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Research on soil pressure in nine cabins of opened bottom elliptical barrel structure using penetration of negative pressure method
Acta Mechanica Solida Sinica, Vol. 28, No. 5, October, 2015 Published by AMSS Press, Wuhan, China
ISSN 0894-9166
RESEARCH ON SOIL PRESSURE IN NINE CABINS OF OPENED BOTTOM ELLIPTICAL BARREL STRUCTURE USING PENETRATION OF NEGATIVE PRESSURE METHOD⋆⋆ Xiaozhong Zhang⋆ (School of Civil and Architectural Engineering, Guizhou University of Engineering Science, Bijie 551700, China)
Received 22 March 2013, revision received 6 April 2015
ABSTRACT An investigation is made on the soil pressure in a nine cabin opened bottom elliptical barrel structure. The calculation models using the penetration of negative pressure method have been developed. The first calculation model is is for the construction stage involving three zones, namely, passive, transitional, and active established for the soil pressure in cabins. The other calculation model is based on the use stage, with the two (passive and active) zones for the soil pressure in cabins. The height of zones and the theoretical analytical solutions of inner soil pressure are derived. The analytical formulas of the models are proved using the finite element method and experimental data, and the formulas are analyzed in the inner soil pressure in the same condition. The calculation models can be used for other multi-position structural design or construction.
KEY WORDS opened bottom elliptical barrel structure, soil pressure, calculation, passive zone, transitional zone, active zone
I. INTRODUCTION As a special structure, an opened bottom elliptical barrel structure with nine cabins is composed of a reinforced concrete elliptical barrel structure and a bottom protection stone. The special structure is composed of an elliptical barrel bottom and two upper cylindrical barrels. The bottom barrel is elliptical in shape and with nine cabins, the upper barrels being joined by ring beam with bottom barrel. The shape of the special structure is shown in Fig.1. The opened bottom elliptical barrel structure with nine cabins can directly be inserted into soft soil as a convenient construction, which can be applied in a variety of complex conditions. This structure has good prospects for application for its ability to reduce the construction period and construction costs. However, the special structure is greatly limited for lack of theoretical support. In particular, the mechanism of the inner soil and the structure duting normal work is yet unclear. Many core issues of the mechanism need to be further studied. The inner soil pressure in the special structure is the most important technical issue for structural stabilization and normal operation[1–3] indispensable to accurate calculation of the inner pressure of the structure for improvements of the design and construction method. As soil pressure within the structure is related to the structural ⋆
Corresponding author. E-mail: [email protected] Project supported by Open Fund Project of Hunan Province Research Center for Safety Control Technology and Equipment of Bridge Engineering (Changsha University of Science & Technology) (No. 13KC05). ⋆⋆
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stability analysis and foundation settlement, this article focuses on the inner soil pressure calculation model for different stages, the research results could provide a scientific reference for multi-compartment structures. The inner soil pressure of large cylindrical structures has been studied by many researchers, who proposed different methods for calculating the inner soil pressure for the special structure. The inner soil pressure for single-cabin researched by some scholars[4, 5], which was divided into three zones according to the angle of internal friction of soil. The inner soil pressure is divided into three zones from top to bottom based on model calculation[6–9] . The inner soil pressure of opened bottom cylindrical structure has approximately been calculated using active soil pressure and Yeung Sum formula by some researchers[10, 11]. The calculation model of inner soil pressure is developed using foundation soil for transmission media of inner and outside soil pressure[12] . The empirical formulas of calculating inner soil pressure for single-cabin cylindrical structures are given according to the experimental data. Shen et al. analyzed the influence on the working performance of the cylindrical bucket foundation structure by the soil consolidation. They developed a three-dimensional elastic-plastic structure-soil interaction finite element model to obtain the variation trend under consolidation of the soil pressure on the cylinder wall[4] . Xiao and Wang established a model based on the Lanczos method for the system of bucket foundation breakwater and soil foundation. The result showed that inner soil pressure was an important factor in structural stability[6] . Previous studies only considered the diameter of cylinder and the friction angle of soil. In addition, there are many other Influencing factors such as the load applied on the structure, the weight and the compressibility of soil, the coefficient of foundation deformation and reaction force. Meanwhile, the soil pressure was defined barely from test data. The conclusions lack a theoretical basis[13–16] . The finite element method and theoretical analysis were used to produce a three dimension Elastic-plastic mechanical model of basal soil at the bottom of a large cylindrical structure, which was used to calculate the inner soil pressure[17–21] . The soil pressure under axisymmetric vertical loading was divided into two zones[22–25] . The stability of the opened bottom elliptical barrel structure with nine cabins was better compared with the large cylindrical structure. It is found by experiment that, the inner soil pressure of the special structure under axisymmetric vertical loading was divided into three zones: active zone, transitional zone and passive zone. However, under horizontal loading, it was only divided into two zones: active zone and passive zone. In order to accurately describe the characteristics of inner soil of the structure, the inner soil pressure calculation models of three areas in the construction stage and two areas in the use stage were established based on experimental results. The theoretical analytical solutions of inner soil pressure and the height of every zone for construction stage and use stage were derivedand the validity of the model was demonstrated under a same working condition.
Fig. 1. Structure with elliptical barrel.
II. CALCULATION MODEL IN CONSTRUCTION STAGE In the construction stage, the inner soil pressure calculation model is shown in Fig.2. The pressure of soil is divided into three zones which are active zone, transitional zone and passive zone respectively. The demarcation point of the three zones are y = h0 and y = h1 as shown in Fig.2. Parameters of the model are as follows. The height of the barrel is H. The cross-sectional area of the barrel is F . The cross-sectional area of the barrel wall is F ′ . The perimeter of the contact area between the soil and the
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Fig. 2. Calculation model in construction stage.
bucket wall is u.The unit weight of the soil is γ. The unit weight of the barrel wall is γ ′ . The compression modulus of soil is ES . Since there is a cover plate at the bottom of the barrel, the gravity of the cover plate and the gravity above it are acting upon the padding and the barrel wall evenly. The even load is q. The foundation support upon the padding is σ. The foundation support under the barrel wall is σ ′ . The lateral pressure coefficient of the barrel wall is K. The frictional factor between the soil and the bucket wall is f . The coefficient of deformation for the foundation of the barrel bottom is ks . A differential thin element is taken at y in the barrel, as is shown in Figs.3, 4 and 5.
Fig. 3. Calculation unit of soil pressure in active zone.
Fig. 4. Calculation unit of soil pressure in passive zone.
Fig. 5. Calculation unit of soil pressure in transitional zone.
2.1. The Soil Pressure in the Active Zone In the active zone, the loading of the differential thin element is shown in Fig.3. The forces on it are as follows: the vertical pressure on the element is pyz , the vertical counter-force at the bottom is pyz + dpyz . The friction between the padding and the barrel wall is pxz f = Kf pyz . The gravity of the differential thin element is γ. According to the equilibrium of forces, we can get dpyz u = γ − Kf pyz (1) dy F Equation (1) meets the boundary conditions: y = 0, pyz = q. By solving the differential equation, we can get uKf uKf γF pyz = 1 − e− F y + qe− F y (2) uKf The friction of the barrel wall is uKf uKf γF f pxz = 1 − e− F y + Kf qe− F y (3) u
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In the equation, lateral pressure coefficient K = 1 − sin ϕ. ϕ is internal friction angle. f is the frictional factor between the soil and the barrel wall, and f = tan δ. δ is the normalized value between the soil and the barrel wall, and δ = 2ϕ/3. 2.2. The Soil Pressure in the Passive Zone In the passive zone, the loading of soil is shown in Fig.4. The calculation is the same as that for the active zone, the equilibrium equation being u dpyb = γ + Kf pyb (4) dy F In Eq.4, the boundary condition is met: y = H, pyb = σ, where b represents the passive zone. By solving the differential equation, we can get i uKf uKf γF h pyb = − 1 − e− F (H−y) + σe− F (H−y) (5) uKf The frictional force of the barrel wall is i uKf uKf γF h f pxb = − 1 − e− F (H−y) + Kf σe− F (H−y) (6) u 2.3. The Inner Soil Pressure of the Transitional Zone In the transitional zone, the loading of soil is shown in Fig.5. The calculation is the same as that for the active zone, the equilibrium equation being dpyg =γ (7) dy where g represents the transitional zone. After integration, we can get pyg = γy + A (8) In the equation above, A is a constant. 2.4. The Determination of the Interface of the Three Areas At the interface between the active zone and passive zone, pyz = pyg . According to Eqs.(2) and (8), we can get uKf uKf γF 1 − e− F h0 + qe− F h0 = γh0 + A (9) uKf At the interface between the passive zone and transitional zone, pyb = pyg . According to Eqs.(5) and (8), we can get i uKf uKf γF h − 1 − e− F (H−h1 ) + σe− F (H−h1 ) = γh1 + A (10) uKf From Eqs.(9) and (10), we can get uKf 2γF γF γF − uKf (H−h1 ) F − + +σ e + − q e− F h0 − γ(h1 − h0 ) = 0 uKf uKf uKf According to the equilibrium of forces for the soil in the vertical direction, we can get Z h0 Z H Fσ − Fq + pxz f udy − pxb f udy − γHF = 0 0
(11)
(12)
h1
γ is the effective unit weight. According to Eqs.(3), (6) and (12), we can get uKf 2γF 2 γF 2 γF 2 − uKf h 0 − + γF (h0 − h1 ) + − Fq e F + + F σ e− F (H−h1 ) = 0 uKf uKf uKf According to Eqs.(11) and (13), we can get h0 and h1 .
(13)
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2.5. The Counter-Force of the Foundation Since the soil at the bottom is mollisol, according to the Winkler foundation model, the foundation settlement of the bottom soil S and the foundation settlement of the bottom of the barrel wall S ′ are as follows: σ σ′ S = , S′ = (14) ks ks where ks represents the stiffness of soil. According to the deformation coordination condition, the decrement of the passive zone is the difference between foundation settlement of the bottom of the barrel wall and the foundation settlement of the bottom soil in the cabin. Which means: ∆ = S′ − S =
σ′ σ − ks ks
(15)
Considering the soil in the cabin and the barrel as a whole, according to the force equilibrium condition, we can get F F (16) σ ′ = q + γ ′ H + ′ (q + γH) − ′ σ F F According to Eqs.(15) and (16), we can get σ=q+
H F′ ′ ′ (F γ + F γ) − ks ∆ F + F′ F + F′
(17)
The decrement of the passive zone can be calculated by soil mechanics formula (Terzaghi onedimensional consolidation theory): h Z H i uKf 1 F γF 1 γF (H−h1 ) F pyb (y)dy = +σ 1−e (H − h1 ) (18) ∆= − ES h1 ES uKf uKf uKf According to Eqs.(11), (13), (17) and (18), we can work out the counter-force of the soil mass in the cabin and counter-force of the barrel wall.
III. CALCULATION MODEL IN THEUSE STAGE The opened bottom elliptical barrel structure with nine cabins is subjected to horizontal wave force during the use stage. It will tilt under a horizontal load, which will destroy the pressure distribution of the soil under a vertical load. Then the inner soil pressure needs to be analyzed further. 3.1. Calculation Model The opened bottom elliptical barrel structure with nine cabins is subjected to horizontal wave force as well as vertical load. According to model experiment, the soil and the barrel will move around point C under horizontal wave force (Fig.6). Point C is between the right ribbed plate and central shaft[15] . The transitional zone in the cabin is not obvious, and only active zone and passive zone are left. The height of the right side of the active zone is h0r , and the height of the left side of the active zone is h0l . As shown in Fig.6, the soil in the cabin is subjected to vertical load q and horizontal force PC . The horizontal pressure force of the barrel wall on the inner soil is Ph . The frictional resistance of the barrel wall to the soil mass is τ . The horizontal shearing force is T . The counter-force of the bottom is σ. The distance from the axis of rotation to the structure center is a. 3.2. The Determination of Rotational Axis The location of the rotational axis is related to horizontal force, and the calculation model under horizontal force is shown in Fig.7. The counter-force of the barrel bottom is supported by the right side of the rotational axis and distributed linearly on the right side. The frictional resistance of the barrel wall o the soil is balanced in the vertical direction and, according to the balance of the vertical load, we can get γHF − Pσ = 0
(19)
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Fig. 6. Calculation models of soil pressure in use stage.
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Fig. 7. Calculation model of soil pressure for horizontal force.
In the equation above, Pσ is the resultant force of the foundation support and a function of unknown quantities a and σy max . Taking moments about O , we can get MPC − MG − Mσ − Mτ = 0
(20)
In the equation above, MPC is the moment of the wave force about O, and a given value. MG is the moment of soil gravity about O, and it is the function of unknown quantities a. Mσ is the moment of soil reaction force at the bottom about O, and a function of unknown quantities a and σy . Mτ is the moment of friction resistance about O, and a function of unknown quantity a. According to Eqs.(19) and (20), we can obtain the value of a and of σy max . 3.3. The Reactionary Force at the Barrel Bottom in the Use Stage The calculation model is shown in Fig.6, and according to the force equilibrium in the vertical direction, we can get qF + γHF − Pσs = 0 (21) In the equation above, Pσs is the resultant force of foundation support and a function of unknown quantities σmin and σmax . Taking moments about O , we can get MPC − MG − Mσs − Mτs − Mqs = 0
(22)
In the equation above, Mσs is moment of soil reaction force at the bottom about O in use stage and a function of unknown quantities σmin and σmax . Mτs is the moment of friction resistance about O in use stage. Mqs is the moment of vertical load about O in use stage. According to Eqs.(21) and (22), we can get the value of σmin and σmax . 3.4. The Inner Soil Pressure in the Cabin in Use Stage In the active zone, we can apply formula (2) since the condition is the same. psyz =
uKf uKf γF 1 − e− F y + qe− F y uKf
(23)
psyz is the soil pressure of any point in the active zone. In the passive zone, the forces are shown in Fig.4. The calculation is the same as that for the active zone, and the equilibrium equation is Eq.(4). On the left side, y = H, psyb = σmin , we can get the
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pressure stress of the soil at any point on the left side in the passive zone by solving the differential equation. i uKf uKf γF h 1 − e− F (H−y) + σmin e− F (H−y) psybl = − (24) uKf s pyzl is the pressure stress of the soil at any point on the left side in the passive zone. On the right side, y = H, pyb = σmax , so we can get the pressure stress of the soil at any point on the right side in the passive zone by solving the differential equation. i uKf uKf γF h 1 − e− F (H−y) + σmax e− F (H−y) psybr = − (25) uKf psyzr is the pressure stress of the soil at any point on the right in the passive zone. In the middle area,, the calculation is to be made according to linear interpolation. On the left side, the following equation will be met on the interface between active zone and passive zone. According to Eqs.(23) and (24), we can get q − uKf F H 1 + 1 − [1 − ukf /(γF )q][1 + ukf /(γF )σ ]e min F ln h0l = H + (26) uKf 1 + ukf /(γF )σmin
h0l is the height of active zone of the soil in the cabin on the left side. According to Eqs.(23) and (25) we can get the height of active zone of the soil in the cabin on the right side. q − uKf F H 1 − [1 − ukf /(γF )q][1 + ukf /(γF )σ ]e 1 + max F (27) ln h0r = H + uKf 1 + ukf /(γF )σmax
h0r is the height of active zone of the soil in the cabin on the right side. The calculation of interface in the middle area is to be made according to linear interpolation. The pressure stress of the soil in the cabin is to be dealt with according to Eqs.(23), (24) and (25). The height of passive zone and active zone is calculated according to Eqs.(26) and (27).
IV. THE CARRYING CAPACITY FOR THE FORMER SITE The checking computation of carrying capacity for the bottom is the main leading indicator which guarantees that the structure meets the working performance, as is shown in Fig.8. In the use stage, the local stress of the former site is the maximum stress of the whole structure, which needs checking computation. According to Eq.(16) , we can calculate the maximum stress σ ′ on the former site when the structure is under gravity. According to Eqs.(19) and (20), we can calculate the maximum stress σy max at y = H when the structure is under a horizontal load. The maximum stress at the bottom of the former site is σmax = σ ′ + σy max
(28)
The allowable bearing capacity of the bottom is determined by the eigenvalue of the bearing capacity according to the shearing strength index. fa = fak + ηd γ(b − 3) + ηb γm (d − 0.5)
(29)
In the equation above: fak = Mb γx b + Md γm d + Mc c, fak is the eigenvalue of the bearing capacity for the foundation soil, and Mb , Md , MC are bearing capacity factors, whose values are in accord with the Code for design of buildings; b is the width of the bottom of foundation; c is normalized value of the cohesion in the depth range including the width of the short side; γx is the natural gravity of the soil under foundation; γm is weighted average gravity of the soil above foundation, and the gravity of soil under ground water level is floating gravity; fa is revised eigenvalue of the bearing capacity for the foundation soil; ηb , ηd are correction factors of bearing capacity of the foundation soil in the width and depth of the foundation; d is the buried depth of the foundation. The carrying capacity of the foundation should satisfy the following equation: σmax ≤ fa
(30)
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Fig. 8. The reaction forces of elliptical barrel structure.
V. VERIFICATION OF CALCULATION According to survey and design information[15] , the following working conditions are to be met for computational analysis. The barrel below is completely immersed in the soil , and the elevation of the mud surface is ∇ − 5.5.0 m. The elevation of the barrel bottom is ∇ − 13.18 m. The cover plate on the mud surface is ∇0.38 m meters in depth. As for the upper barrel, the elevation of the barrel top is ∇11.5 m, and the elevation of the barrel bottom is ∇ − 5.6 m. The extremely high water level before the barrel is ∇7.21 m. The barrel is reinforced concrete structure, as is shown in Fig.1(b). The wave load is shown in Table 1, in which H1% represents the maximum wave height, T represents the wave period. Table 1. The parameters of wave
Design level Extreme high water level 6.56 m Extreme low water level −0.68 m
H1% (m) 6.72 2.82
T (s) 8.76 8.76
Wave length (m) 84.1 57
Direction ES ES
5.1. Numerical Simulation Analysis in the Construction Stage The values of h0 and h1 for the soil in the cabin in the construction stage and the counter-force of the barrel bottom are calculated by Eqs.(11), (12) and (13). The calculation results are shown in Table 2 and Fig.9. Table 2. The calculating results in construction stage
Items Computational results of the formula in this paper Numerical results Experiment results[15] Computational results[12]
h0 (m) 5.270 5.321 5.178 5.667
h1 (m) 6.337 6.415 6.225 6.577
σ (kPa) 97.325 105.363 95.480 110.675
σ ′ (kPa) 148.657 155.761 137.431 176.324
The model is shown in Figs.10 and 11, In order to reflect the model of the soil structure truly, the soil depth is 5 times as large as the cylinder structure height, and the soil width is 5 times as large as the cylinder structure diameter. The soil constitutive model can rationally reflect the Mohr-Coulomb and Drucke-Prager elastic-plastic model of the nonlinear elastic-plastic soil. The contact surface between barrel and soil is highly nonlinear in order to simulate the discontinuous nonlinear phenomena, such as real slide, detachment on the contact surface between barrel and soil. The contact surface is set on the surface between soil and structure in order to overcome the disadvantage of the twisting gridding inability to reflect the real condition. The type of soil element is C3D8R, the number of elements is 29020, the number of nodal points is 32942. The type of construction unit is C3D8RC3D4, and the
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number of elements for a single barrel is 16031. The number of nodal points is 6640. The total element number is 45051, and the number of nodal points is 39582. The material parameter values are as follows: The soil parameter for each layer is shown in Table 3. The opened bottom elliptical barrel structure is reinforced concrete C30, and its density is 2500 kg/m3 . The modulus of elasticity E = 3.0 × 104 MPa. The Poisson’s ratio is 0.167. The frictional factor of the contact surface is as follows: The frictional factor of the contact surface between the barrel top and soil is 0.04. The frictional factor of the contact surface between the barrel side and first soil layer is 0.04. The frictional factor of the contact surface between the barrel side and second soil layer is 0.2. The boundary conditions are as follows: The horizontal plane displacement of boundaries around the foundation soil are zero, and the displacement for the bottom is zero in three directions. Table 3. Parameters for soil
The first soil layer The second soil layer The third soil layer The fourth soil layer
Cohesion (kPa) 7 39 18 32
Friction angle (◦ ) 2.5 11.3 6.2 6.2
Modulus of compression (MPa) 1.67 5.08 2.85 7.9
Poisson’s ratio 0.4 0.35 0.35 0.35
The numerical calculation results of the soil pressure in the cabin in the construction stage is shown in Fig.12. The soil pressure in the cabin is divided into three areas, the active zone, the passive zone and the transitional zone. The basis stress under the barrel wall is obviously larger than the basis stress in the cabin. The specific height of the three areas and the specific results of the basis stress are shown in Table 2. The calculation results of the model in the paper are most close to experimental results.
Fig. 9. The pressure of soil in construction stage (unit: kPa).
At the same time, vertical distribution of the soil pressure in the cabin is shown in Fig.9. The calculation results of the model in the paper are most close to experimental results, which confirms the correctness of the soil pressure calculation model in the construction stage in this paper, and the soil pressure calculation model has higher accuracy than empirical formula and numerical simulation results. 5.2. Numerical Simulation Analysis in the Use Stage The calculation of soil pressure in the use stage is the same as that with the construction stage. Computational analysis including analytic solutions, arithmetic solution, and empirical equation is
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Fig. 10. Finite element model of elliptical barrel structure.
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Fig. 11. Finite element model of soil with structure.
Fig. 12. Numerical results of soil pressure in construction stage.
carried out for the elliptical barrel structure under the same working condition, with the results compared with model experiment results. The height of the active zone and the passive zone and the maximum basis stress are calculated, as is shown in Table 4 and Fig.13. Table 4. Results in use stage
Items The results calculated by the formula in the paper Numerical results Experiment results[15] Results using empirical formula[12]
h0l (m) 7.656 7.539 7.452 7.647
h0r (m) 6.342 6.278 6.348 6.37
σmax (kPa) 291.554 293.464 302.756 /
The soil pressure in the cabin is divided into two areas, the upper area and the bottom area in Fig.14, which confirms the correctness of the division of two areas in the soil in the use stage. The contact surface between active zone and passive zone is an inclined surface, which is constant with the model in the paper (Fig.6). The specific height of the two areas and the specific results of the basis stress are shown in Table 4. The calculation results of the model in the paper are most close to experimental results after comparison. At the same time, vertical distribution of the soil pressure(right side) in the cabin is shown in Fig.13. The calculation results of the model in the paper are most close to experimental results, which confirms the correctness of the soil pressure calculation model in the use stage in the paper, and the soil pressure calculation model has higher accuracy than empirical formula and numerical simulation results. 5.3. The Carrying Capacity for the Former Site The carrying capacity for the former site is calculated according to formula (28) for the opened bottom elliptical barrel structure. And the numerical calculation method, gravity structure calculation method and model experiment method are adopted for comparison. The calculation results are shown
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in Table 5. The carrying capacity calculated by each method can meet the demand of the structure, but the results obtained with the gravity structure calculation method are different from model experiment results, which shows gravity structure calculation method is not suitable for nine cabins opened bottom elliptical barrel structure. The calculation results of the model in the paper are most close to experimental results, which confirms the correctness and high accuracy of the calculation model in the construction stage in the paper.
Fig. 14. Numerical results of pressure of soil in cabin in use stage. Fig. 13. The pressure of soil with cabin in use stage (right) (unit: kPa).
Table 5. Computation of the carrying capacity of the former site (kPa)
The results calculated by the formula in the paper Stress of the former site 325.64 Allowable bearing capacity of the basis
Gravity structure calculation method 301.47 fa = 411.608 kPa
Numerical results 332.78
Experiment results 323.57
VI. CONCLUSIONS The inner soil pressure calculation model of opened bottom elliptical barrel structure is confirmed. In the construction stage, the inner soil pressure is divided into three areas: active zone, passive zone and transitional zone, and the interface between areas is almost a horizontal plane. In the use stage, the inner soil pressure is divided into two areas: active zone and passive zone, and the interface between areas is not horizontal but oblique. Furthermore, the active zone on wave side is smaller than that on the lee-side. The calculation results of the model in the paper are closer to experimental results and numerical simulation results than the calculation results by the empirical formula.
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[6] Xiao,Z. and Wang,Y.Z., Finite element analysis for dynamic stability of bucket foundation breakwater. Journal of Transport Science and Engineering, 2014, 30(4): 65-72. [7] Li,W., Study and application of plug-in breakwater structure with bucket-box foundation. Tianjin Science & Technology, 2011, 2: 30-32. [8] Zhang,X.Z., Yao,W.J. and Cheng,Z.K., Settlement analysis of multi-barrel structure warehouse using penetration of negative pressure method in construction stage. Journal of Chang’an University (Natural Science Edition), 2015, 35(1): 91-97. [9] Liu,J.Q., Calculation of settlement and filler pressure on open cylinder. Port Engineering Technology, 1999, 4: 11-16. [10] Liu,J.Q., Deformation of large-diameter cylindrical buried structures. Chinese Journal of Geotechnical Engineering, 1994, 16(2): 64-72. [11] Shu,X.W., Bie,S.A. and Wang,C.S., Force mode and reasonable scale of breakwater structure with bucketbox foundation. Journal of Tianjin University, 2012, 45(8): 700-707. [12] Liu,J.Q. and Meng,X.J., Evaluation of inner soil pressure on opened bottom cylindrical structure. China Ocean Engineering, 2004, 18(1): 21-34. [13] Xiao,Z., Wang,Y.Z. and Ji,C.N., Stability analysis of semi-circular breakwater on soft foundation under combined loading. Rock and Soil Mechanics, 2014, 35(3): 789-794, 800. [14] Liu,J.Q., Chen,B. and Wang,H.Y., Determination of the critical value of deflection for embedded cylindrical structures. China Ocean Engineering, 2005, 19(3): 37-40. [15] Xu,W., Lianyungang Port breakwater cross-section of tube-type structure model test report. Shanghai: CCCC Third Harbor Consultants Co. Ltd., 2011. [16] Leavachif,C.H., Application of Thin Shell in Hydraulic Constructions. Beijing: The People’s Communications Publishing House, 1982. [17] Chen,W.J., Port Engineering. Beijing: The People’s Communications Publishing House, 1989. [18] Hung,L.C. and Kim,S.R., Evaluation of vertical and horizontal bearing capacities of bucket foundations inclay. Ocean Engineering, 2012, 52: 75-82. [19] Zhu,C.H., Research on computation of the static filler pressure inside buried large-diameter cylinder. Port Engineering Technology, 2002, 3: 39-43. [20] Yao,W.J. , Xiong,S. and Chen,J.L., Study on dynamic plastic displacement to large-diameter cylindrical structure. Port & Waterway Engineering, 2009, 11: 11-17. [21] Lin,P., Yao,W.J. and Zhang,J., Effect of different forms of cylindrical bucket foundation structure upon anti-overturning ability of cylindrical bucket foundation structure. China Harbour Engineering, 2013, 6: 30-35, 52. [22] Fraldi,M. and Guarracino,F., Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections. International Journal of Solids and Structures, 2010, 47(2): 216-223. [23] Wang,Y.Z., Large-diameter cylindrical structure calculation and applications in engineering. Beijing: The People’s Communications Publishing House, 2008. [24] Yang,X.L. and Huang,F., Collapse mechanism of shallow funnel based on nonlinear Hoek-Brown failure criterion. Tunnelling and Underground Space Technology, 2011, 26(6): 686-691. [25] Shi,Y.J., Wu,M.L. and Jiang,X.L., Experimental researches on reflective and transmitting performance of quarter circular breakwater under regular and irregular waves. China Ocean Engineering, 2011, 25(3): 469-487.
ISSN 0894-9166
RESEARCH ON SOIL PRESSURE IN NINE CABINS OF OPENED BOTTOM ELLIPTICAL BARREL STRUCTURE USING PENETRATION OF NEGATIVE PRESSURE METHOD⋆⋆ Xiaozhong Zhang⋆ (School of Civil and Architectural Engineering, Guizhou University of Engineering Science, Bijie 551700, China)
Received 22 March 2013, revision received 6 April 2015
ABSTRACT An investigation is made on the soil pressure in a nine cabin opened bottom elliptical barrel structure. The calculation models using the penetration of negative pressure method have been developed. The first calculation model is is for the construction stage involving three zones, namely, passive, transitional, and active established for the soil pressure in cabins. The other calculation model is based on the use stage, with the two (passive and active) zones for the soil pressure in cabins. The height of zones and the theoretical analytical solutions of inner soil pressure are derived. The analytical formulas of the models are proved using the finite element method and experimental data, and the formulas are analyzed in the inner soil pressure in the same condition. The calculation models can be used for other multi-position structural design or construction.
KEY WORDS opened bottom elliptical barrel structure, soil pressure, calculation, passive zone, transitional zone, active zone
I. INTRODUCTION As a special structure, an opened bottom elliptical barrel structure with nine cabins is composed of a reinforced concrete elliptical barrel structure and a bottom protection stone. The special structure is composed of an elliptical barrel bottom and two upper cylindrical barrels. The bottom barrel is elliptical in shape and with nine cabins, the upper barrels being joined by ring beam with bottom barrel. The shape of the special structure is shown in Fig.1. The opened bottom elliptical barrel structure with nine cabins can directly be inserted into soft soil as a convenient construction, which can be applied in a variety of complex conditions. This structure has good prospects for application for its ability to reduce the construction period and construction costs. However, the special structure is greatly limited for lack of theoretical support. In particular, the mechanism of the inner soil and the structure duting normal work is yet unclear. Many core issues of the mechanism need to be further studied. The inner soil pressure in the special structure is the most important technical issue for structural stabilization and normal operation[1–3] indispensable to accurate calculation of the inner pressure of the structure for improvements of the design and construction method. As soil pressure within the structure is related to the structural ⋆
Corresponding author. E-mail: [email protected] Project supported by Open Fund Project of Hunan Province Research Center for Safety Control Technology and Equipment of Bridge Engineering (Changsha University of Science & Technology) (No. 13KC05). ⋆⋆
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stability analysis and foundation settlement, this article focuses on the inner soil pressure calculation model for different stages, the research results could provide a scientific reference for multi-compartment structures. The inner soil pressure of large cylindrical structures has been studied by many researchers, who proposed different methods for calculating the inner soil pressure for the special structure. The inner soil pressure for single-cabin researched by some scholars[4, 5], which was divided into three zones according to the angle of internal friction of soil. The inner soil pressure is divided into three zones from top to bottom based on model calculation[6–9] . The inner soil pressure of opened bottom cylindrical structure has approximately been calculated using active soil pressure and Yeung Sum formula by some researchers[10, 11]. The calculation model of inner soil pressure is developed using foundation soil for transmission media of inner and outside soil pressure[12] . The empirical formulas of calculating inner soil pressure for single-cabin cylindrical structures are given according to the experimental data. Shen et al. analyzed the influence on the working performance of the cylindrical bucket foundation structure by the soil consolidation. They developed a three-dimensional elastic-plastic structure-soil interaction finite element model to obtain the variation trend under consolidation of the soil pressure on the cylinder wall[4] . Xiao and Wang established a model based on the Lanczos method for the system of bucket foundation breakwater and soil foundation. The result showed that inner soil pressure was an important factor in structural stability[6] . Previous studies only considered the diameter of cylinder and the friction angle of soil. In addition, there are many other Influencing factors such as the load applied on the structure, the weight and the compressibility of soil, the coefficient of foundation deformation and reaction force. Meanwhile, the soil pressure was defined barely from test data. The conclusions lack a theoretical basis[13–16] . The finite element method and theoretical analysis were used to produce a three dimension Elastic-plastic mechanical model of basal soil at the bottom of a large cylindrical structure, which was used to calculate the inner soil pressure[17–21] . The soil pressure under axisymmetric vertical loading was divided into two zones[22–25] . The stability of the opened bottom elliptical barrel structure with nine cabins was better compared with the large cylindrical structure. It is found by experiment that, the inner soil pressure of the special structure under axisymmetric vertical loading was divided into three zones: active zone, transitional zone and passive zone. However, under horizontal loading, it was only divided into two zones: active zone and passive zone. In order to accurately describe the characteristics of inner soil of the structure, the inner soil pressure calculation models of three areas in the construction stage and two areas in the use stage were established based on experimental results. The theoretical analytical solutions of inner soil pressure and the height of every zone for construction stage and use stage were derivedand the validity of the model was demonstrated under a same working condition.
Fig. 1. Structure with elliptical barrel.
II. CALCULATION MODEL IN CONSTRUCTION STAGE In the construction stage, the inner soil pressure calculation model is shown in Fig.2. The pressure of soil is divided into three zones which are active zone, transitional zone and passive zone respectively. The demarcation point of the three zones are y = h0 and y = h1 as shown in Fig.2. Parameters of the model are as follows. The height of the barrel is H. The cross-sectional area of the barrel is F . The cross-sectional area of the barrel wall is F ′ . The perimeter of the contact area between the soil and the
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Fig. 2. Calculation model in construction stage.
bucket wall is u.The unit weight of the soil is γ. The unit weight of the barrel wall is γ ′ . The compression modulus of soil is ES . Since there is a cover plate at the bottom of the barrel, the gravity of the cover plate and the gravity above it are acting upon the padding and the barrel wall evenly. The even load is q. The foundation support upon the padding is σ. The foundation support under the barrel wall is σ ′ . The lateral pressure coefficient of the barrel wall is K. The frictional factor between the soil and the bucket wall is f . The coefficient of deformation for the foundation of the barrel bottom is ks . A differential thin element is taken at y in the barrel, as is shown in Figs.3, 4 and 5.
Fig. 3. Calculation unit of soil pressure in active zone.
Fig. 4. Calculation unit of soil pressure in passive zone.
Fig. 5. Calculation unit of soil pressure in transitional zone.
2.1. The Soil Pressure in the Active Zone In the active zone, the loading of the differential thin element is shown in Fig.3. The forces on it are as follows: the vertical pressure on the element is pyz , the vertical counter-force at the bottom is pyz + dpyz . The friction between the padding and the barrel wall is pxz f = Kf pyz . The gravity of the differential thin element is γ. According to the equilibrium of forces, we can get dpyz u = γ − Kf pyz (1) dy F Equation (1) meets the boundary conditions: y = 0, pyz = q. By solving the differential equation, we can get uKf uKf γF pyz = 1 − e− F y + qe− F y (2) uKf The friction of the barrel wall is uKf uKf γF f pxz = 1 − e− F y + Kf qe− F y (3) u
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In the equation, lateral pressure coefficient K = 1 − sin ϕ. ϕ is internal friction angle. f is the frictional factor between the soil and the barrel wall, and f = tan δ. δ is the normalized value between the soil and the barrel wall, and δ = 2ϕ/3. 2.2. The Soil Pressure in the Passive Zone In the passive zone, the loading of soil is shown in Fig.4. The calculation is the same as that for the active zone, the equilibrium equation being u dpyb = γ + Kf pyb (4) dy F In Eq.4, the boundary condition is met: y = H, pyb = σ, where b represents the passive zone. By solving the differential equation, we can get i uKf uKf γF h pyb = − 1 − e− F (H−y) + σe− F (H−y) (5) uKf The frictional force of the barrel wall is i uKf uKf γF h f pxb = − 1 − e− F (H−y) + Kf σe− F (H−y) (6) u 2.3. The Inner Soil Pressure of the Transitional Zone In the transitional zone, the loading of soil is shown in Fig.5. The calculation is the same as that for the active zone, the equilibrium equation being dpyg =γ (7) dy where g represents the transitional zone. After integration, we can get pyg = γy + A (8) In the equation above, A is a constant. 2.4. The Determination of the Interface of the Three Areas At the interface between the active zone and passive zone, pyz = pyg . According to Eqs.(2) and (8), we can get uKf uKf γF 1 − e− F h0 + qe− F h0 = γh0 + A (9) uKf At the interface between the passive zone and transitional zone, pyb = pyg . According to Eqs.(5) and (8), we can get i uKf uKf γF h − 1 − e− F (H−h1 ) + σe− F (H−h1 ) = γh1 + A (10) uKf From Eqs.(9) and (10), we can get uKf 2γF γF γF − uKf (H−h1 ) F − + +σ e + − q e− F h0 − γ(h1 − h0 ) = 0 uKf uKf uKf According to the equilibrium of forces for the soil in the vertical direction, we can get Z h0 Z H Fσ − Fq + pxz f udy − pxb f udy − γHF = 0 0
(11)
(12)
h1
γ is the effective unit weight. According to Eqs.(3), (6) and (12), we can get uKf 2γF 2 γF 2 γF 2 − uKf h 0 − + γF (h0 − h1 ) + − Fq e F + + F σ e− F (H−h1 ) = 0 uKf uKf uKf According to Eqs.(11) and (13), we can get h0 and h1 .
(13)
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2.5. The Counter-Force of the Foundation Since the soil at the bottom is mollisol, according to the Winkler foundation model, the foundation settlement of the bottom soil S and the foundation settlement of the bottom of the barrel wall S ′ are as follows: σ σ′ S = , S′ = (14) ks ks where ks represents the stiffness of soil. According to the deformation coordination condition, the decrement of the passive zone is the difference between foundation settlement of the bottom of the barrel wall and the foundation settlement of the bottom soil in the cabin. Which means: ∆ = S′ − S =
σ′ σ − ks ks
(15)
Considering the soil in the cabin and the barrel as a whole, according to the force equilibrium condition, we can get F F (16) σ ′ = q + γ ′ H + ′ (q + γH) − ′ σ F F According to Eqs.(15) and (16), we can get σ=q+
H F′ ′ ′ (F γ + F γ) − ks ∆ F + F′ F + F′
(17)
The decrement of the passive zone can be calculated by soil mechanics formula (Terzaghi onedimensional consolidation theory): h Z H i uKf 1 F γF 1 γF (H−h1 ) F pyb (y)dy = +σ 1−e (H − h1 ) (18) ∆= − ES h1 ES uKf uKf uKf According to Eqs.(11), (13), (17) and (18), we can work out the counter-force of the soil mass in the cabin and counter-force of the barrel wall.
III. CALCULATION MODEL IN THEUSE STAGE The opened bottom elliptical barrel structure with nine cabins is subjected to horizontal wave force during the use stage. It will tilt under a horizontal load, which will destroy the pressure distribution of the soil under a vertical load. Then the inner soil pressure needs to be analyzed further. 3.1. Calculation Model The opened bottom elliptical barrel structure with nine cabins is subjected to horizontal wave force as well as vertical load. According to model experiment, the soil and the barrel will move around point C under horizontal wave force (Fig.6). Point C is between the right ribbed plate and central shaft[15] . The transitional zone in the cabin is not obvious, and only active zone and passive zone are left. The height of the right side of the active zone is h0r , and the height of the left side of the active zone is h0l . As shown in Fig.6, the soil in the cabin is subjected to vertical load q and horizontal force PC . The horizontal pressure force of the barrel wall on the inner soil is Ph . The frictional resistance of the barrel wall to the soil mass is τ . The horizontal shearing force is T . The counter-force of the bottom is σ. The distance from the axis of rotation to the structure center is a. 3.2. The Determination of Rotational Axis The location of the rotational axis is related to horizontal force, and the calculation model under horizontal force is shown in Fig.7. The counter-force of the barrel bottom is supported by the right side of the rotational axis and distributed linearly on the right side. The frictional resistance of the barrel wall o the soil is balanced in the vertical direction and, according to the balance of the vertical load, we can get γHF − Pσ = 0
(19)
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Fig. 6. Calculation models of soil pressure in use stage.
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Fig. 7. Calculation model of soil pressure for horizontal force.
In the equation above, Pσ is the resultant force of the foundation support and a function of unknown quantities a and σy max . Taking moments about O , we can get MPC − MG − Mσ − Mτ = 0
(20)
In the equation above, MPC is the moment of the wave force about O, and a given value. MG is the moment of soil gravity about O, and it is the function of unknown quantities a. Mσ is the moment of soil reaction force at the bottom about O, and a function of unknown quantities a and σy . Mτ is the moment of friction resistance about O, and a function of unknown quantity a. According to Eqs.(19) and (20), we can obtain the value of a and of σy max . 3.3. The Reactionary Force at the Barrel Bottom in the Use Stage The calculation model is shown in Fig.6, and according to the force equilibrium in the vertical direction, we can get qF + γHF − Pσs = 0 (21) In the equation above, Pσs is the resultant force of foundation support and a function of unknown quantities σmin and σmax . Taking moments about O , we can get MPC − MG − Mσs − Mτs − Mqs = 0
(22)
In the equation above, Mσs is moment of soil reaction force at the bottom about O in use stage and a function of unknown quantities σmin and σmax . Mτs is the moment of friction resistance about O in use stage. Mqs is the moment of vertical load about O in use stage. According to Eqs.(21) and (22), we can get the value of σmin and σmax . 3.4. The Inner Soil Pressure in the Cabin in Use Stage In the active zone, we can apply formula (2) since the condition is the same. psyz =
uKf uKf γF 1 − e− F y + qe− F y uKf
(23)
psyz is the soil pressure of any point in the active zone. In the passive zone, the forces are shown in Fig.4. The calculation is the same as that for the active zone, and the equilibrium equation is Eq.(4). On the left side, y = H, psyb = σmin , we can get the
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pressure stress of the soil at any point on the left side in the passive zone by solving the differential equation. i uKf uKf γF h 1 − e− F (H−y) + σmin e− F (H−y) psybl = − (24) uKf s pyzl is the pressure stress of the soil at any point on the left side in the passive zone. On the right side, y = H, pyb = σmax , so we can get the pressure stress of the soil at any point on the right side in the passive zone by solving the differential equation. i uKf uKf γF h 1 − e− F (H−y) + σmax e− F (H−y) psybr = − (25) uKf psyzr is the pressure stress of the soil at any point on the right in the passive zone. In the middle area,, the calculation is to be made according to linear interpolation. On the left side, the following equation will be met on the interface between active zone and passive zone. According to Eqs.(23) and (24), we can get q − uKf F H 1 + 1 − [1 − ukf /(γF )q][1 + ukf /(γF )σ ]e min F ln h0l = H + (26) uKf 1 + ukf /(γF )σmin
h0l is the height of active zone of the soil in the cabin on the left side. According to Eqs.(23) and (25) we can get the height of active zone of the soil in the cabin on the right side. q − uKf F H 1 − [1 − ukf /(γF )q][1 + ukf /(γF )σ ]e 1 + max F (27) ln h0r = H + uKf 1 + ukf /(γF )σmax
h0r is the height of active zone of the soil in the cabin on the right side. The calculation of interface in the middle area is to be made according to linear interpolation. The pressure stress of the soil in the cabin is to be dealt with according to Eqs.(23), (24) and (25). The height of passive zone and active zone is calculated according to Eqs.(26) and (27).
IV. THE CARRYING CAPACITY FOR THE FORMER SITE The checking computation of carrying capacity for the bottom is the main leading indicator which guarantees that the structure meets the working performance, as is shown in Fig.8. In the use stage, the local stress of the former site is the maximum stress of the whole structure, which needs checking computation. According to Eq.(16) , we can calculate the maximum stress σ ′ on the former site when the structure is under gravity. According to Eqs.(19) and (20), we can calculate the maximum stress σy max at y = H when the structure is under a horizontal load. The maximum stress at the bottom of the former site is σmax = σ ′ + σy max
(28)
The allowable bearing capacity of the bottom is determined by the eigenvalue of the bearing capacity according to the shearing strength index. fa = fak + ηd γ(b − 3) + ηb γm (d − 0.5)
(29)
In the equation above: fak = Mb γx b + Md γm d + Mc c, fak is the eigenvalue of the bearing capacity for the foundation soil, and Mb , Md , MC are bearing capacity factors, whose values are in accord with the Code for design of buildings; b is the width of the bottom of foundation; c is normalized value of the cohesion in the depth range including the width of the short side; γx is the natural gravity of the soil under foundation; γm is weighted average gravity of the soil above foundation, and the gravity of soil under ground water level is floating gravity; fa is revised eigenvalue of the bearing capacity for the foundation soil; ηb , ηd are correction factors of bearing capacity of the foundation soil in the width and depth of the foundation; d is the buried depth of the foundation. The carrying capacity of the foundation should satisfy the following equation: σmax ≤ fa
(30)
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Fig. 8. The reaction forces of elliptical barrel structure.
V. VERIFICATION OF CALCULATION According to survey and design information[15] , the following working conditions are to be met for computational analysis. The barrel below is completely immersed in the soil , and the elevation of the mud surface is ∇ − 5.5.0 m. The elevation of the barrel bottom is ∇ − 13.18 m. The cover plate on the mud surface is ∇0.38 m meters in depth. As for the upper barrel, the elevation of the barrel top is ∇11.5 m, and the elevation of the barrel bottom is ∇ − 5.6 m. The extremely high water level before the barrel is ∇7.21 m. The barrel is reinforced concrete structure, as is shown in Fig.1(b). The wave load is shown in Table 1, in which H1% represents the maximum wave height, T represents the wave period. Table 1. The parameters of wave
Design level Extreme high water level 6.56 m Extreme low water level −0.68 m
H1% (m) 6.72 2.82
T (s) 8.76 8.76
Wave length (m) 84.1 57
Direction ES ES
5.1. Numerical Simulation Analysis in the Construction Stage The values of h0 and h1 for the soil in the cabin in the construction stage and the counter-force of the barrel bottom are calculated by Eqs.(11), (12) and (13). The calculation results are shown in Table 2 and Fig.9. Table 2. The calculating results in construction stage
Items Computational results of the formula in this paper Numerical results Experiment results[15] Computational results[12]
h0 (m) 5.270 5.321 5.178 5.667
h1 (m) 6.337 6.415 6.225 6.577
σ (kPa) 97.325 105.363 95.480 110.675
σ ′ (kPa) 148.657 155.761 137.431 176.324
The model is shown in Figs.10 and 11, In order to reflect the model of the soil structure truly, the soil depth is 5 times as large as the cylinder structure height, and the soil width is 5 times as large as the cylinder structure diameter. The soil constitutive model can rationally reflect the Mohr-Coulomb and Drucke-Prager elastic-plastic model of the nonlinear elastic-plastic soil. The contact surface between barrel and soil is highly nonlinear in order to simulate the discontinuous nonlinear phenomena, such as real slide, detachment on the contact surface between barrel and soil. The contact surface is set on the surface between soil and structure in order to overcome the disadvantage of the twisting gridding inability to reflect the real condition. The type of soil element is C3D8R, the number of elements is 29020, the number of nodal points is 32942. The type of construction unit is C3D8RC3D4, and the
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number of elements for a single barrel is 16031. The number of nodal points is 6640. The total element number is 45051, and the number of nodal points is 39582. The material parameter values are as follows: The soil parameter for each layer is shown in Table 3. The opened bottom elliptical barrel structure is reinforced concrete C30, and its density is 2500 kg/m3 . The modulus of elasticity E = 3.0 × 104 MPa. The Poisson’s ratio is 0.167. The frictional factor of the contact surface is as follows: The frictional factor of the contact surface between the barrel top and soil is 0.04. The frictional factor of the contact surface between the barrel side and first soil layer is 0.04. The frictional factor of the contact surface between the barrel side and second soil layer is 0.2. The boundary conditions are as follows: The horizontal plane displacement of boundaries around the foundation soil are zero, and the displacement for the bottom is zero in three directions. Table 3. Parameters for soil
The first soil layer The second soil layer The third soil layer The fourth soil layer
Cohesion (kPa) 7 39 18 32
Friction angle (◦ ) 2.5 11.3 6.2 6.2
Modulus of compression (MPa) 1.67 5.08 2.85 7.9
Poisson’s ratio 0.4 0.35 0.35 0.35
The numerical calculation results of the soil pressure in the cabin in the construction stage is shown in Fig.12. The soil pressure in the cabin is divided into three areas, the active zone, the passive zone and the transitional zone. The basis stress under the barrel wall is obviously larger than the basis stress in the cabin. The specific height of the three areas and the specific results of the basis stress are shown in Table 2. The calculation results of the model in the paper are most close to experimental results.
Fig. 9. The pressure of soil in construction stage (unit: kPa).
At the same time, vertical distribution of the soil pressure in the cabin is shown in Fig.9. The calculation results of the model in the paper are most close to experimental results, which confirms the correctness of the soil pressure calculation model in the construction stage in this paper, and the soil pressure calculation model has higher accuracy than empirical formula and numerical simulation results. 5.2. Numerical Simulation Analysis in the Use Stage The calculation of soil pressure in the use stage is the same as that with the construction stage. Computational analysis including analytic solutions, arithmetic solution, and empirical equation is
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Fig. 10. Finite element model of elliptical barrel structure.
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Fig. 11. Finite element model of soil with structure.
Fig. 12. Numerical results of soil pressure in construction stage.
carried out for the elliptical barrel structure under the same working condition, with the results compared with model experiment results. The height of the active zone and the passive zone and the maximum basis stress are calculated, as is shown in Table 4 and Fig.13. Table 4. Results in use stage
Items The results calculated by the formula in the paper Numerical results Experiment results[15] Results using empirical formula[12]
h0l (m) 7.656 7.539 7.452 7.647
h0r (m) 6.342 6.278 6.348 6.37
σmax (kPa) 291.554 293.464 302.756 /
The soil pressure in the cabin is divided into two areas, the upper area and the bottom area in Fig.14, which confirms the correctness of the division of two areas in the soil in the use stage. The contact surface between active zone and passive zone is an inclined surface, which is constant with the model in the paper (Fig.6). The specific height of the two areas and the specific results of the basis stress are shown in Table 4. The calculation results of the model in the paper are most close to experimental results after comparison. At the same time, vertical distribution of the soil pressure(right side) in the cabin is shown in Fig.13. The calculation results of the model in the paper are most close to experimental results, which confirms the correctness of the soil pressure calculation model in the use stage in the paper, and the soil pressure calculation model has higher accuracy than empirical formula and numerical simulation results. 5.3. The Carrying Capacity for the Former Site The carrying capacity for the former site is calculated according to formula (28) for the opened bottom elliptical barrel structure. And the numerical calculation method, gravity structure calculation method and model experiment method are adopted for comparison. The calculation results are shown
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in Table 5. The carrying capacity calculated by each method can meet the demand of the structure, but the results obtained with the gravity structure calculation method are different from model experiment results, which shows gravity structure calculation method is not suitable for nine cabins opened bottom elliptical barrel structure. The calculation results of the model in the paper are most close to experimental results, which confirms the correctness and high accuracy of the calculation model in the construction stage in the paper.
Fig. 14. Numerical results of pressure of soil in cabin in use stage. Fig. 13. The pressure of soil with cabin in use stage (right) (unit: kPa).
Table 5. Computation of the carrying capacity of the former site (kPa)
The results calculated by the formula in the paper Stress of the former site 325.64 Allowable bearing capacity of the basis
Gravity structure calculation method 301.47 fa = 411.608 kPa
Numerical results 332.78
Experiment results 323.57
VI. CONCLUSIONS The inner soil pressure calculation model of opened bottom elliptical barrel structure is confirmed. In the construction stage, the inner soil pressure is divided into three areas: active zone, passive zone and transitional zone, and the interface between areas is almost a horizontal plane. In the use stage, the inner soil pressure is divided into two areas: active zone and passive zone, and the interface between areas is not horizontal but oblique. Furthermore, the active zone on wave side is smaller than that on the lee-side. The calculation results of the model in the paper are closer to experimental results and numerical simulation results than the calculation results by the empirical formula.
References [1] Zhou,Z.Z., Chen,B.Z. and Liu,J.Q., The research of model experiment and calculating method for retaining wall of large-diameter-open tubes. Geotechnical Engineer, 1991, 4: 83-90. [2] Xu,J. and Wang,D.Y., Numerical simulation of large diameter cylindrical structure lamming. China Ocean Engineering, 2008, 22(3): 513-520. [3] Zhou,X.R. , Wang,H. and Han,G.J., Design and calculation of the large-diameter cylinder shell structure. Port Engineering Technology, 1995, 2: 22-30. [4] Shen,D., Yao,W.J. and Chen,Z.K., Influence of soil consolidation upon working performance of cylindrical bucket foundation structure. Port & Waterway Engineering, 2014, 10: 149-155. [5] Wang,Y.J. and Meng,Q.W., New formulas of earth pressure on large successive cylinders. China Ocean Engineering, 1998, 12(4): 443-452.
Vol. 28, No. 5
Xiaozhong Zhang: Soil Pressure in Nine Cabins of Elliptical Barrel Structure
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