盾构管片结构设计算例.doc

A Design of Shield Tunnel Lining Part One: Design Data(1) Function of TunnelThe planned tunnel is to be used as a subway tunnel.(2) Design ConditionsDimensions of SegmentType of segment: RC, Flat typeDiameter of segmental lining: D0=9500mmRadius of centroid of segmental lining: Rc=4550mmWidth of segment: b=1200mmThickness of segment: t=400mmGround ConditionsOverburden: H=12.3mGroundwater table: G.L.+0.6m =12.3+0.6=12.9mN Value: N=50Unit weight of soil: =18kN/m3Submerged unit weight of soil: =8kN/m3Angle of internal friction of soil: =30oCohesion of soil: c=0 kN/m2Coefficient of reaction: k=50MN/m3Coefficient of lateral earth pressure: =0.4Surcharge: P0=39.7kN/m2Soil condition: SandyMaterials The grade of concrete: C30Nominal strength: fck=20.1N/mm2Allowable compressive strength: fc=14.3N/mm2Allowable tensile strength: ft=1.43N/mm2Elastic modules: E=3.0104N/mm2 The type of steel bars: HRB335Allowable strength: fy= fy’= 300N/mm2 BoltYield strength: fBy=240N/mm2Shear strength: =150N/mm2 Parameters for joint spring:18070 (if inside part of lining is tensile)32100 (if outside part of lining is tensile)Design Method How to compute member forces?Force method (Part Two) and Elastic equation method (Part Three) are used respectively to calculate member forces. How to check the safety of lining? Limit state method based on the national code GB50010-2002 is used to check the safety of lining. (3) Geometric Design of Shield LiningThe shield lining is fitted with 9 segmental pieces (one Key-type segment, two B-type segments and six other segments) as shown in Figure 1. Central angle of each segment piece is 40 degrees. Figure 1 The cross section of the shield liningPart Two: Computation by Force Method (1) Load ConditionsJudgment of Tunnel Type (by Terzaghi’s formula) Figure 2 Judgment of tunnel typeSo the designed tunnel is a shallow tunnel.Load Types and Partial Factors Table 1 shows the loads should be considered in the design and corresponding partial factors.Table 1 Load Types and Partial FactorsLoad typesPartial factorsLoad typesPartial factorsSurcharge1.4Earth pressure1.2Dead load1.2Subgrade reaction1.2Water pressure1.2　　Computation of Loads Computation element is a 1.2 meter (width of segment) part along the longitudinal direction, and Figure 3 shows the load condition to compute member forces of the segmental lining.Figure 3 Load condition of the designed tunnel Vertical pressure at tunnel crownEarth pressure:Water pressure: Vertical pressure at tunnel bottomWhere =Unit weight of RC segment=26kN/m2 Lateral pressure at tunnel crownEarth pressure:Water pressure: Lateral pressure at tunnel bottomWhere Dc=Computational diameter= Average self-weight Lateral resistance pressure= (2420.623-272.918-445.891+π14.976) 1034.554/[24(0.83.01041066.410-3+0.0454601064.554)]= 2.2910410-3m Where Displacement of lining at tunnel springReduction factor of model rigidity = 0.8Modulus of elasticity of segment = 3.0104N/mm2Moment of inertia of area of segment = 1/121.20.43 = 6.410-3m4Coefficient of reaction = 50MN/m3 the angle measured from the vertical direction around the tunnel (2) Computation of Member Forces Figure 4 shows the simplified model of the segmental lining.Figure 4 Simplified model diagram for calculation Calculation data (if inside part of lining is tensile) (if outside part of lining is tensile) Coefficients CalculationNote: if the joint just located at 180 degree of the half-ring lining, then its stiffness contribution to the whole structure should be considered as half of the total value. The values of coefficients by force-method equations can be summarized as shown in Table 2.Table 2 Coefficients in force-method equations Then the bending moment and axial force (per 1.2m) acting at the crown can be obtained by the following equations: Member Forces By using the following equations, member forces of the segmental lining can be calculated and the results are shown in Table 3. The internal bending moment (), axial force () and shear force () (per unit length) due to a unit force x1=1 or x2=1 can be derived asThe lining forces caused by surrounding pressures can be determined by accumulating the six loading cases as defined in Figure 4.Where Mpj, Npj, Qpj are the bending moment, the axial force and the shear force (per unit length) under the jth loading, respectively.For loading case 1, For loading case 2, For loading case 3, For loading case 4, 。