sections as shown in Figure 2 and calculate hy­ draulic head difference between the failure surface and the tunnel face in each section. Then calculate ___ Ground Surface the hydraulic gradient in each 'section and seepage .»-~-~"'-,-..-ff Q `““ 1 .... forces. By summing up all the seepage forces, the to­ <3-..-.,__,___~-~ :"-- _,___-¢:;fL":;=---.__, ::Z"'--1" 1%­ ‘ tal seepage force acting on the tunnel face can be ob­ ‘ ~E55E°’§5‘I§E5-£i€f5=;' --r""&"’ -..1-:>;=-;;:=_>~> - 3-¢:?'~;=-:°:I1":=_-¢=2°if'°"' -::‘- -:Z°-- ¢::‘~-- ' _a tained. Next, calculate the average seepage pressure H " ,==;;:-¢f1‘fE3- '- g by dividing the total seepage force by the total fail­ - ~ Groundxrrater ure area. Finally, determine the seepage pressure ra­ lE ?‘l)?..:i?‘5i£`°$»\‘:°.__ Leve ~ l. l tio, SPR that is the ratio of the average seepage pres­ sure to the hydrostatic pressure at the .same groundwater level. Q Face ’l ,_,,.,.----~---~~»..._______, 1 : gl ia"/J"“---..__ `“-~4.__ * 2.2 Example problem iNw `~"""""'~\`.. ..... ,.- i ,,.5 ....-. »-. ....,-1' The schematic diagram for modeling and obtaining the seepage forces acting on the tunnel face accord­ Figure 3. 3-Dimensional conditioni for seepage analysis. ing to the variation of the groundwater level(H) and the tunnel depth(C) is illustrated in Figure 3. The tunnel has a circular cross section with a diameter equal to 5 .0m. The properties of the ground material used for analysis are presented in Table 1. 80 - _ _ ter in the mathematical model, because hydraulic -4- C/D=2.0 head alters simultaneously with the process of exca­ » -e- C/D=3;0 vation (Goodman, 1965). 6; _ -9- C/D=4.0 E 6° " 1 3.2 Numerical' model with the consideration of exca­ -3‘3 Water-proof_ Type vation advance rate 03 “E 40 ­ Anagnostou(1993) studied the effect of the excava­ Q Drainage Type tion advance rate on the hydraulic head around the is tunnel and suggested a modified goveming equation for the groundwater flow analysis. The effect of con­ 5°I-A 20 ­ _ tinuous tunnel excavation on the piezometric head 3 <5 can be analyzed by reformulating and solving the V/ diffusion equation within a frame of reference which 0 -1 ' A | ' | ' | ' | ' | is fixed to the advancing tunnel face. The original O 1 2 3 4 5 diffusion equation is shown in equation (2). Groundwater Level Ratio, H/D dh 6 6h Figure 4. Average seepage pressure with the variation of the H/D ratio. S 5 = 5; (k E) (2) where s is the specific storage coefficient, k is the coefficient of permeability, and h is the hydraulic 100­ head. From the view of the frame of reference at the tunnel face, the hydraulic head distribution shows a -I-CUD=-2.0 § 30- -e-C/D=3.0 quasi-steady state and the original diffusion equation Q __ -6-C/D=4.0 is reformulated as equation (3) provided that the 83 tunnel axis is parallel to X, and that the ground is iso­ O.
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