A calculation method for vertical loads above pipe jacking considering the loss effect of sandy soil strata

Abstract

The present invention discloses a method for calculating the vertical load above a pipe jacking project that takes into account the loss effect of sandy soil layers. The method comprises the following steps: constructing a theoretical analysis model and determining key parameters of the theoretical analysis model based on the design parameters of the pipe jacking project; determining the state of the pipe jacking project and determining a corresponding theoretical analysis model based on the state of the pipe jacking project; and calculating the vertical load acting on the pipe jacking arch based on the theoretical analysis model of the state of the pipe jacking project and the soil arching effect and mechanical equilibrium theory. The method of the present invention can be applied to the calculation and analysis of the vertical load above the pipe jacking project that takes into account the loss effect of sandy soil layers, providing a reference for the prediction of lateral friction resistance during the pipe jacking process.

Description

Technical Field

[0001] The invention belongs to the technical field of pipe jacking construction, and in particular relates to a method for calculating the vertical load above the pipe jacking taking into account the loss effect of sandy soil layers. Background Art

[0002] Pipe jacking is a trenchless technology. It is widely used in water supply, sewage, oil and gas pipelines, transportation tunnels and pipe curtain projects because of its characteristics such as fast construction speed, small disturbance to the surrounding environment during the construction process, high construction quality and high adaptability to the formation. The jacking force is the most important parameter in the pipe jacking construction process. It directly determines the selection of the pipe jacking machine, the pipe wall thickness and the design of the reaction wall structure. It has received the attention of many scholars and designers. During the pipe jacking process, the jacking force applied to the pipe is balanced by the end resistance and the side friction resistance between the pipe side wall and the soil. Since the pipeline is a linear structure, as the jacking length increases, the side friction resistance gradually dominates the jacking force. To date, many scholars have proposed different theoretical models and empirical formulas for the side friction resistance of pipe jacking, which can be roughly divided into three types:

[0003] (1) Empirical formula based on statistical evaluation of field data. This empirical formula fully utilizes the advantages of engineering analogy, thereby simplifying tedious calculations to a certain extent. However, empirical formulas are often time-sensitive. With the gradual development of pipe jacking equipment and technology, and the fact that even the same type of soil may have huge differences in conditions in different regions, the predicted results of existing empirical formulas may differ from the actual results.

[0004] (2) Empirical formula obtained by fitting indoor test results. Although indoor test results can be used to predict lateral friction resistance in a targeted manner, the model similarity ratio and the simulation of pipe jacking technology are difficult to guarantee, and require a lot of manpower, material and financial resources, which is not convenient for widespread application.

[0005] (3) Theoretical model based on the Tayzaghi sliding gate test. This model essentially uses the soil pressure around the pipe plus the product of the pipe section's own weight and the corresponding friction coefficient to calculate the lateral friction resistance. Due to its clear physical meaning and simple calculation method, it is favored by many scholars and national standards. The key to this model's calculation method lies in how to determine the vertical load above the pipeline.

[0006] In terms of vertical load calculation above the jacking pipe, Pellet-BeaucourandK aStner (2002) believed that the Terzaghi theoretical model could be used to calculate the vertical load above the pipeline. However, as the buried depth of the pipeline increases, the shear sliding zone caused by the pipe jacking construction remains within the stratum and does not extend to the surface. The Terzaghi theoretical model still has certain limitations. In response to this, Zhang (2016) established a relationship between the shear sliding zone extension height and the stratum loss rate by introducing the soil volume expansion coefficient. He assumed that the soil above the shear sliding zone acts on the top of the shear sliding zone with its own weight stress, and then derived the vertical load acting on the pipe jacking under the deep buried state. However, based on the two-dimensional discrete element numerical results of the sliding gate test, Lai (2018) pointed out that there is an unloading zone of a certain height between the loose zone and the undisturbed zone. This unloading zone also exhibits a certain soil arching effect and has a significant impact on the vertical load above the pipe jacking. Wan (2019) and Lin (2022a) conducted in-depth research on the unloading zone above the loose zone, and derived the analytical formula of load transfer in the unloading zone through certain assumptions, and then obtained the vertical load above the jacking pipe.

[0007] In summary, theoretical research on the vertical load above the jacking pipe has made great progress. However, the current theoretical model still has the following two limitations: (1) As the unloading zone connecting the undisturbed zone and the loose zone, the existing model does not consider the transition and continuous effects of its mechanical response characteristics; (2) When the formation loss caused by construction disturbance is small, a stable shear sliding zone has not yet formed inside the formation, and the existing model cannot calculate the vertical load above the jacking pipe in this case. Although Lin (2022b) obtained the vertical load above the jacking pipe when the formation loss rate is relatively small by constructing a fitting function, the empirical parameters in the function need to be obtained in advance through a sliding gate test, which greatly limits the application of this method. Summary of the Invention

[0008] To overcome the shortcomings of the prior art, the present invention provides a method for calculating the vertical load above a pipe jacking operation that takes into account the effects of sandy soil loss. This method can be divided into a shallow model, a first transition model, a second transition model, a first deep model, and a second deep model, based on different stratum losses and pipe jacking depths. The appropriate model is selected for calculation based on the actual pipe jacking situation.

[0009] To achieve the above object, the present invention provides a method for calculating the vertical load above the jacking pipe taking into account the loss effect of the sandy soil layer, comprising:

[0010] Constructing a theoretical analysis model and determining key parameters of the theoretical analysis model according to the design parameters of the pipe jacking project;

[0011] Determine the state of the pipe jacking and determine the corresponding theoretical analysis model based on the state of the pipe jacking;

[0012] Based on the theoretical analysis model of the state of the jacking pipe, the vertical load acting on the jacking pipe arch is calculated according to the soil arch effect and mechanical equilibrium theory.

[0013] Preferably, the pipe jacking engineering design parameters include but are not limited to the buried depth of the pipe jacking, the outer diameter of the pipe jacking machine and the pipe jacking, the volume expansion coefficient of the sand, and the internal friction angle;

[0014] The key parameters of the theoretical analysis model include but are not limited to the formation loss rate, the height of the sand failure zone above the jacking pipe, the height of the soil arching zone, and the height of the undisturbed zone.

[0015] Preferably, the process of determining the state of the pipe jacking includes:

[0016] According to the formation loss effect caused by the outer diameter of the pipe jacking machine being larger than the outer diameter of the subsequent pipe jacking during construction, as well as the influence of the buried depth of the pipe jacking and the formation loss effect, the area above the pipe jacking construction is divided into the sand failure zone, the soil arch zone and the undisturbed zone in sequence.

[0017] Preferably, the process of determining the corresponding theoretical analysis model according to the state of the pipe jacking includes:

[0018] When the failure zone extends to the surface, the failure zone is only a rectangle, and the soil arch zone and the undisturbed zone do not exist, and a shallow buried analysis model is constructed;

[0019] When the failure zone is composed of a rectangle and a parabola, and the soil arch area above the sand failure zone extends to the surface, the undisturbed zone does not exist, and the first transition model is constructed;

[0020] When the failure zone is only parabolic and the soil arch area above the sand failure zone extends to the surface, the undisturbed zone does not exist and the second transition model is constructed;

[0021] When the failure zone is composed of rectangle and parabola, and the soil arch zone does not extend to the surface, the first deep buried model is constructed;

[0022] When the failure zone is only parabolic and the soil arch zone does not extend to the surface, the second deep buried model is constructed.

[0023] Preferably, shear sliding zones are formed on both sides of the failure zone and the stable strata, and the friction stress on the shear sliding zones causes a principal stress deflection effect in the failure zone, which manifests as a maximum principal stress arch;

[0024] The soil arch zone serves as a transition zone between the undisturbed zone and the failure zone. The principal stress deflection angle at the bottom is the same as that in the failure zone, and no principal stress deflection effect occurs at the top. The lateral pressure coefficient and the principal stress deflection angle vary linearly with height.

[0025] The undisturbed area is not affected by the pipe jacking construction, and the lateral pressure coefficient is the static earth pressure coefficient, and acts on the top of the soil arch area with its own weight.

[0026] Preferably, the shape of the fracture surface at the top of the failure zone is consistent with the shape of the principal stress trace in the failure zone;

[0027] When the pipe jacking model is a shallow buried model, a first transition model, and a first deep buried model, the principal stress deflection angle in the failure zone is determined according to the internal friction angle of the sand;

[0028] When the pipe jacking model is the second transition model and the second deep buried model, the principal stress deflection angle in the failure zone is determined by the formation loss rate and the sand volume expansion coefficient.

[0029] Preferably, after the principal stress in the failure zone is deflected, the principal stress trace is a parabola with a reasonable arch axis.

[0030] Preferably, when the jacking pipe is a shallow buried model, the height of the failure zone is the buried depth of the jacking machine;

[0031] When the jacking pipe is of other models, the height of the failure zone is determined by the sand volume expansion coefficient and the formation loss rate.

[0032] Preferably, based on a theoretical analysis model of the state of the jacking pipe and in accordance with the soil arching effect and mechanical equilibrium theory, the process of calculating the vertical load acting on the jacking pipe arch includes:

[0033] The soil arch area is divided into m parts along the mid-span height. Each part is assumed to be a three-hinged arch structure with a reasonable arch axis. The product of the load acting on the top of each three-hinged arch and the horizontal lateral pressure coefficient is the horizontal thrust acting on the arch foot of the three-hinged arch. Part of the load acting on the top of the three-hinged arch is balanced by the horizontal thrust of the arch foot, and the other part is transferred to the top of the next three-hinged arch structure until the load acting on the top of the failure zone is obtained.

[0034] Preferably, based on a theoretical analysis model of the state of the jacking pipe and in accordance with the soil arching effect and mechanical equilibrium theory, the process of calculating the vertical load acting on the jacking pipe arch includes:

[0035] When the parabolic failure zone and the soil arch zone have a tendency to separate, the parabolic failure zone acts on the area below with its own weight. After determining the load of the soil arch zone, the load of the failure zone is calculated according to different models.

[0036] Among them, when the jacking pipe model is a shallow buried model, the vertical load acting on the jacking pipe is obtained by calculating the limit equilibrium theory;

[0037] When the pipe jacking model is the first transition model and the first deep buried model, the parabolic failure zone acts on the top of the rectangular failure zone with its own weight. The load acting on the top of the rectangular failure zone and the vertical load acting on the pipe jacking are calculated based on the deadweight of the parabolic failure zone.

[0038] When the jacking pipe model is the second transition model and the second deep buried model, the vertical load acting on the jacking pipe is calculated based on the deadweight of the parabolic failure zone.

[0039] Compared with the prior art, the present invention has the following advantages and technical effects:

[0040] The present invention can calculate the vertical load on the jacking pipe under different conditions, and the calculation and solution are convenient, which can be applied in engineering practice. In addition, compared with existing algorithms, the algorithm has more reasonable assumptions and the obtained vertical load on the jacking pipe is more consistent with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0042] Figure 1 Schematic diagram of an embodiment of the present invention;

[0043] Figure 2 This is a load calculation diagram for the soil arch area of ​​transition model 1 according to an embodiment of the present invention;

[0044] Figure 3 This is a load calculation diagram for the soil arch area of ​​transition model 2 according to an embodiment of the present invention;

[0045] Figure 4 This is a load calculation diagram for the soil arch area of ​​the deep buried model 1 according to an embodiment of the present invention;

[0046] Figure 5 Load calculation diagram of soil arch area of ​​deep buried model 2 according to an embodiment of the present invention;

[0047] Figure 6 This is a failure zone load calculation diagram for an embodiment of the present invention;

[0048] Figure 7 A comparison chart of the vertical load above the jacking pipe and the sliding door test results of an embodiment of the present invention;

[0049] Figure 8 A finite element numerical model diagram of an embodiment of the present invention;

[0050] Figure 9 A comparison diagram of the failure area of ​​an embodiment of the present invention and the numerical simulation results;

[0051] Figure 10This is a graph showing the change in the normalized vertical load above the jacking pipe as a function of the depth-to-diameter ratio when the internal friction angle changes according to an embodiment of the present invention;

[0052] Figure 11 This is a graph showing the change in the normalized vertical load above the jacking pipe versus the soil volume expansion coefficient when the depth-to-diameter ratio changes according to an embodiment of the present invention;

[0053] In the figure, D is the outer diameter of the jacking pipe, B is the outer diameter of the jacking machine, C is the buried depth of the jacking machine arch, H1 is the height of the soil arch area, H2 is the height of the parabolic failure area, H3 is the height of the rectangular failure area, K0 is the static earth pressure coefficient, K l is the lateral pressure coefficient of the failure zone under transition model 1 and deep buried model 1, K gl is the lateral pressure coefficient of the failure zone under transition model 2 and deep buried model 2, K T0-1 is the lateral pressure coefficient at the top of the soil arch area under transition model 1, K T0-2 is the lateral pressure coefficient at the top of the soil arch area under transition model 2, q0 is the load acting on the top of the soil arch area from the undisturbed area, and q S is the load of the soil arch area acting on the top of the parabolic failure zone, q P is the load of the parabolic failure zone acting on the top of the rectangular failure zone, q F is the vertical load acting on the top pipe, q Ti-1 is the load transferred from the i-th soil arch to the next soil arch under transition model 1, q Ti-2 is the load transferred from the i-th soil arch to the next soil arch under transition model 2, q i-1 is the load transferred from the i-th soil arch to the next soil arch in deep buried model 1, q Ti-2 is the load transferred from the i-th soil arch to the next soil arch in deep buried model 2, q TGi-1 is the self-weight load of the i-th soil arch under transition model 1, q TGi-2 is the self-weight load of the i-th soil arch under transition model 2, q Gi-1 is the self-weight load of the i-th soil arch under deep buried model 1, q Gi-2 is the self-weight load of the i-th soil arch under deep buried model 2, W p is the deadweight of the parabolic failure zone, θ T0 is the principal stress deflection angle of the top of the soil arch area under transition model 1, θ0 is the principal stress deflection angle of the failure area under transition model 1 and deep buried model 1, ξ T0 is the principal stress deflection angle of the top of the soil arch area under transition model 2, ξ is the principal stress deflection angle of the failure area under transition model 2 and deep buried model 2, m is the number of parts the soil arch area is divided into along the height, L Ti-1 is the length of the arch foot of the i-th soil arch under transition model 1, L Ti-2 is the length of the arch foot of the i-th soil arch under transition model 2, L i-1 is the length of the arch foot of the i-th soil arch under deep buried model 1, Li-2 is the length of the arch foot of the i-th soil arch under deep buried model 2, F Ti-1 is the horizontal thrust of the i-th soil arch foot under transition model 1, F Ti-2 is the horizontal thrust of the i-th soil arch foot under transition model 2, F i-1 is the horizontal thrust of the i-th soil arch foot under deep buried model 1, F i-2 is the horizontal thrust at the foot of the i-th soil arch under deep buried model 2. DETAILED DESCRIPTION

[0054] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0055] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0056] like Figure 1-11 As shown, this embodiment provides a method for calculating the vertical load above the jacking pipe considering the loss effect of the sand layer, including:

[0057] S1. Construct theoretical analysis model;

[0058] S2. Determine key parameters in the theoretical analysis model, such as the formation loss rate, the height of the sand failure zone above the jacking pipe, the height of the soil arching zone, and the height of the undisturbed zone, based on the design parameters of the jacking project (such as the jacking pipe burial depth, the outer diameter of the jacking machine and the jacking pipe, the sand volume expansion coefficient, and the internal friction angle);

[0059] S3, determining the state of the pipe jacking and the corresponding theoretical model;

[0060] S4. Based on the soil arch effect and mechanical equilibrium theory, derive the theoretical formula to calculate the vertical load acting on the jacking pipe.

[0061] Furthermore, during construction, if the outer diameter of the pipe jacking machine is slightly larger than the outer diameter of the subsequent pipe jacking, it will cause a formation loss effect. Influenced by the buried depth of the pipe jacking and the formation loss effect, there will be a sand failure zone, a soil arch zone, and an undisturbed zone above the pipe jacking construction. The theoretical models constructed under different conditions are as follows:

[0062] When the failure zone extends to the surface, the failure zone is only a rectangle. At this time, the soil arch zone and the undisturbed zone do not exist, and a shallow buried analysis model can be constructed.

[0063] When the failure zone is composed of a rectangle and a parabola, and the soil arching area above the sand failure zone extends to the surface, the undisturbed zone does not exist, and transition model 1 can be constructed;

[0064] When the failure zone is only parabolic and the soil arching area above the sand failure zone extends to the surface, the undisturbed zone does not exist and transition model 2 can be constructed;

[0065] When the failure zone is composed of rectangles and paraboloids, and the soil arch zone does not extend to the surface, deep buried model 1 can be constructed;

[0066] When the failure zone is only parabolic and the soil arch zone does not extend to the surface, a deep buried model 2 can be constructed.

[0067] Furthermore, shear sliding zones are formed on both sides of the failure zone and the stable strata, and the friction stress on the shear sliding zone causes a principal stress deflection effect in the failure zone, which manifests as a maximum principal stress arch; the soil arch zone serves as a transition area between the undisturbed zone and the failure zone, and the principal stress deflection angle at the bottom is the same as that in the failure zone, no principal stress deflection effect occurs at the top, and the lateral pressure coefficient and the principal stress deflection angle change linearly with the height; the undisturbed zone is not affected by the jacking construction, the lateral pressure coefficient is the static soil pressure coefficient, and the soil arch zone acts on the top with its own weight.

[0068] Furthermore, the shape of the fracture surface at the top of the failure zone is consistent with the shape of the principal stress trace in the failure zone. When the jacking pipe model is a shallow buried model, transition model 1, and deep buried model 1, the principal stress deflection angle in the failure zone reaches θ0; when the jacking pipe model is a transition model 2 and a deep buried model 2, the principal stress deflection angle in the failure zone is determined by the formation loss rate and the sand volume expansion coefficient.

[0069] Furthermore, after the principal stress in the failure zone is deflected, the principal stress trace is a parabola with a reasonable arch axis.

[0070] When the pipe jacking model is the shallow buried model, transition model 1, and deep buried model 1, the expression of the principal stress trace in the failure zone is:

[0071]

[0072] Where: B is the outer diameter of the pipe jacking machine, φ is the internal friction angle of sand, and θ0 is the principal stress deflection angle of the failure zone under the shallow buried model, transition model 1, and deep buried model 1.

[0073] According to the principal stress deflection theory, the lateral pressure coefficient of the failure zone under the shallow buried model, transition model 1 and deep buried model 1 can be obtained as:

[0074]

[0075] Among them: K a is the active earth pressure coefficient, K l is the pressure coefficient on the upper side of the shear sliding zone.

[0076] When the pipe jacking model is transition model 2 and deep buried model 2, the expression of the principal stress trace is:

[0077]

[0078] Where: ξ is the principal stress deflection angle of the failure zone under transition model 2 and deep buried model 2, D is the outer diameter of the jacking pipe,

[0079] According to the principal stress deflection theory, the lateral pressure coefficient of the failure zone under transition model 2 and deep buried model 2 can be obtained as:

[0080]

[0081] Furthermore, when the jacking pipe is a shallow buried model, the height of the failure zone is the buried depth of the jacking machine; when the jacking pipe is other models, the height of the failure zone can be determined by the sand volume expansion coefficient and the formation loss rate.

[0082] The expression of formation loss rate is:

[0083]

[0084] Where: V l is the formation loss rate caused by pipe jacking.

[0085] The volume expression of over-excavation of pipe jacking machine is:

[0086]

[0087] Where: V L The volume of over-excavation by the pipe jacking machine.

[0088] The relationship between the over-excavation volume of the pipe jacking machine and the volume of the failure zone is:

[0089]

[0090] Where: V is the volume of the failure zone, α is the volume expansion coefficient of sand, which can be obtained from indoor soil tests.

[0091] When the pipe jacking model is transition model 1 and deep buried model 1, the height of the failure zone rectangle is:

[0092]

[0093] Where: H2 is the height of the failure area rectangle.

[0094] When the pipe jacking model is transition model 2 and deep buried model 2, the expression of the parabolic failure zone height is:

[0095]

[0096] Where: H2 is the height of the parabola in the failure zone.

[0097] Furthermore, the height of the soil arch area can be determined based on experience, model tests or numerical simulations, and the expression is:

[0098] H1=0.4B

[0099] Where: H1 is the height of the soil arch area.

[0100] Furthermore, the soil arch area can be divided into m parts along the mid-span height evaluation, and each part can be assumed to be a three-hinged arch structure with a reasonable arch axis. The product of the load acting on the top of each three-hinged arch and the horizontal lateral pressure coefficient is the horizontal thrust acting on the arch foot of the three-hinged arch; part of the load acting on the top of the three-hinged arch is balanced by the horizontal thrust of the arch foot, and the other part is transferred to the top of the next three-hinged arch structure until the load acting on the top of the failure zone is obtained.

[0101] Furthermore, the loads in different areas are calculated sequentially from the ground surface to the top of the jacking pipe. The loads in the undisturbed area under different models are calculated as follows:

[0102] When the pipe jacking model is deep buried model 1, the load expression acting on the top of the soil arch area is:

[0103] q0=(C-H1-H2-H3)γ

[0104] Among them: C is the buried depth of the pipe jacking machine.

[0105] When the pipe jacking model is deep buried model 2, the load expression acting on the top of the soil arch area is:

[0106] q0=(C-H1-H2)γ

[0107] Furthermore, after determining the load of the undisturbed area, the load of the soil arch area under different models is calculated as follows:

[0108] (1) Calculation method of soil arch area load in transition model 1;

[0109] When the pipe jacking model is transition model 1, the expressions of the lateral pressure coefficient and principal stress deflection angle at the top of the soil arch area are:

[0110]

[0111] Among them: K T0-1 is the lateral pressure coefficient at the top of the soil arch area under transition model 1, θ T0 is the principal stress deflection angle at the top of the soil arch area under transition model 1.

[0112] After the soil arch area is divided into m parts, the expressions of the lateral pressure coefficient and principal stress deflection angle of the i-th soil arch are:

[0113]

[0114] Among them: K Tai-1 is the lateral pressure coefficient of the i-th soil arch under transition model 1, θ Tai-1 is the principal stress deflection angle of the i-th soil arch under transition model 1.

[0115] The self-weight stress expression of the i-th soil arch is:

[0116]

[0117] Where: q TGi-1 is the self-weight stress of the i-th soil arch under transition model 1.

[0118] The length and height of the arch foot of the i-th soil arch are expressed as:

[0119]

[0120] Where: L Ti-1 is the length of the arch foot of the i-th soil arch under transition model 1, f Tai-1 is the height of the i-th soil arch under transition model 1.

[0121] According to the boundary condition i=1, q T0-1 = 0, the load expression acting on the top of the failure zone under transition model 1 can be obtained as:

[0122]

[0123] Where: q S is the load acting on the top of the failure zone.

[0124] (2) Load calculation method for soil arch area in transition model 2;

[0125] When the pipe jacking model is transition model 2, the expressions of the lateral pressure coefficient and principal stress deflection angle at the top of the soil arch area are:

[0126]

[0127] Among them: K T0-2 is the lateral pressure coefficient at the top of the soil arch area under transition model 2, ξ T0 is the principal stress deflection angle at the top of the soil arch area under transition model 2.

[0128] After the soil arch area is divided into m parts, the expressions of the lateral pressure coefficient and principal stress deflection angle of the i-th soil arch are:

[0129]

[0130] Among them: K Tai-2is the lateral pressure coefficient of the i-th soil arch under transition model 2, ξ Tai-2 is the principal stress deflection angle of the i-th soil arch under transition model 1.

[0131] The self-weight stress expression of the i-th soil arch is:

[0132]

[0133] Where: q TGi-2 is the self-weight stress of the i-th soil arch under transition model 2.

[0134] The length and height of the arch foot of the i-th soil arch are expressed as:

[0135]

[0136] Where: L Ti-2 is the length of the arch foot of the i-th soil arch under transition model 2, f Tai-2 is the height of the i-th soil arch under transition model 2.

[0137] According to the boundary condition i=1, q T0-2 = 0, the load expression acting on the top of the failure zone under transition model 2 can be obtained as:

[0138]

[0139] (3) Calculation method of soil arch area load in deep buried model 1;

[0140] When the pipe jacking model is deep buried model 1, the lateral pressure coefficient and principal stress deflection angle at the top of the soil arch area are K0 and 0, respectively. After the soil arch area is divided into m parts, the lateral pressure coefficient and principal stress deflection angle of the i-th soil arch are expressed as follows:

[0141]

[0142] Among them: K ai-1 is the lateral pressure coefficient of the i-th soil arch under deep buried model 1, θ ai-1 is the principal stress deflection angle of the i-th soil arch under overburden model 1.

[0143] The self-weight stress expression of the i-th soil arch is:

[0144]

[0145] Where: q Gi-1 is the self-weight stress of the i-th soil arch under deep buried model 1.

[0146] The length and height of the arch foot of the i-th soil arch are expressed as:

[0147]

[0148] Where: L i-1 is the length of the arch foot of the i-th soil arch under deep buried model 1, f ai-1 is the arch height of the i-th soil arch under deep buried model 1.

[0149] According to the boundary condition i = 1, q0-1 = (C-H1-H2-H3)γ, the load expression acting on the top of the failure zone under the deep buried model 1 can be obtained as:

[0150]

[0151] (4) Calculation method of soil arch area load in deep buried model 2;

[0152] When the pipe jacking model is deep buried model 2, the lateral pressure coefficient and principal stress deflection angle at the top of the soil arch area are K0 and 0, respectively. After the soil arch area is divided into m parts, the lateral pressure coefficient and principal stress deflection angle of the i-th soil arch are expressed as follows:

[0153]

[0154] Among them: K ai-2 is the lateral pressure coefficient of the i-th soil arch under deep buried model 2, ξ ai-2 is the principal stress deflection angle of the i-th soil arch under overburden model 2.

[0155] The self-weight stress expression of the i-th soil arch is:

[0156]

[0157] Where: q Gi-2 is the self-weight stress of the i-th soil arch under deep buried model 1.

[0158] The length and height of the arch foot of the i-th soil arch are expressed as:

[0159]

[0160] Where: L i-2 is the length of the arch foot of the i-th soil arch under deep buried model 2, f ai-2 is the height of the i-th soil arch under deep buried model 2.

[0161] According to the boundary condition i=1, q 0-2 =(C-H1-H2)γ, the load expression acting on the top of the failure zone under deep buried model 2 can be obtained as:

[0162]

[0163] Furthermore, the parabolic failure zone and the soil arch zone tend to separate, and the parabolic failure zone acts on the area below with its own weight. After determining the load of the soil arch zone, the failure zone load under different models is calculated as follows:

[0164] (1) Calculation method of load in failure zone of shallow buried model;

[0165] When the pipe jacking model is a shallow buried model, the vertical load acting on the pipe jacking can be calculated using the limit equilibrium theory:

[0166]

[0167] (2) Load calculation method for transition model 1 and deep buried model 1;

[0168] When the pipe jacking model is transition model 1 and deep buried model 1, the parabolic failure zone acts on the top of the rectangular failure zone with its own weight, and the expression is:

[0169]

[0170] Where: W p is the deadweight of the parabolic failure zone.

[0171] The load expression acting on the top of the rectangular failure zone is:

[0172]

[0173] Where: q P is the load acting on the top of the rectangular failure zone.

[0174] The vertical load acting on the top pipe is expressed as:

[0175]

[0176] Where: q F It is the vertical load acting on the top pipe.

[0177] (3) Load calculation method for transition model 2 and deep buried model 2;

[0178] When the pipe jacking model is transition model 2 and deep buried model 2, the deadweight expression of the parabolic failure zone is:

[0179]

[0180] The vertical load acting on the top pipe is expressed as:

[0181]

[0182] The calculation method proposed by the present invention is further described in detail below with reference to the accompanying drawings.

[0183] First, different theoretical analysis models (shallow buried model, transition model 1, transition model 2, deep buried model 1 and deep buried model 2) are constructed, such as Figure 1 As shown; secondly, according to the design parameters of the jacking project (such as the buried depth of the jacking pipe, the outer diameter of the jacking machine and the jacking pipe, the volume expansion coefficient of the sand, the internal friction angle, etc.), determine the key parameters such as the formation loss rate, the height of the sand failure zone above the jacking pipe, the height of the soil arch zone and the height of the undisturbed zone in the theoretical analysis model; then, determine the state of the jacking pipe and the corresponding theoretical analysis model; according to the soil arch effect and mechanical equilibrium theory, derive the theoretical formula to calculate the vertical load acting on the jacking pipe. Among them, the load calculation models of the soil arch zone and the rectangular failure zone described in the theoretical analysis model are as follows: Figure 2-Figure 6 shown.

[0184] (1) Comparison with sliding door test results

[0185] The model test results given by Zhu (2012) are compared with the algorithm proposed in this paper. Figure 7 It can be seen that the calculation results of the algorithm provided by the present invention are relatively close to the model test results, which verifies the accuracy and superiority of the algorithm provided by the present invention.

[0186] (2) Comparison with the failure area of ​​numerical results

[0187] Establish a two-dimensional finite element numerical model, such as Figure 8 As shown. The calculation results of the failure zone above the jacking pipe are obtained by numerical calculation. The calculation results of this algorithm are compared with the numerical results, as shown in Figure 9 As shown in Figure 2, it can be seen that the failure zone contour proposed by this algorithm is in good agreement with the numerical results.

[0188] (3) Figure 10 and Figure 11 Curves showing the normalized vertical load on the pipe as a function of depth-to-diameter ratio for different internal friction angles and the soil volume expansion coefficient for different depth-to-diameter ratios are presented. During the engineering design phase, the vertical load acting on the pipe can be quickly determined based on the pipe design parameters and engineering geological survey parameters.

[0189] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for calculating the vertical load above a jacking pipe considering the loss effect of sandy soil strata, characterized in that: include: Constructing a theoretical analysis model and determining key parameters of the theoretical analysis model according to the design parameters of the pipe jacking project; Determine the state of the pipe jacking and determine the corresponding theoretical analysis model based on the state of the pipe jacking; Based on the theoretical analysis model of the pipe jacking state, the vertical load acting on the pipe jacking arch is calculated according to the soil arch effect and mechanical equilibrium theory. The process of determining the corresponding theoretical analysis model according to the state of the pipe jacking includes: When the failure zone extends to the surface, the failure zone is only a rectangle, and the soil arch zone and the undisturbed zone do not exist, so a shallow buried model is constructed. When the failure zone is composed of a rectangle and a parabola, and the soil arch area above the sand failure zone extends to the surface, the undisturbed zone does not exist, and the first transition model is constructed; When the failure zone is only parabolic and the soil arch area above the sand failure zone extends to the surface, the undisturbed zone does not exist and the second transition model is constructed; When the failure zone is composed of rectangle and parabola, and the soil arch zone does not extend to the surface, the first deep buried model is constructed; When the failure zone is only parabolic and the soil arch zone does not extend to the surface, the second deep buried model is constructed; Based on the theoretical analysis model of the pipe jacking state, and according to the soil arching effect and mechanical equilibrium theory, the process of calculating the vertical load acting on the pipe jacking arch includes: The soil arch area is divided into m equal parts along the mid-span height. Each part is assumed to be a three-hinged arch structure with a reasonable arch axis. The product of the load acting on the top of each three-hinged arch and the horizontal lateral pressure coefficient is the horizontal thrust acting on the arch foot of the three-hinged arch. Part of the load acting on the top of the three-hinged arch is balanced by the horizontal thrust of the arch foot, and the other part is transferred to the top of the next three-hinged arch structure until the load acting on the top of the failure zone is obtained. Based on the theoretical analysis model of the pipe jacking state, and according to the soil arching effect and mechanical equilibrium theory, the process of calculating the vertical load acting on the pipe jacking arch includes: When the parabolic failure zone and the soil arch zone have a tendency to separate, the parabolic failure zone acts on the area below with its own weight. After determining the load of the soil arch zone, the load of the failure zone is calculated according to different models. Among them, when the jacking pipe model is a shallow buried model, the vertical load acting on the jacking pipe is obtained by calculating the limit equilibrium theory; When the pipe jacking model is the first transition model and the first deep buried model, the parabolic failure zone acts on the top of the rectangular failure zone with its own weight. The load acting on the top of the rectangular failure zone and the vertical load acting on the pipe jacking are calculated based on the deadweight of the parabolic failure zone. When the jacking pipe model is the second transition model and the second deep buried model, the vertical load acting on the jacking pipe is calculated based on the deadweight of the parabolic failure zone.

2. The method according to claim 1, characterized in that The design parameters of the pipe jacking project include the buried depth of the pipe jacking machine and the outer diameter of the pipe jacking machine, the volume expansion coefficient of the sand, and the internal friction angle; The key parameters of the theoretical analysis model include the formation loss rate, the height of the sand failure zone above the jacking pipe, the height of the soil arching zone, and the height of the undisturbed zone.

3. The method according to claim 1, characterized in that The process of determining the state of the pipe jacking includes: According to the formation loss effect caused by the outer diameter of the pipe jacking machine being larger than the outer diameter of the subsequent pipe jacking during construction, as well as the influence of the buried depth of the pipe jacking and the formation loss effect, the area above the pipe jacking construction is divided into the sand failure zone, the soil arch zone and the undisturbed zone in sequence.

4. The method according to claim 1, wherein The two sides of the failure zone form shear sliding zones with the stable strata, and the friction stress on the shear sliding zones causes a principal stress deflection effect in the failure zone, forming a maximum principal stress arch; The soil arch zone serves as a transition zone between the undisturbed zone and the failure zone. The principal stress deflection angle at the bottom is the same as that in the failure zone, and no principal stress deflection effect occurs at the top. The lateral pressure coefficient and the principal stress deflection angle vary linearly with height. The undisturbed area is not affected by the pipe jacking construction, and the lateral pressure coefficient is the static earth pressure coefficient, and acts on the top of the soil arch area with its own weight.

5. The method according to claim 1, wherein The shape of the fracture surface at the top of the failure zone is consistent with the shape of the principal stress trace in the failure zone; When the pipe jacking model is a shallow buried model, a first transition model, and a first deep buried model, the principal stress deflection angle in the failure zone is determined according to the internal friction angle of the sand; When the pipe jacking model is the second transition model and the second deep buried model, the principal stress deflection angle in the failure zone is determined by the formation loss rate and the sand volume expansion coefficient.

6. The method according to claim 5, characterized in that After the principal stress in the failure zone is deflected, the principal stress trace is a parabola with a reasonable arch axis.

7. The method according to claim 1, characterized in that When the jacking pipe is a shallow buried model, the height of the failure zone is the buried depth of the jacking machine; When the jacking pipe is of other models, the height of the failure zone is determined by the sand volume expansion coefficient and the formation loss rate.

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