A study on the tree dimensional effect of seepage force on the stability of cofferdam

A STUDY ON THE THREE-DIMENSIONAL EFFECT OF SEEPAGE FORCE ON THE STABILITY OF COFFERDAM NOVEMBER 2010 MASTER OF ENGINEERING DANG CHI LIET M095610 TOYOHASHI UNIVERSITY OF TECHNOLOGY ABSTRACT Cofferdams are temporary structures built to create dry conditions during construction in riverbeds and in the bottom of lakes With such structures, the inflow of groundwater as well as free water can be presented and these structures are designed to resist the lateral earth pressures and water pressures For excavation depths of up to 12 m the braced-sheet piled cofferdam is generally more economical than the cellular and caisson type cofferdams They are thus frequently employed during the construction of piers and abutments of bridges with medium span The collapse of cofferdams could occur due to the upward seepage force at the base even though they are designed to adequately resist the lateral thrust of the soil and water Such a failure is generally regard as boiling type or piping type of failure Sometimes a small leakage of water can initiate such a failure, which eventually leads to the sudden disintegration of the whole base Even with noticeable deformation, a cofferdam can generally be considered to perform successfully if dry condition is prevailed during the construction works and the inflow of water is smaller than the amount pumped out at the site A boiling type of failure only can be detriment to the performance of the cofferdam but also can affect the construction schedule and create changes in the design of the permanent structures During the boiling phenomenon, the upward seepage force is large enough to carry the sand and silt size particles with the discharge It is also a progressive type of failure wherein sudden flooding can occur inside the cofferdam with the continuous discharge of soil grains Thus a piping connection is made under the tip of the sheetpiles between the inside and the outside of the cofferdam Once boiling has occurred at the base floor, the original consistency, strength, and the stiffness of the natural ground is lost and this results in an inadequate bearing capacity at the base level Additionally, the influence of boiling can cause irreparable and severe damages to the ongoing construction works in the nearby structures, as well as the traffic and other human activities in the neighboring area Thus it is always important to ensure that boiling type of failures not occur in cofferdams This study aims to investigate the properly mathematical formulation of soil materials and conditions for analysis of the transient response behavior of excavation ground base subjected to upward seepage force, excess pore water pressure increasing by excavation process in cofferdam or auxiliary structures of foundation constructions in sand layer below ground water table Fundamentals of finite element method and finite element method for flow problem are also introduced in this study The program code for calculation the stability of excavation base in cofferdam which combines governing equations from the theoretical calculation of flow problem and those formulations based on finite element method for steady-state flow problem analysis is compiled The purpose in this work is also to consider the stability analysis methods of cofferdam proposed previously A detailed study was carried out to clarify the cause of boiling type of failure in braced sheetpiled cofferdam as used for the construction of bridge piers The finite element method of analysis conducted here for better understanding the seepage boiling failure phenomenon includes the seepage analysis in 2-D plane condition as well as 3-D condition An example of problem associated with boiling type of failure inside cofferdam for Daiichi-Shinkawa Bridge was introduced and the cause of the problem was adequately determined and discussed by review from the analytical results of the problem by self-resetting program based on finite element method Additionally, the author conducted a series of calculations for influence factors on boiling type failure inside cofferdam and found out general trend for the effect of each influence factors from the plots and described their relationships Furthermore, the author adequately proposed a simplified estimation method for design and check out the stability of cofferdam from the analytical results of the program code CONTENTS Chapter INTRODUCTION 1.1 General Introduction 1.2 Brief Literature Review of Previous Studies on Boiling Type Failure of Cofferdams .2 1.3 Composition of the Present Thesis Chapter THEORY OF SEEPAGE COMPUTATIONS 2.1 Darcy’s Law 2.2 Steady-State Flow Equations 2.3 Boundary Condition for Flow Problem .10 Chapter FUNDAMENTALS FOR GROUND STABILITY ANALYSIS OF COFFERDAM 3.1 Introduction 11 3.2 Finite Element Method for Flow Problem 12 3.2.1 Governing Equations for Flow Problem .12 3.2.2 Formulation of Governing Equation in Finite Element 12 3.2.3 Weak Form of Boundary Problem for Flow Behavior .15 3.2.4 Interpretation of Weak Form of Governing Equation for Flow Problem.16 Chapter A STUDY ON THE THREE-DIMENSIONAL EFFECT OF SEEPAGE FORCE ON THE STABILITY OF COFFERDAM 4.1 Design Method Used in Japan and Authorized by the Japanese Road Association .20 4.2 The Definition of Safety Factors Employed in This Study .21 4.3 Investigation of the Boiling Type of Failure inside the Cofferdam 23 4.4 Condition of the Damaged Ground 25 4.5 Investigation of the Factor of Safety 27 4.6 Parametric Investigation and Study of the Influence Factors on the boiling Type of Failure inside Cofferdam 31 -i- 4.6.1 Effect of Dimensional Analytical Condition .32 4.6.2 Effect of Depth of Permeable Layer 33 4.6.3 Effect of Excavation Area and Anisotropic Permeability Layer 34 4.6.4 Effect of Weight of Footing Construction inside Cofferdam 35 4.6.5 Summary 37 4.7 A Simplified Estimation Method for the Factor of Safety against Boiling Type of Failure 38 4.7.1 Influence Factor of Shape of Cofferdam 45 4.7.2 Influence Factor of Sheetpile Penetration Depth of Cofferdam .53 4.7.3 The effect of Depth of Excavation 60 4.7.4 The Effect of Size of Excavation 69 Chapter CONCLUSIONS AND RECOMMENDATIONS 5.1 Conclusions 77 5.2 Recommendations 77 ACKNOWLEDGEMENT 79 REFERENCES .80 - ii - LIST OF FIGURES Fig 1.1.1 Side view of new Daiichi-Shinkawa Bridge .2 Fig 2.2.1 Components of discharge velocity at six faces of an element of soil .8 Fig 4.1.1 Illustrated flow net and distribution of hydraulic potential in 2-D condition 21 Fig 4.2.1 Schematic diagram for the determination of factor of safety against boiling type of failure 22 Fig 4.2.2 Analytical condition for the determination of factor of safety against boiling type of failure 23 Fig 4.3.1 Cofferdam for Pier No of Daiichi-Shinkawa Bridge 24 Fig 4.3.2 the installation of H-pile in cofferdam 24 Fig 4.3.3 Cofferdam just after the boiling type of failure occurred was filled with muddy water flow into the cofferdam 25 Fig 4.4.1 Soil profile of the damaged ground inside the cofferdam .26 Fig 4.4.2 the elevation of the damaged ground 27 Fig 4.4.3 Damaged cofferdam from boiling 27 Fig 4.5.1 Distribution of equi-potential line from 3-D FEM analysis of cofferdam for Pier No of Daiichi-Shinkawa Bridge 29 Fig 4.6.1 Fundamental dimensions of the cofferdam employed in the parametric study 32 Fig 4.6.1.1 Influence of analytical condition on the seepage inside and around cofferdam .33 Fig 4.6.2.1 Effects of the depth of permeable layer .34 Fig 4.6.3.1 Effects of excavation area and anisotropic permeability on the seepage inside and around cofferdam 35 Fig 4.6.4.1 Effects of footing on the seepage 36 Fig 4.6.4.2 Influence of some factors on the factor of safety against boiling type of failure in the cofferdam 36 Fig 4.7.1 Parameters employed in the program for the dimensions and soil properties of cofferdam .41 Fig 4.7.2 Safety factor in cofferdam as a function of the normalized horizontal space 44 iii Fig 4.7.3 Schematic diagram of steps to analyze finding out the safety of factor for the design of cofferdam 44 Fig 4.7.1.1 Factors of safety of Fsa and Fsb as a function of aspect ratio ba/bb in fundamental case .47 Fig 4.7.1.2 Factor of safety Fsa as a function of aspect ratio ba/bb 47 Fig 4.7.1.3 Factor of safety Fsb as a function of aspect ratio ba/bb 48 Fig 4.7.1.4 Seepage pressure ratio ha/H as a function of aspect ratio ba/bb 49 Fig 4.7.1.5 Maximum upward hydraulic gradient imax as a function of aspect ratio ba/bb 49 Fig 4.7.1.6 the ratio (Fsa)rectangle/(Fsa)square as a function of aspect ratio ba/bb 50 Fig 4.7.1.7 the ratio (Fsb)rectangle/(Fsb)square as a function of aspect ratio ba/bb 51 Fig 4.7.1.8 the ratio of (imax)rectangle to (imax)square as a function of aspect ratio ba/bb 51 Fig 4.7.1.9 (ha/di)rectangle/( ha/di)square ratio as a function of aspect ratio ba/bb 52 Fig 4.7.2.1 Safety factor Fsa as a function of the penetration depth ratio di/bb 55 Fig 4.7.2.2 Safety factor Fsb as a function of the penetration depth ratio di/bb 56 Fig 4.7.2.3 Seepage force ratio ha/H as a function of the penetration depth ratio di/bb 56 Fig 4.7.2.4 Maximum upward hydraulic gradient imax as a function of the penetration depth ratio di/bb 57 Fig 4.7.2.5 Factor of safety Fsa normalized by its value as di = bb/6 as a function of the penetration depth ratio di/bb 58 Fig 4.7.2.6 Factor of safety Fsb normalized by its value as di = bb/6 as a function of the penetration depth ratio di/bb 59 Fig 4.7.2.7 Maximum upward hydraulic gradient imax normalized by its value at di = bb/6 as a function of the penetration depth ratio di/bb 59 Fig 4.7.2.8 Seepage pressure ratio ha/di normalized by its value at di = bb/6 as a function of the penetration depth ratio di/bb 60 Fig 4.7.3.1 Safety factor Fsa at the penetration depth ratio di = bb/6 as a function of excavation depth ratio (do-di)/bb 62 Fig 4.7.3.2 Safety factor Fsb at the penetration depth ratio di = bb/6 as a function of excavation depth ratio (do-di)/bb 63 Fig 4.7.3.3 Maximum hydraulic gradient imax at the penetration depth ratio di = bb/6 as a function of excavation depth ratio (do-di)/bb 64 iv Fig 4.7.3.4 Seepage pressure ratio ha/H at the penetration depth ratio di = bb/6 as a function of excavation depth ratio (do-di)/bb 64 Fig 4.7.3.5 the ratio (imax)*(bb/H) as a function of as a function of excavation depth ratio (do-di)/bb 65 Fig 4.7.3.6 the ratio (ha/di)*(bb/H) as a function of as a function of excavation depth ratio (do-di)/bb 66 Fig 4.7.4.1 Safety factor Fsa as a function of size ratio (ba/bb)i/(ba/bb)1 70 Fig 4.7.4.2 Safety factor Fsb as a function of size ratio (ba/bb)i/(ba/bb)1 71 Fig 4.7.4.3 Seepage pressure ratio as a function of size ratio (ba/bb)i/(ba/bb)1 72 Fig 4.7.4.4 Maximum hydraulic gradient as a function of size ratio (ba/bb)i/(ba/bb)1 72 Fig 4.7.4.5 the ratio ( Fsa ) (ba / b b )i /( Fsa ) (ba / b b )1 as a function of size ratio (ba/bb)i/(ba/bb)1 73 Fig 4.7.4.6 the ratio ( Fsb ) ( ba / b b )i /( Fsb ) ( ba / b b )1 as a function of size ratio (ba/bb)i/(ba/bb)1 73 Fig 4.7.4.7 the ratio (imax ) ( ba / bb )i /(imax )( ba / bb )1 as a function of size ratio (ba/bb)i/(ba/bb)1 74 Fig 4.7.4.8 the ratio ( / H ) (ba / bb )i /( / H ) (ba / bb )1 as a function of size ratio (ba/bb)i/(ba/bb)1 75 v LIST OF TABLES Table 1.2.1 was prepared for the summary of literature review Table 4.5.1 Calculation parameters for boiling type of failure in some cofferdams for bridge construction in Japan 30 Table 4.5.2 Calculation results for boiling type of failure in some cofferdams for bridge construction in Japan .30 Table 4.6.1 Analytical conditions for case study of the influence factors on boiling type of failure in the cofferdams for bridge construction 31 Table 4.7.1 Parameters using in the calculation of the effect of the dimensions of horizontal space .43 Table 4.7.1.1 Calculation results for the effect of shape of cofferdam 44 Table 4.7.2.1 Calculation results for the effect of penetration depth of sheetpile 54 Table 4.7.3.1 Calculation results for the effect of excavation depth .61 Table 4.7.4.1 Values of Shape factors, Penetration depth factors, and Reference value of seepage force and maximum hydraulic gradient .68 Table 4.7.4.1 Calculation results for the effect of excavation size 69 vi NOTATIONS γ′ - submerged unit weight of soil [L-2MT-2] γw - unit weight of water [L-2MT-2] A - base area of the soil prism [L2] aa, ab - dimensions of footing [L] ba, bb - excavation width [L] d - penetration depth of sheetpile [L] d´ - excavation depth [L] Fs - factor of safety against boiling Fsa - factor of safety against boiling derived from the balance of seepage force and gravity force on the prism of soil mass Fsb - factor of safety against boiling derived from the comparison of maximum upward hydraulic gradient of groundwater, imax with its critical value ic Gs - specific gravity of soil grains H – hydraulic potential head [L] - average groundwater potential head which correspond to the pressure applied to the bottom of the soil prism [L] ic - critical hydraulic gradient imax - maximum upward hydraulic gradient at the surface kh, kv - horizontal and vertical coefficient of permeability [LT-1] l – permeable layer thickness [L] n - porosity SPT - Standard Penetration Test U - upward seepage force acting on the soil prism [L-1MT-2] V - volume of the soil prism [L3] ν - seepage velocity [L/T] W′ - submerged weight of the prism [L-1MT-2] vii Chapter shown in Fig 4.7.2.7 and the value of Npi could be fitted by the hyperbolic equation to the trend shown as follows Npi = (imax ) 5.75 = 0.039 + d (imax ) di =bb / (1 + 30* i ) bb (4.7.3.14) To obtain the reference seepage force (ha/di)o and reference maximum hydraulic gradient (imax)o, the value of (ha/di)*(bb/H) and (imax)*(bb/H) of square cofferdam at the penetration depth di = bb/6 are calculated from the calculations results in the examination of the effect of excavation depth in section 4.7.3 and are plotted with the excavation depth ratio (do-di)/bb as shown in Fig 4.7.3.5 and Fig 4.7.5.6 And the calculation results could be fitted by hyperbolic equation to the general trend curve shown as follows From Fig 4.7.3.5, equation for the trend of (imax)*(bb/H) is shown below (imax ) *(bb / H ) = 2.968 + 1.05 d − di (1 + 1.35* o ) bb (4.7.3.15) From Fig 4.7.3.6, equation for the trend of (ha/di)*(bb/H) is shown below (ha / di ) *(bb / H ) = 3.173 + 1.09 d − di (1 + 1.4* o ) bb (4.7.3.16) The values of the derived coefficients are given in table 4.7.4.1 shown below Table 4.7.4.1 Values of Shape factors, Penetration depth factors, and Reference value of seepage force and maximum hydraulic gradient Influence factors Seepage force Shape factors Penetration depth factors ( Reference value Approach Maximum hydraulic gradient N sh = 0.889 + 0.27 b (1 + 0.6 a ) bb N si = 0.867 + N ph = 0.028 + 7.45 d (1 + 40 * i ) bb N pi = 0.039 + b ) * ( b ) = 3.173 + di H 1.09 d − di (1 + 1.4 * o ) bb - 68 - 0.58 b (1 + a ) bb 5.75 d (1 + 30 * i ) bb b (imax )*( b ) = 2.968 + H 1.05 d −d (1 + 1.35* o i ) bb Chapter 4.7.4 The Effect of Size of Excavation A series of calculations are performed in cases from the analytical conditions of the parametric investigation by changing the excavation size of cofferdam from to 10 to illustrate the effect of excavation size to the stability of cofferdam as shown in table 4.7.4.1 The calculation parameters utilized and presented in table 4.7.4.1 The factors of safety Fsa and Fsb of cofferdam are calculated by the program ‘FEMBoil3D’ according to the corresponding parameters in each case as listed in table 4.7.4.1 After that the seepage pressure ratio ha/H and the maximum hydraulic gradient imax are calculated based on Eq 4.2.2 and Eq 4.2.3 The results are also shown in table 4.7.4.1 Next, mesh drawings for those cases can be made by the program ‘ContDraw3D’ to simulate the mesh generation, equipotential line, and flow vector in x-z and y-z plane (at center line, inside, and outside of sheetpile wall), in x-y plane at sheetpile tip And then, the results for Fsa, Fsb, ha/H, and imax with the penetration depth ratio di/bb are shown in Fig 4.7.4.1 to Fig 4.7.4.4 Table 4.7.4.1 Calculation results for the effect of excavation size H 8 8 8 8 8 di do-di 6 6 6 6 6 6 6 6 6 6 ba 12 18 24 30 36 42 48 54 60 bb 12 18 24 30 36 42 48 54 60 H di do-di 10 10 10 10 10 10 10 10 10 10 ba 12 18 24 30 36 42 48 54 60 bb 12 18 24 30 36 42 48 54 60 Fundamental condition, case Fsa Fsb ha/H imax 0.99 0.99 0.754 1.008 1.17 1.22 0.642 0.819 1.28 1.38 0.588 0.727 1.33 1.46 0.562 0.684 1.36 1.50 0.551 0.666 1.38 1.53 0.543 0.653 1.39 1.55 0.538 0.647 1.39 1.55 0.539 0.647 1.39 1.54 0.541 0.649 1.38 1.54 0.543 0.651 Deeper excavation, case Fsa Fsb ha/H imax 0.57 0.59 0.698 1.705 0.67 0.72 0.594 1.388 0.73 0.79 0.551 1.264 0.75 0.82 0.535 1.216 0.75 0.83 0.530 1.200 0.76 0.84 0.525 1.186 0.76 0.85 0.524 1.183 0.77 0.85 0.518 1.171 0.77 0.85 0.519 1.172 0.77 0.85 0.519 1.173 - 69 - ha/di 1.006 0.857 0.784 0.749 0.735 0.724 0.718 0.719 0.721 0.724 (ba/bb)i/(ba/bb)1 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 ha/di 1.745 1.485 1.378 1.336 1.325 1.311 1.309 1.296 1.296 1.298 (ba/bb)i/(ba/bb)1 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Chapter H 8 8 8 8 8 di do-di 6 6 6 6 6 ba 12 18 24 30 36 42 48 54 60 bb 12 18 24 30 36 42 48 54 60 Shallower penetration depth, case Fsa Fsb ha/H imax ha/di 0.70 0.72 0.709 1.387 1.419 0.81 0.87 0.614 1.152 1.229 0.87 0.95 0.573 1.057 1.147 0.90 0.98 0.555 1.015 1.111 0.91 1.00 0.549 1.000 1.098 0.92 1.01 0.542 0.985 1.084 0.93 1.02 0.540 0.981 1.081 0.94 1.03 0.534 0.970 1.069 0.94 1.03 0.534 0.970 1.069 0.94 1.04 0.530 0.962 1.060 (ba/bb)i/(ba/bb)1 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 From Fig 4.7.4.1 to 4.7.4.2, the factor of safety tends to increase with excavation size ratio (ba/bb)i/(ba/bb)1 and converges to a certain value in the case of larger cofferdam The factor of safety in a large cofferdam is about 23-39 % higher than the safety factor in a square cofferdam ba = bb = by mean of balance of gravity force and seepage force Fsa and is about 31-55 % higher than the factor of safety of a square cofferdam ba = bb = by the method of ratio of maximum hydraulic gradient to critical gradient Fsb These figures also state that the safety factor calculated according to ‘Directions for Road and earthworks’ of JRA are much lager than by finite element method, not enough safe, sometimes boiling type failure therefore occurred as shown in table 4.5.2 Accordingly the consideration of the effect of excavation size in this study can be applied to the design of cofferdam enough conservative 1.6 case 1, JRA 1.5 Square, (ba/bb)i/(ba/bb)1 = 1.4 Safety factor, Fsa 1.3 case case case 1.2 1.1 case 3, JRA 1.0 0.9 case 2, JRA 0.8 0.7 0.6 0.5 10 11 Size ratio, (ba/bb)i/(ba/bb)1 Fig 4.7.4.1 Safety factor Fsa as a function of size ratio (ba/bb)i/(ba/bb)1 - 70 - Chapter 1.6 1.5 case 1, JRA 1.4 Safety factor, Fsa 1.3 case case case 1.2 1.1 1.0 case 3, JRA 0.9 0.8 case 2, JRA 0.7 0.6 Square, (ba/bb)i/(ba/bb)1 = 0.5 10 11 Size ratio, (ba/bb)i/(ba/bb)1 Fig 4.7.4.2 Safety factor Fsb as a function of size ratio (ba/bb)i/(ba/bb)1 From Fig 4.7.4.3 and Fig 4.7.4.4, the seepage pressure ratio and maximum hydraulic gradient are decreasing with excavation size ratio (ba/bb)i/(ba/bb)1 and also converge to a certain value in the case of a larger size cofferdam The value of seepage pressure force is ranging from 0.52 to 0.75 in this calculation in which it assumes equal to 0.50 in 2-D cases as given by the “Directions for road and earthworks” And the results show that the seepage pressure ratio in the case of large size cofferdam is about 17-21 % lower than those of the square cofferdam ba = bb = and maximum hydraulic gradient is about 35-53 % lower than those cases as well To clarify a trend of the effect of the size of cofferdam, the factor of safety, seepage pressure ratio, and maximum hydraulic gradient of larger size cofferdams are normalized by those of square cofferdam ba = bb = as shown from Fig 4.7.4.5 to Fig 4.7.4.8, respectively From this figures, obviously the same trend is found for case to case 3, in which soil condition is homogeneous The trend from this calculation can fit well with hyperbolic equation as follows: From Fig 4.7.4.5, the fitted equation for the trend of factor of safety based on balance of seepage force and gravity force of rectangular cofferdam normalized by factor of safety of square cofferdam is derived below - 71 - Chapter ( Fsa )(ba / b b )i /( Fsa )(ba / b b )1 = 1.3549 − 0.8555 (b / b ) (1 + 0.55 a b i ) (ba / b b )1 (4.7.4.1) From this trend, ( Fsa )(ba / b b )i /( Fsa )(ba / b b )1 in the case of large size cofferdam is about 33.85% higher than that of square cofferdam ba = bb = 0.85 Square, (ba/bb)i/(ba/bb)1 = Seepage pressure ratio, (ha/H) 0.80 0.75 0.70 0.65 case case case 0.60 0.55 0.50 10 11 Size ratio, (ba/bb)i/(ba/bb)1 Fig 4.7.4.3 Seepage pressure ratio as a function of size ratio (ba/bb)i/(ba/bb)1 2.0 Square, (ba/bb)i/(ba/bb)1 = Maximum hydraulic gradient, (imax) 1.8 1.6 case case case 1.4 1.2 1.0 0.8 0.6 10 11 Size ratio, (ba/bb)i/(ba/bb)1 Fig 4.7.4.4 Maximum hydraulic gradient as a function of size ratio (ba/bb)i/(ba/bb)1 - 72 - Chapter 1.50 1.45 Square, (ba/bb)i/(ba/bb)1 = 1.40 1.30 case case case 1.25 a b i a (Fsa)(b /b ) / (Fsa)(b /b ) b 1.35 1.20 (Fsa)(b /b ) /(Fsa)(b /b ) = 1.3549 - 0.8555/(1 + 0.55*x)^2 a b i a b General trend 1.15 1.10 1.05 1.00 10 11 Size ratio, x = (ba/bb)i/(ba/bb)1 Fig 4.7.4.5 The ratio ( Fsa )(ba / b b )i /( Fsa )(ba / b b )1 as a function of size ratio (ba/bb)i/(ba/bb)1 1.60 1.55 Square, (ba/bb)i/(ba/bb)1 = 1.50 1.40 case case case a (Fsa)(b /b ) / (Fsa)(b /b ) b 1.45 1.35 a b i 1.30 1.25 (Fsa)(b /b ) /(Fsa)(b /b ) = 1.4672 - 1.1252/(1 + 0.55*x)^2 1.20 General trend a b i a b 1.15 1.10 1.05 1.00 10 11 Size ratio, x = (ba/bb)i/(ba/bb)1 Fig 4.7.4.6 The ratio ( Fsb )(ba / b b )i /( Fsb )( ba / b b )1 as a function of size ratio (ba/bb)i/(ba/bb)1 From Fig 4.7.4.6, the fitted equation for the trend of safety factor based on the comparison of maximum hydraulic gradient and its critical gradient normalized by the factor of safety of square cofferdam ba = bb = is shown as follows - 73 - Chapter ( Fsb )(ba / b b )i /( Fsb )(ba / b b )1 = 1.4672 − 1.1252 (b / b ) (1 + 0.55 a b i ) (ba / b b )1 (4.7.4.2) Equation 4.7.4.2 represents an alternative method for determining the relationship between size ratio (ba/bb)i/(ba/bb)1 and safety factor Fsb for the stability analysis of large cofferdam based on a small square cofferdam ba = bb = From the general trend of this equation, ( Fsb )(ba / b b )i /( Fsb )( ba / b b )1 ratio in the large size cofferdam is about 44.18% larger than that of a small cofferdam ba = bb = 1.00 0.95 General trend (imax)(b /b ) /(imax)(b /b ) = 0.685 + 1.266/(1 + x)^2 a b i a b 0.85 0.80 case case case a b i (imax)(b /b ) /(imax) (ba/bb)1 0.90 0.75 0.70 0.65 Square, (ba/bb)i/(ba/bb)1 = 0.60 10 11 Size ratio, x= (ba/bb) /(ba/bb) i Fig 4.7.4.7 The ratio (imax )(ba / bb )i /(imax )( ba / bb )1 as a function of size ratio (ba/bb)i/(ba/bb)1 From Fig 4.7.4.7, the fitted equation for the general trend of maximum hydraulic gradient imax of large size cofferdam normalized by maximum hydraulic gradient of a small cofferdam ba = bb = as presented below (imax )(ba / bb )i /(imax )(ba / bb )1 = 0.685 + 1.266 (b / b ) (1 + a b i ) (ba / bb )1 (4.7.4.3) From this trend, (imax )(ba / bb )i /(imax )( ba / bb )1 ratio in the case of large cofferdam is about 30.64% smaller than that of a small cofferdam ba = bb = - 74 - Chapter 1.00 0.95 General trend 0.90 (ha/di)(b /b ) /(ha/di)(b /b ) = 0.7394 + 0.874/(1 + 0.83*x)^2 b i a b 0.85 case case case 0.80 a b i (ha/di)(b /b ) /(ha/di) (ba/bb)1 a 0.75 0.70 Square, (ba/bb)i/(ba/bb)1 = 0.65 10 11 Size ratio, x= (ba/bb) /(ba/bb) i Fig 4.7.4.8 The ratio (ha / H )( ba / bb )i /(ha / H )(ba / bb )1 as a function of size ratio (ba/bb)i/(ba/bb)1 Finally from Fig 4.7.4.8, the fitted equation for the general trend of seepage pressure ratio of large size cofferdam normalized by seepage pressure ratio of a small cofferdam ba = bb = is shown below (ha / H )(ba / bb )i (ha / H )(ba / bb )1 Equation 4.7.4.4 shows = 0.7394 + that by 0.874 (b / b ) (1 + 0.83 a b i ) (ba / bb )1 associating (4.7.4.4) correction factor (ha / H )( ba / bb )i /(ha / H )(ba / bb )1 dependent on size ratio (ba/bb)i/(ba/bb)1 is used for the stability analysis of large-rectangular cofferdam based on the point of view of consideration of small cofferdam ba = bb = The general trend of this equation the ratio (ha / H )( ba / bb )i /(ha / H )(ba / bb )1 in the case of large size cofferdam is about 25.29% higher than that of a small cofferdam ba = bb = To estimate the value of Fsa, Fsb, ha/H, and imax for a cofferdam to take into account the effect of excavation size of cofferdam, it is needed to know the value of Fsa, Fsb, ha/H, and imax of small cofferdam at ba = bb = Therefore, more calculation can be - 75 - Chapter done to notice the effect of excavation size to the factor of safety, seepage pressure ratio, and maximum hydraulic gradient of square cofferdam at size ba = bb = Size factor can be defined Nzh from the examination of the effect of excavation size of cofferdam The value of ha/di normalized by its value ha/di at ba = bb = is calculated from the results of the study of effect of excavation size and is plotted as shown in Fig 4.7.4.8 Then, we could get size factor Nzh from this plot Nzh = (ha / H )(ba / bb )i (ha / H )( ba / bb )1 = 0.7394 + 0.874 (b / b ) (1 + 0.83 a b i ) (ba / bb )1 (4.7.4.5) Additionally, the value of Nzi is probably obtained from the plot of maximum hydraulic gradient imax normalized by maximum hydraulic gradient imax at size of excavation of ba = bb = as shown in Fig 4.7.4.7 and the value of Nzi could be fitted by the hyperbolic equation to the trend shown as follows Nzi = (imax )(ba / bb )i (imax )( ba / bb )1 = 0.685 + 1.266 (b / b ) (1 + a b i ) (ba / bb )1 (4.7.4.6) Therefore equations 4.7.3.7 and 4.7.3.8 can be rewritten as ha/di = (ha/di)0*Nzh*Nph and; imax = (imax)0*Nzi*Npi (4.7.4.7) (4.7.4.8) From empirical formulae as given in equations 4.7.4.7 and 4.7.4.8, the effect of excavation size, sheetpile penetration depth, excavation depth, excavation area, and the depth of impermeable layer are combined together And the safety factors of cofferdam are calculated according to equations 4.7.3.5 and 4.7.3.6 - 76 - Chapter Chapter CONCLUSIONS AND RECOMMENDATIONS 5.1 Conclusions The results of this study show that the effect of analytical condition is substantial; the factor of safety obtained from 3-D condition is much lower than that proposed by the ‘Directions for Road and Earthworks’ Thus, the parametric study is extended in 3-D condition And a simplified estimation method has been derived by empirical formulae based on the parametric investigation influent on the stability within cofferdam Some comments are given here: • The factors of safety tend to increase with respect to aspect ratio ba/bb and converge to a certain value in the case of long cofferdam • The factors of safety increase with the penetration depth ratio di/bb and the relationship is roughly linear • The difference in the factors of safety between different impermeable layer depths is relatively small but when the sheetpile penetrate close to impermeable base, the factor of safety is dramatically increased • The factors of safety decrease with the excavation depth ratio (do-di)/bb with more or less the same seepage pressure ratio acting to the soil prism • The safety factors tend to rise up with respect to size ratio (ba/bb)i/(ba/bb)1 and converge to a certain value in the case of larger cofferdam • From the results of parametric study, the simplified estimation method the factor of safety for design cofferdam by using empirical formulae is presented The method can be applied for the range of ba/bb between to 15, di/bb between 1/6 to 1.8, (do-di)/bb between to 1.6, and (ba/bb)i/(ba/bb)1 between to 10 • The simplified estimation method in this study is based on 3-D seepage which is more realistic and more conservative than method proposed by the ‘Directions for Road and Earthworks’ which the required factor of safety is 1.5, thus, in the design, lower factor of safety can be employed - 77 - Chapter 5.2 Recommendations In the design of temporary structure such as cofferdam, this type of simplified estimation approach is probably convenient for the estimation of factor of safety It is recommended for a future research to extend this type of simplified estimation method for other types of structure such as double wall type cofferdam But in the case of permanent structure, more sophisticated method such as finite element method is recommended in the design to account on the effect of non-uniform boundary condition, non-homogeneous condition of soil such as layered soil, interaction between soil and sheetpile regarding deformation and failure, etc - 78 - ACKNOWLEDGEMENT ACKNOWLEDGEMENT I would like to express my sincere gratitude to Professor Kinya Miura of Toyohashi University of Technology for his invaluable guidance and support to my research I also wish to express my deep gratitude to Professor Makoto Kawamura for his extremely valuable advice I wish to express special thanks to Dr Shingo Morimasa for his valuable suggestion in many part of this study I believe that this work could not be done well without their help of members of the GeoMechanics Groups, Toyohashi University of Technology I am also grateful to Mr Yusuke Uchikura helped various aspect of this study and my life I am also grateful to all professors of Architecture and Civil Engineering Department for their useful lectures and friendly comments My sincere thanks wish to express to university staffs for their kind assistance I wish to express my deep acknowledgement to OSG Scholarship Foundation for their financial support to my research Last but not least, I would like to express respect to Mr Kim Chay, my contemporary, for his encouragement and valuable advices in all aspect of my work and school life - 79 - REFERENCES REFERENCES Bazant, Z (1963) “Ergcbnisse der Berechnung der Stabilitat gegen Hydraulischen Grundbruch mit Hilfe der Elektronen Rechenanlage.” (In German), Proceedings, International Conference on Soil Mechanics and Foundation Engineering, Budapest, 215-223 Bauer, G E., (1973) “Water and seepage pressure considerations on sheeted cofferdams.” Proceedings, First Hydraulics Conference, Edmonton, 483-502 Bauer, G E., Scott, J D., Shields, D H (1978) “Basal failure of a deep sheeted excavation in sand.” Proceedings, Thirty first Canadian Geotechnical Conference, Winnipeg, 483-502 Bauer, G E., Scott, J D., Shields, D H., and Wilson, N E (1980) “The hydraulic failure of a cofferdam.” Canadian Geotechnical Journal, 17(4), 574-583 Benmebarek, N., Benmebarek, S., Kastner, R (2005) “Numerical studies of seepage failure of sand within a cofferdam.” Computers and Geotechnics, Vol 32, P.264-273 Dividenkoff, R N., and Franke, O L (1965) “Untersuchung der raumlichen Sickerstromung in cinc umspundete Baugrube in offenen Gewassern.” (In German), Die Bautechnik, 9, pp 298-307 Furukawa, M., Ido, K., Miura, K and Imafuku, M (1993) “Anisotropy of permeability of sand deposits.” Twenty-eighth Annual Meeting of JGS, 2225-2228 (in Japanese) Furukawa, M., Miura K., Ido, K and Imafuku, M (1993) “Measurement and analysis on seepage force inside the double sheetpile cofferdam for bridge footing.” Twenty eighth Annual Meeting of JGS, 2267-2270 (in Japanese) Griffiths, D V (1994) “Seepage beneath unsymmetric cofferdams.” Geotechnique, 44(2), 297-305 10 Imafuku, M., Ikeda, K and Ohtomo, T (1991) “A proposal for the safety construction works in the cofferdam for bridge pier.” Thirty fourth Technical Meeting of Hokkaido Development Bureau, Session on 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sheeted excavations.” Canadian Geotechnical Journal, 7, 136-144 18 Miura, K., Imafuku, M., Furukawa M., and Nagasawa, M.: "Ground Failure due to Seepage Force in River Cofferdams," JGS, Tsuchi-to-Kiso, Vol.47, No 4, pp.7-10, (1999), in Japanese 19 Richart, F E., Jr., and Schmertmann, J H (1957) “The effect of seepage on the stability of sea walls.” In Selected papers from Proceedings, Sixth Conference on Coastal Engineering, Florida Engineering and Industrial Experiment Station, Bulletin Series, 101, 105-126 20 Tanaka T (2002) “Boiling occurred within a braced cofferdam due to twodimensionally concentrated seepage flow.” In the 3rd international symposium, geotechnical aspects of underground construction in soft ground, Toulouse, France, p.33-40 21 Japanese Road Association (1976) ‘Directions for Road Earthworks – Retaining Wall, Culvert and Temporary Structures’, 240-242 (in Japanese) 22 JGS (1985): Thesaurus for Geotechnical Engineering, 106-107 (in Japanese) 23 Terzaghi, K (1943) Theoretical soil mechanics, John Wiley and Sons, New York, NY, 257-261 - 81 - REFERENCES 24 Terzaghi, K., Peck, R B., Mesri, G (1996) Soil mechanics in engineering practice, John Wiley and Sons, New York, NY, 222-223 25 Teng, W C (1962) Foundation design, Prentice-Hall, Englewood Cliffs, N.J., 389391 - 82 - ... square base Fig 4.6.1 Fundamental dimensions of the cofferdam employed in the parametric study 4.6.1 Effect of Dimensional Analytical Condition The effect of the analytical conditions on the seepage. .. A STUDY ON THE THREE -DIMENSIONAL EFFECT OF SEEPAGE FORCE ON THE STABILITY OF COFFERDAM In this chapter, a method for estimating the three -dimensional seepage force in cofferdam is described Then,... the cofferdam analysis problem The consideration of balance of gravity force on the prism of soil mass adjacent to sheetpile and seepage force was also determined having the relationship to the