A calculation method for the jacking force of a shield machine considering the influence of slope and radius of curvature

Abstract

The present invention provides a method for calculating the jacking force of a shield machine considering the influence of slope and radius of curvature, including calculating the frictional resistance between the shield shell and the surrounding soil mass; calculating the frontal resistance of the cutter head; calculating the frictional force between the segment and the shield tail, the resistance of the towing trailer, and the penetration resistance of the cutting ring; calculating the resistance caused by the component of the self-weight of the shield machine along the tunnel axis during uphill tunneling; calculating the turning thrust difference of the shield machine; calculating the jacking force of the shield machine according to the frictional resistance between the shield shell and the surrounding soil mass, the frontal resistance of the cutter head, the frictional force between the segment and the shield tail, the resistance of the towing trailer, the penetration resistance of the cutting ring, the resistance caused by the component of the self-weight of the shield machine along the tunnel axis, and the turning thrust difference of the shield machine. The present invention considers the influence of slope and radius of curvature conditions on the jacking force of the shield machine, adds two key sub-item resistances, improves the calculation accuracy of the jacking force of the shield machine, and makes up for the technical defect of ignoring slope and radius of curvature in the existing calculation method.

Description

Technical Field

[0001] The present invention relates to the technical field of underground drilling, and particularly relates to a method for calculating the thrust force of a shield machine considering the influence of slope and radius of curvature. Background Art

[0002] A shield machine is an underground excavation and drilling equipment that integrates optics, mechanics, electricity, hydraulics, sensing, and information technologies, and has functions such as excavating and cutting soil, transporting soil residue, assembling tunnel linings, and measuring and guiding deviation correction. During the tunnel excavation and drilling process of the shield machine, due to the dynamic adjustment of the shield machine posture, the shield tunneling parameters in the large slope and small radius section are significantly different from those in the straight and flat slope section. If the shield construction in the straight and flat slope section is still considered, it will cause the imbalance between the supporting force of the shield excavation face and the soil pressure in front, exacerbate the impact of construction on the surrounding strata, increase the risk of the shield deviating from the tunnel design axis, and further exacerbate the uneven stress of the segments. The current calculation method cannot solve the problem of selecting shield tunneling parameters in the large slope and small radius section. Summary of the Invention

[0003] The purpose of the present invention is to overcome the above deficiencies in the prior art, and provides a method for calculating the thrust force of a shield machine considering the influence of slope and radius of curvature, which solves the problem that the current calculation method cannot solve the problem of selecting shield tunneling parameters in the large slope and small radius section.

[0004] To solve the above problems, the present invention provides a method for calculating the thrust force of a shield machine considering the influence of slope and radius of curvature, which is characterized by including the following steps:

[0005] Step 1: According to the friction force calculation model between the shield shell and the surrounding soil, calculate the vertical soil pressure and lateral soil pressure acting on the shield shell, and obtain the sum of the components of the vertical soil pressure and lateral soil pressure in the radial direction of the shield as the radial soil pressure. Select the friction coefficient between the shield shell and the surrounding soil, and calculate the friction resistance between the shield shell and the surrounding soil;

[0006] Step 2: According to the cutter head face soil pressure calculation model and the force analysis of the soil micro-elements in the soil bin, calculate the cutter head face soil pressure and the friction resistance between the inner wall of the soil bin and the soil respectively, and calculate the cutter head face resistance according to the cutter head face soil pressure and the friction resistance between the inner wall of the soil bin and the soil;

[0007] Step 3: Calculate the friction force between the segment and the shield tail, the resistance of the towing trailer, and the penetration resistance of the cutting ring;

[0008] Step 4: Calculate the resistance caused by the component of the self-weight of the shield machine along the tunnel axis during uphill tunneling;

[0009] Step 5: Calculate the torques on the rotation center caused by the incremental soil pressure of the shield shell and the incremental soil pressure of the cutterhead respectively according to the changes in the soil pressure around the shield shell and the soil pressure of the cutterhead, and calculate the turning thrust difference of the shield machine according to the torques on the rotation center caused by the incremental soil pressures of the shield shell and the cutterhead.

[0010] Step 6: Calculate the jacking thrust of the shield machine according to the frictional resistance between the shield shell and the surrounding soil, the frontal resistance of the cutterhead, the frictional force between the segment and the shield tail, the resistance of the towing trailer, the penetration resistance of the cutting ring, the resistance caused by the component of the self-weight of the shield machine along the tunnel axis, and the turning thrust difference of the shield machine.

[0011] The above method for calculating the jacking thrust of a shield machine considering the influence of slope and radius of curvature is characterized in that in the above Step 1:

[0012] When the shield machine is tunneling in a curved section, due to the geometric characteristics of the curve, the extrusion pressure of the inner soil on the shield shell is significantly greater than that of the outer side, so the frictional force between the inner side of the curve of the shield shell and the soil is also greater than that of the outer side; therefore, the frictional force between the shield shell and the surrounding soil should be calculated according to the inner side and the outer side of the curve, and the frictional resistance between the shield shell and the surrounding soil can be calculated by the product of the radial soil pressure acting on the shield shell and the friction coefficient between the shield shell and the surrounding soil; the soil pressure acting on the shield shell can be divided into vertical soil pressure and lateral soil pressure according to the direction, and the sum of the components of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is the radial soil pressure. Since there are differences in soil pressure above and below the shield machine, it is necessary to calculate in two parts, upper and lower; specifically including:

[0013] 101. Calculate the vertical soil pressure dP e1 and the lateral soil pressure dq e1 acting on the microelement of the upper half of the shield shell:

[0014] dP e 1 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0015] dq e 1 ′ = K 0 dP e 1 ′ = ( 1 − sin f i ) c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0016] In the formula: K 0 is the coefficient of earth pressure at rest, ; γ is the unit weight of the soil layer, in kN / m 3 ; h N is the distance from the top of the cutterhead to the ground surface, in m; R D is the radius of the cutterhead, in m; β is the tunneling slope of the shield machine, in 。 ; φ i is the internal friction angle of the soil, in о ; θ is the angle between the calculation point and the horizontal line of the cutterhead, in о; l is the distance from the calculation element to the cutter head surface, with the unit of m;

[0017] According to the vertical soil pressure dP e1 and the lateral soil pressure dq e1 , calculate the soil pressure on the upper half of the micro-elements per unit length in the radial direction of the contact surface between the shield shell and the soil mass :

[0018] d s i 1 = dP e 1 ′ sin i + dq e 1 ′ cos i = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0019] 102. Calculate the vertical soil pressure dP e2 and the lateral soil pressure dq e2 :

[0020] dP e 2 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L

[0021] dq e 2 ′ = K 0 dP e 2 ′ = ( 1 − sin f i ) { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L }

[0022] In the formula: W is the weight of the shield main machine, with the unit of kN.

[0023] According to the vertical soil pressure dP e2 and the lateral soil pressure dq e2 , calculate the soil pressure on the upper half of the micro-elements per unit length in the radial direction of the contact surface between the shield shell and the soil mass :

[0024] d s i 2 = dP e 2 ′ sin i + dq e 2 ′ cos i = { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ] ;

[0025] 103. Calculate the frictional forces df 1 and df 2 :

[0026] df 1 = ndf 1 = n h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0027] df 2 = h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0028] In the formula: n is the friction force difference coefficient between the inner and outer sides of the curve, obtained by calculating and analyzing the engineering monitoring data, n = 1.1; η is the friction coefficient between the shield shell and the surrounding soil mass, generally ;

[0029] 104. Calculate the frictional force df on the infinitesimal elements of the lower half of the inner and outer shield shells of the curve 3 and df 4 :

[0030] df 3 = or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } [ sin i + ( 1 − sin f i ) cos i ]

[0031] df 4 = ndf 3 = n or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0032] 105. Calculate the frictional resistance F between the shield shell and the surrounding soil mass 1 :

[0033] ;

[0034] The above shield machine jacking force calculation method considering the influence of slope and radius of curvature is characterized in that the earth pressure on the cutter head front in step two is the vertical earth pressure p e and the lateral earth pressure q e the resultant force in the normal direction of the cutter head, and the soil chamber pressure σ α are equal in magnitude and opposite in direction;

[0035] The calculation method of the cutter head front resistance includes:

[0036] 201. Calculate the vertical earth pressure dP on the infinitesimal elements of the upper half of the cutter head e1 and the lateral earth pressure dq e1 :

[0037] dP e 1 = c [ h N + ( R D − r sin i ) cos β ]

[0038] dq e 1 = K 0 dP e 1 = ( 1 − sin f ) c [ h N + ( R D − r sin i ) cos β ]

[0039] According to the vertical earth pressure dP on the infinitesimal elements of the upper half of the cutter head e1 and the lateral earth pressure dq e1 , calculate the earth pressure on the infinitesimal elements of the upper half of the cutter head :

[0040] d s α 1 = dP e 1 sin β + dq e 1 cos β = c [ h N + ( R D − r sin i ) cos β ] ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0041] 202. Calculate the vertical earth pressure dP on the infinitesimal elements of the lower half of the cutter head e2 and the lateral earth pressure dq e2 :

[0042] dP e 2 = c [ h N + ( R D − r sin i ) cos β ] + W π R D L

[0043] dq e 2 = K 0 dP e 2 = ( 1 − sin f ) { c [ h N + ( R D − r sin i ) cos β ] + W π R D L }

[0044] According to the vertical earth pressure dP e2 and the lateral earth pressure dq e2 received by the infinitesimal element in the lower half of the cutter head, calculate the earth pressure received by the infinitesimal element in the upper half of the cutter head:

[0045] d s α 2 = dP e 2 sin β + dq e 2 cos β = { c [ h N + ( R D − r sin i ) cos β ] + W π R D L } ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0046] 203. Calculate the frontal earth pressure dF on the infinitesimal element on the cutter head surface 2-1 :

[0047]

[0048] According to the frontal earth pressure dF 2-1 on the infinitesimal element on the cutter head surface, integrate both sides of the equation according to the upper and lower parts of the cutter head, and consider the influence of the cutter head opening ratio to calculate the frontal earth pressure F 2-1 of the cutter head:

[0049]

[0050] In the formula: is the cutter head opening ratio.

[0051] 204. Calculate the force on the infinitesimal element of the soil mass in the soil bin:

[0052]

[0053] According to the force on the infinitesimal element of the soil mass in the soil bin, since the magnitude of the axial stress σ l in the direction of the tunnel axis received by the infinitesimal element is equal to the soil bin pressure σ α , integrate both sides of the equation according to the upper and lower parts of the cutter head to calculate the frictional resistance F 2-2 between the inner wall of the soil bin and the soil mass:

[0054]

[0055] In the formula: l ch is the length of the soil pressure bin, in m; v is the Poisson's ratio of the soil mass.

[0056] 205. Calculate the frontal resistance F 2 of the cutter head:

[0057] F 2 = F 2 − 1 + F 2 − 2 = ( ∫ 0 R D ∫ 0 π d s α 1 rd i dr + ∫ 0 R D ∫ π 2 π d s α 2 rd i dr ) [ ( 1 − oh ch ) + ( e 2 tan f R D v 1 − v l ch − 1 ) ] .

[0058] The above shield machine thrust calculation method considering the influence of slope and radius of curvature is characterized in that in step three:

[0059] The frictional force F between the segment and the shield tail 3 , the resistance F of the trailing trailer 4 and the penetration resistance F of the cutting ring 5 are calculated by the following formula:

[0060]

[0061] In the formula, n 4 is the number of segment rings in the shield tail; W s is the self-weight of each segment ring, in kN; D 0 is the outer diameter of the segment, in m; b w is the contact length between each shield tail seal brush and the pipe ring, in m; p T is the pressure of the shield tail seal brush, in kPa; n 5 is the number of layers of the shield tail seal brush; μ 3 is the friction coefficient between the shield tail seal brush and the segment; μ 2 is the rolling friction coefficient between the wheels of the trailing trailer and the inverted arch surface or between the steel wheels and the track; W p is the self-weight of the trailing trailer, in kN; D is the outer diameter of the front shield, in m; D i is the inner diameter of the front shield, in m; P 3 is the average soil pressure of the formation at the insertion point of the cutting ring, in kPa; t is the depth of the cutting ring inserted into the formation, in m; P m is the average soil pressure acting on the shield, in kPa.

[0062] For the above method for calculating the thrust force of a shield machine considering the influence of slope and radius of curvature, it is characterized in that when tunneling uphill in step four, the resistance F caused by the component of the self-weight of the shield machine along the tunnel axis s is calculated using the following formula:

[0063]

[0064] For the above method for calculating the thrust force of a shield machine considering the influence of slope and radius of curvature, it is characterized in that for the turning thrust difference in step five, since the moment arms of the left and right thrusts are the same when the shield cylinders are advancing, the torque M generated when the shield machine advances one ring of segments is the difference between the left and right thrusts, where:

[0065] The torque M can be obtained by the sum of the torque M of the increase in the soil pressure on the shield shell during the rotation of the shield around the rotation center 1 and the torque M of the increase in the soil pressure on the cutter head around the rotation center 2 , specifically including:

[0066] 501. Calculate the increase in the soil pressure on the shield shell Δσ:

[0067]

[0068] Wherein, k t is the soil spring constant, with the unit of kN / m; S is the horizontal displacement of the soil around the shield shell, with the unit of m; E s is the elastic modulus of the soil, with the unit of kPa; E p is the elastic modulus of the shield machine, with the unit of kPa; I p is the moment of inertia of the shield machine, with the unit of m 4 ;

[0069] Calculate the total torque M q on the rotation center O 1 from the incremental shield shell soil pressure Δσ:

[0070]

[0071] Wherein, the rotation angle , δ g in radians when the shield machine advances one ring of segments; l is the width of each ring of segments, with the unit of m; R is the radius of curvature of the tunnel, with the unit of m; L q is the length of the front shield, with the unit of m;

[0072] 502. Calculate the horizontal displacement S´ and the incremental cutterhead soil pressure Δσ´ at any point on the cutterhead:

[0073]

[0074] ;

[0075] Calculate the total torque M q on the rotation center O 2 from the incremental cutterhead soil pressure Δσ´:

[0076] ;

[0077] 503. Calculate the shield machine turning thrust difference F 6 :

[0078] .

[0079] The above method for calculating the jacking force of a shield machine considering the influence of slope and radius of curvature is characterized in that the jacking force F is calculated according to the following formula:

[0080] .

[0081] Compared with the prior art, the present invention takes into account the influence of slope and curvature radius conditions on the jacking force of a shield machine, adds two key sub-resistances: the resistance caused by the component of the shield self-weight along the tunnel axis and the turning thrust difference, improves the traditional jacking force calculation formula, makes the calculation result close to the actual situation, can effectively guide the design of the shield machine jacking force, improves the calculation accuracy of the shield machine jacking force, and makes up for the technical defect of ignoring slope and curvature radius in the existing calculation method.

[0082] The following will further describe the invention in detail through the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] The accompanying drawings forming a part of this application are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0084] Figure 1 It is a schematic diagram of the calculation model of the friction force between the shield shell and the surrounding soil for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention;

[0085] Figure 2 It is a schematic diagram of the friction force partition of the shield shell for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention;

[0086] Figure 3 It is a schematic diagram of the calculation model of the cutter head soil pressure for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention;

[0087] Figure 4 It is a schematic diagram of the force on the soil micro-element in the soil bin for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention;

[0088] Figure 5 It is a schematic diagram of the change in the soil pressure around the shield shell for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention;

[0089] Figure 6 It is a schematic diagram of the increment of the shield shell soil pressure for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention;

[0090] Figure 7 It is a schematic diagram of the change in the cutter head soil pressure for a shield machine jacking force calculation method considering the influence of slope and curvature radius according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0091] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way limits the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0092] This embodiment provides a calculation method for the thrust force of a shield machine considering the influence of slope and radius of curvature, including the following steps:

[0093] Step 1, according to the friction force calculation model between the shield shell and the surrounding soil, calculate the vertical soil pressure and lateral soil pressure acting on the shield shell, and obtain the sum of the radial components of the two in the radial direction of the shield as the radial soil pressure. Select the friction coefficient between the shield shell and the surrounding soil, and calculate the friction resistance between the shield shell and the surrounding soil.

[0094] Furthermore, when the shield machine is tunneling in a curved section, due to the geometric characteristics of the curve, the extrusion force of the inner soil on the shield shell is significantly greater than that of the outer side. Therefore, the friction force between the inner side of the curve of the shield shell and the soil is also greater than that of the outer side. Therefore, the friction force between the shield shell and the surrounding soil should be calculated according to the inner side and the outer side of the curve, and the friction resistance between the shield shell and the surrounding soil can be calculated by multiplying the radial soil pressure acting on the shield shell by the friction coefficient between the shield shell and the surrounding soil. The soil pressure acting on the shield shell can be divided into vertical soil pressure and lateral soil pressure according to the direction. The sum of the radial components of the two in the radial direction of the shield is the radial soil pressure. Since there are differences in soil pressure above and below the shield machine, it is necessary to calculate in two parts:

[0095] Calculate the vertical soil pressure dP received by the microelement in the upper half of the shield shell e1 and the lateral soil pressure dq e1 :

[0096] dP e 1 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0097] dq e 1 ′ = K 0 dP e 1 ′ = ( 1 − sin f i ) c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0098] In the formula: K 0 is the coefficient of earth pressure at rest, ; γ is the unit weight of the soil layer, in kN / m 3 ; h N is the distance from the top of the cutter head to the ground surface, in m; R D is the radius of the cutter head, in m; β is the tunneling slope of the shield machine, in 。 ; φi is the internal friction angle of soil, with the unit о ; θ is the angle between the calculation point and the horizontal line of the cutter head, with the unit о ; l is the distance from the calculation element to the cutter head surface, with the unit m;

[0099] According to the vertical soil pressure dP e1 and the lateral soil pressure dq e1 , calculate the soil pressure on the upper half of the shield shell per unit length in the radial direction of the contact surface between the shield shell and the soil mass :

[0100] d s i 1 = dP e 1 ′ sin i + dq e 1 ′ cos i = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0101] Calculate the vertical soil pressure dP e2 and the lateral soil pressure dq e2 :

[0102] dP e 2 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L

[0103] dq e 2 ′ = K 0 dP e 2 ′ = ( 1 − sin f i ) { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L }

[0104] In the formula: W is the weight of the shield main body, with the unit kN.

[0105] According to the vertical soil pressure dP e2 and the lateral soil pressure dq e2 , calculate the soil pressure on the upper half of the shield shell per unit length in the radial direction of the contact surface between the shield shell and the soil mass :

[0106] d s i 2 = dP e 2 ′ sin i + dq e 2 ′ cos i = { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0107] Calculate the frictional force df 1 on the upper half of the shield shell on the inner and outer sides of the curve and df 2 :

[0108] df 1 = ndf 1 = n h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0109] df 2 = h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0110] Where: n is the friction force difference coefficient between the inner and outer sides of the curve, and n = 1.1 is obtained by calculating and analyzing the engineering monitoring data; η is the friction coefficient between the shield shell and the surrounding soil mass, generally .

[0111] Calculate the frictional force df on the lower part of the micro-elements of the inner and outer sides of the shield shell 3 and df 4 :

[0112] df 3 = or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } [ sin i + ( 1 − sin f i ) cos i ]

[0113] df 4 = ndf 3 = n or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0114] Calculate the frictional resistance F between the shield shell and the surrounding soil mass 1 :

[0115]

[0116] Step 2: According to the cutter head face earth pressure calculation model and the force of the soil mass micro-elements in the soil bin, calculate the cutter head face earth pressure and the frictional resistance between the inner wall of the soil bin and the soil mass respectively, and calculate the cutter head face resistance according to the cutter head face earth pressure and the frictional resistance between the inner wall of the soil bin and the soil mass.

[0117] Furthermore, the calculation method of the cutter head face resistance includes:

[0118] The cutter head face earth pressure is the resultant force of the vertical earth pressure p e and the lateral earth pressure q e in the normal direction of the cutter head, which is equal in magnitude and opposite in direction to the soil bin pressure σ α ;

[0119] Calculate the vertical earth pressure dP on the upper part of the cutter head micro-elements e1 and the lateral earth pressure dq e1 :

[0120] dP e 1 = c [ h N + ( R D − r sin i ) cos β ]

[0121] dq e 1 = K 0 dP e 1 = ( 1 − sin f ) c [ h N + ( R D − r sin i ) cos β ]

[0122] According to the vertical earth pressure dP e1 and the lateral earth pressure dq e1 on the upper part of the cutter head micro-elements, calculate the earth pressure on the upper part of the cutter head micro-elements :

[0123] d s α 1 = dP e 1 sin β + dq e 1 cos β = c [ h N + ( R D − r sin i ) cos β ] ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0124] Calculate the vertical earth pressure dP on the infinitesimal element in the lower half of the cutter head e2 and the lateral earth pressure dq e2 :

[0125] dP e 2 = c [ h N + ( R D − r sin i ) cos β ] + W π R D L

[0126] dq e 2 = K 0 dP e 2 = ( 1 − sin f ) { c [ h N + ( R D − r sin i ) cos β ] + W π R D L }

[0127] Based on the above, calculate the vertical earth pressure dP on the infinitesimal element in the lower half of the cutter head e2 and the lateral earth pressure dq e2 , and calculate the earth pressure on the infinitesimal element in the upper half of the cutter head :

[0128] d s α 2 = dP e 2 sin β + dq e 2 cos β = { c [ h N + ( R D − r sin i ) cos β ] + W π R D L } ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0129] Calculate the frontal earth pressure dF on the infinitesimal element on the cutter head surface 2-1 :

[0130]

[0131] Based on the frontal earth pressure dF on the infinitesimal element on the cutter head surface 2-1 , integrate both sides of the equation according to the upper and lower parts of the cutter head, considering the influence of the cutter head opening ratio, and calculate the frontal earth pressure F of the cutter head 2-1 :

[0132]

[0133] In the formula: is the cutter head opening ratio.

[0134] Calculate the force on the infinitesimal element of the soil mass in the soil bin:

[0135]

[0136] Based on the force on the infinitesimal element of the soil mass in the soil bin, since the magnitude of the axial stress σ l along the tunnel axis direction on the infinitesimal element is equal to the soil bin pressure σ α , therefore, integrate both sides of the equation according to the upper and lower parts of the cutter head, and calculate the frictional resistance F between the inner wall of the soil bin and the soil mass 2-2 :

[0137]

[0138] In the formula: l ch is the length of the soil pressure bin, in m; v is the Poisson's ratio of the soil mass.

[0139] Calculate the frontal resistance F of the cutter head 2 :

[0140] F 2 = F 2 − 1 + F 2 − 2 = ( ∫ 0 R D ∫ 0 π d s α 1 rd i dr + ∫ 0 R D ∫ π 2 π d s α 2 rd i dr ) [ ( 1 − oh ch ) + ( e 2 tan f R D v 1 − v l ch − 1 ) ]

[0141] Step 3: Calculate the friction between the segment and the shield tail, the resistance of the towing trailer, and the penetration resistance of the cutting ring.

[0142] Further, the friction F 3 between the segment and the shield tail, the resistance F 4 of the towing trailer, and the penetration resistance F 5 are calculated by the following formulas

[0143]

[0144] where n 4 is the number of segment rings in the shield tail; W s is the self-weight of each segment ring, in kN; D 0 is the outer diameter of the segment, in m; b w is the contact length between each shield tail seal brush and the segment ring, in m; p T is the pressure of the shield tail seal brush, in kPa; n 5 is the number of layers of the shield tail seal brush; μ 3 is the friction coefficient between the shield tail seal brush and the segment; μ 2 is the rolling friction coefficient between the wheels of the trailing gantry and the invert or between the steel wheels and the track; W p is the self-weight of the trailing gantry, in kN; D is the outer diameter of the front shield, in m; D i is the inner diameter of the front shield, in m; P 3 is the average soil pressure of the formation at the insertion point of the cutting ring, in kPa; t is the depth of the cutting ring inserted into the formation, in m; P m is the average soil pressure acting on the shield, in kPa.

[0145] Step 4: Calculate the resistance caused by the component of the self-weight of the shield machine along the tunnel axis during uphill tunneling.

[0146] Further, during uphill tunneling, the resistance F s caused by the component of the self-weight of the shield machine along the tunnel axis is calculated using the following formula:

[0147]

[0148] Step 5: Calculate the torques on the rotation center caused by the increments of the shield shell soil pressure and the cutter head soil pressure respectively according to the changes in the shield shell soil pressure and the cutter head soil pressure, and calculate the turning thrust difference of the shield machine according to the torques on the rotation center caused by the increments of the shield shell and cutter head soil pressures.

[0149] Furthermore, when the shield cylinder is propelled, since the lever arms of the left and right thrusts are the same, the torque M generated when the shield machine advances one ring of segment is the difference between the left and right thrusts, where:

[0150] The torque M can be obtained from the sum of the torque M of the increment of the soil pressure on the shield shell during the rotation of the shield around the rotation center 1 and the torque M of the increment of the soil pressure on the cutter head around the rotation center 2 where:

[0151] Calculate the increment of the soil pressure on the shield shell Δσ:

[0152]

[0153] In the formula, k t is the soil spring constant, with the unit kN / m; S is the horizontal displacement of the soil around the shield shell, with the unit m; E s is the soil elastic modulus, with the unit kPa; E p is the elastic modulus of the shield machine, with the unit kPa; I p is the moment of inertia of the shield machine, with the unit m 4 .

[0154] Calculate the total torque M of the increment of the soil pressure on the shield shell Δσ around the rotation center O q : 1 :

[0155]

[0156] In the formula, the rotation angle of the shield machine when advancing one ring of segment g , δ q with the unit rad; l is the width of each ring of segment, with the unit m; R is the radius of curvature of the tunnel, with the unit m; L

[0157] Calculate the horizontal displacement S´ of any point on the cutter head and the increment of the soil pressure on the cutter head Δσ´:

[0158]

[0159]

[0160] Calculate the total torque M of the increment of the soil pressure on the cutter head Δσ´ around the rotation center O q : 2 :

[0161]

[0162] Calculate the thrust difference F 6 of the shield machine when turning:

[0163]

[0164] Step 6: Calculate the jacking thrust of the shield machine according to the frictional resistance between the shield shell and the surrounding soil mass, the frontal resistance of the cutter head, the frictional force between the segment and the shield tail, the resistance of the towing trailer, the penetration resistance of the cutting ring, the turning thrust difference, the resistance caused by the component of the self-weight of the shield machine along the tunnel axis, and the turning thrust difference of the shield machine.

[0165] Further, the jacking thrust F is calculated according to the following formula:

[0166]

[0167] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius, characterized in that: The steps include: Step 1: According to the friction calculation model between the shield shell and the surrounding soil, the vertical soil pressure and the lateral soil pressure acting on the shield shell are calculated, and the sum of the components of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is obtained as the radial soil pressure. The friction coefficient between the shield shell and the surrounding soil is selected to calculate the friction resistance between the shield shell and the surrounding soil; Step 2: According to the calculation model of the front earth pressure of the cutter disc and the micro-element force of the soil in the soil bin, the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil are calculated respectively, and the front resistance of the cutter disc is calculated according to the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil; Step 3: Calculate the friction between the segment and the shield tail, the resistance of the tractor trailer, and the penetration resistance of the cut ring; Step 4: Calculate the resistance caused by the weight of the shield machine along the tunnel axis when excavating uphill; Step 5: Calculate the torque of the shield shell soil pressure increment and the cutter head soil pressure increment on the rotation center according to the soil pressure change around the shield shell and the cutter head soil pressure change; Calculate the turning thrust difference of the shield machine according to the torque of the shield shell and the cutter head soil pressure increment on the rotation center; Among them, since the force arms of the left thrust and the right thrust are the same when the shield cylinder is advancing, the torque M generated when the shield machine advances each ring of segments is the difference between the left thrust and the right thrust. The torque M can be obtained by the sum of the torque M1 of the shield shell soil pressure increment to the rotation center during the shield rotation process and the torque M2 of the cutterhead soil pressure increment to the rotation center, which specifically includes:

501. Calculate the shield shell soil pressure increment Δσ: In the formula, k t is the soil spring constant; S is the horizontal displacement of the soil around the shield; E s is the elastic modulus of soil; E p is the elastic modulus of the shield machine; I p is the inertia moment of the shield machine; R D is the cutter head radius; According to the shield earth pressure increment Δσ, find its relative to the rotation center O q The total torque M1: In the formula, the turning angle of the shield machine when advancing one ring of segments is δ g Unit: rad; l is the width of each ring segment, unit: m; R is the radius of curvature of the tunnel, unit: m; L q is the length of the front shield, in m; 502. Calculate the horizontal displacement S′ and the cutterhead soil pressure increment Δσ′ of any point on the cutterhead: S′=δ g rcosθ △σ′=kδ g rcosθ; According to the soil pressure increment Δσ′ of the cutter head, find its relative pressure to the rotation center O q The total torque M2:

503. Calculate the turning thrust difference F6 of the shield machine: Where M1 is the shield earth pressure increment relative to the rotation center O q The total torque; M2 is the increment of the cutter head earth pressure on the rotation center O q Total torque of Step 6: Calculate the top thrust of the shield machine based on the friction resistance between the shield shell and the surrounding soil, the front resistance of the cutterhead, the friction between the pipe segment and the shield tail, the resistance of the tractor trailer and the penetration resistance of the cutter ring, the resistance caused by the weight of the shield machine along the tunnel axis, and the turning thrust difference of the shield machine.

2. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: In the step 1: When the shield machine is excavating in a curved section, due to the geometric characteristics of the curve, the squeezing force of the inner soil on the shield shell is significantly greater than that on the outer side, so the friction between the shield shell and the soil on the inner side of the curve is also greater than that on the outer side; therefore, the friction between the shield shell and the surrounding soil should be calculated according to the inner side and the outer side of the curve, and the friction resistance between the shield shell and the surrounding soil can be calculated by multiplying the radial soil pressure acting on the shield shell and the friction coefficient between the shield shell and the surrounding soil; the soil pressure acting on the shield shell can be divided into vertical soil pressure and lateral soil pressure according to the direction, and the sum of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is the radial soil pressure. Since the soil pressure is different between the upper and lower parts of the shield machine, it should be divided into two parts for calculation; specifically including:

101. Calculate the vertical earth pressure dP on the microelement of the upper part of the shield e1 ′ and lateral earth pressure dq e1 ′: dP e1 ′=γ[h N +lsinβ+R D (1-sinθ)cosβ] Where: K0 is the static earth pressure coefficient, γ is the bulk density of soil layer; h N is the distance between the top of the cutterhead and the ground surface; R D is the cutter head radius; β is the tunneling slope of the shield machine; is the internal friction angle of the soil; θ is the angle between the calculation point and the horizontal line of the cutterhead; l is the distance between the calculation microelement and the cutterhead surface; According to the vertical earth pressure dP on the upper part of the shield e1 ′ and lateral earth pressure dq e1 ′, calculate the earth pressure dσ on the upper part of the microelement on the radial unit length of the contact surface between the shield and the soil θ1 : Where: θ is the angle between the calculation point and the horizontal line of the cutterhead; 102. Calculate the vertical earth pressure dP on the microelement of the lower half of the shield e2 ′ and lateral earth pressure dq e2 ′: Where: γ is the soil bulk density; h N is the distance between the top of the cutterhead and the ground surface; l is the distance between the calculation microelement and the cutterhead surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; W is the weight of the shield machine, π is the circumference, and L is the length of the shield shell; According to the vertical earth pressure dP on the microelement of the lower half of the shield e2 ′ and lateral earth pressure dq e2 ′, calculate the earth pressure dσ on the upper part of the microelement on the radial unit length of the contact surface between the shield and the soil θ2 : Where: θ is the angle between the calculation point and the horizontal line of the cutterhead; 103. Calculate the friction forces df1 and df2 on the inner and outer upper parts of the shield shell: Where: n is the difference coefficient of friction between the inner and outer sides of the curve, which is calculated and analyzed based on engineering monitoring data to obtain n = 1.1; η is the friction coefficient between the shield and the surrounding soil, which is generally 104. Calculate the friction forces df3 and df4 on the inner and outer lower half of the shield: Where: η is the friction coefficient between the shield and the surrounding soil, which is generally γ is the bulk density of soil layer; h N is the distance between the top of the cutterhead and the ground surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; W is the weight of the shield machine; π is pi, and L is the length of the shield shell; 105. Calculate the friction resistance F1 between the shield and the surrounding soil: Where: f1 is the friction force on the upper half of the shield shell inside the curve; f2 is the friction force on the upper half of the shield shell outside the curve; f3 is the friction force on the lower half of the shield shell inside the curve; f4 is the friction force on the lower half of the shield shell outside the curve.

3. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: The soil pressure on the front of the cutterhead in step 2 is the vertical soil pressure p e and lateral earth pressure q e The resultant force in the normal direction of the cutterhead and the soil bin pressure σ α Equal in size and opposite in direction; The calculation method of the front resistance of the cutter head includes:

201. Calculate the vertical earth pressure dP on the microelement of the upper half of the cutterhead e1 and lateral earth pressure dq e1 : dP e1 =γ[h N +(R D -rsinθ)cosβ] Where: γ is the soil bulk density; h N is the distance between the top of the cutterhead and the ground surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; K0 is the static earth pressure coefficient, According to the vertical earth pressure dP on the microelement of the upper half of the cutterhead e1 and lateral earth pressure dq e1 , calculate the earth pressure dσ on the upper part of the cutter head α1 : Where: β is the tunneling slope of the shield machine; 202. Calculate the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dq e2 : Where: γ is the soil bulk density; h N is the distance between the top of the cutterhead and the ground surface; l is the distance between the calculation microelement and the cutterhead surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; W is the weight of the shield machine; K0 is the static earth pressure coefficient, According to the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dq e2 , calculate the earth pressure dσ on the upper part of the cutter head α2 : Where: β is the tunneling slope of the shield machine; 203. Calculate the front earth pressure dF on the microelement on the cutterhead surface 2-1 : dF 2-1 =dσ α rdθdr According to the front earth pressure dF on the cutterhead surface microelement 2-1 , integrate both sides of the equation according to the upper and lower parts of the cutterhead, consider the influence of the cutterhead opening rate, and calculate the soil pressure F on the front of the cutterhead 2-1 : Where: ch is the cutter head opening rate; 204. Calculate the soil microelement force in the soil bin: pR D 2 s l +2πR D τdl=πR D 2 (s l +dσ l ) Where: R D is the cutter head radius; σ l is the axial stress; According to the force of the soil microelement in the soil bin, the axial stress σ along the tunnel axis is l The size of the soil bin pressure σ α Equal, so according to the cutter head upper and lower parts of the equation on both sides of the integration, calculate the friction between the soil bin inner wall and the soil F 2-2 : Where: l ch is the length of the earth pressure chamber, in m; v is the Poisson's ratio of the soil; 205. Calculate the front resistance F2 of the cutter disc: Where: F 2-1 is the soil pressure on the front of the cutterhead; F 2-2 It is the frictional resistance between the inner wall of the soil bin and the soil.

4. A method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius as claimed in claim 1, characterized in that: In the step three: The calculation formulas for the friction force F3 between the segment and the shield tail, the resistance F4 of the tractor trailer, and the penetration resistance F5 of the cut ring are as follows: Where n4 is the number of segments in the tail shield; W s is the deadweight of each ring of segments; D0 is the outer diameter of the segments; b w is the contact length between each shield tail sealing brush and the pipe ring; p T is the pressure of the shield tail sealing brush; n5 is the number of layers of the shield tail sealing brush; μ3 is the friction coefficient between the shield tail sealing brush and the pipe segment; μ2 is the rolling friction coefficient between the rear supporting trailer wheel and the supply surface or the steel wheel and the track; W p is the weight of the trailer; D is the outer diameter of the front shield; D i is the inner diameter of the front shield; P3 is the average soil pressure of the stratum where the cut ring is inserted; t is the depth of the cut ring inserted into the stratum; P m is the average earth pressure acting on the shield.

5. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: When excavating uphill in step 4, the resistance F caused by the weight of the shield machine along the tunnel axis s The calculation is done using the following formula: F S =Wsinβ+W p sinβ Where W is the weight of the shield machine; β is the tunneling slope of the shield machine; W p It is the deadweight of the trailer to be equipped later.

6. A method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius as claimed in claim 1, characterized in that: The thrust force F is calculated according to the following formula: <h2 style=";text-align:left;direction:ltr">F = F1 + F2 + F3 + F4 + F5 + F<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> +F6 Where, F1 is the friction resistance between the shield and the surrounding soil; F2 is the front resistance of the cutterhead; F3 is the friction between the segment and the shield tail; F4 is the resistance of the towing trailer; F5 is the penetration resistance of the cut ring; and F6 is the thrust difference of the shield machine when turning.

Images