TWI714858B - An Analytical Method to Calculate the Stress Variation of Tunnel Lining by Deflection - Google Patents
An Analytical Method to Calculate the Stress Variation of Tunnel Lining by Deflection Download PDFInfo
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Abstract
一種透過變位量推求隧道襯砌的應力變化之解析方法,係包括以下步驟:(S1)提供模擬模型,包含三維隧道單元、做為模型邊界之不同的複數個斷面,及其數量足以偵測隧道變形現象之測量變數與其特定斷面變化量所構成之變位模態;(S2)根據該些斷面之變位量測量值計算該隧道單元的相對變位量及該變位模態之組成量且得到襯砌的應力變化之值;以及(S3)比對襯砌應力變化與壁面的裂縫分布,視情況修正該相對變位量及變位模態之計算值以獲得與該裂縫分布相符之應力變化。本發明能在長期監測下預測裂縫發展趨勢、模擬補強工法成效、評估隧道健全度和安全性等,對隧道維護管理最佳化提供實質建議。 An analytical method for estimating the stress change of the tunnel lining through displacement. It includes the following steps: (S1) Provide a simulation model, including three-dimensional tunnel elements, as the boundary of the model, and the number of different sections that are sufficient for detection The displacement mode formed by the measured variables of the tunnel deformation phenomenon and the change of its specific section; (S2) calculate the relative displacement of the tunnel unit and the displacement mode based on the measured values of the displacement of the sections (S3) Compare the stress change of the lining with the crack distribution on the wall, and modify the calculated value of the relative displacement and the displacement mode according to the situation to obtain the value of the crack distribution. The stress changes. The invention can predict the development trend of cracks, simulate the effects of reinforcement construction methods, evaluate the soundness and safety of the tunnel under long-term monitoring, and provide substantial suggestions for the optimization of tunnel maintenance and management.
Description
本發明係關於一種土木工程的模擬方法,尤其適用於模擬變位量導致隧道壁面的應力變化。 The invention relates to a simulation method of civil engineering, and is especially suitable for simulating the stress change of the tunnel wall caused by displacement.
隧道襯砌為隧道表面以磚、石、混凝土或混凝土與鋼線網、鋼筋、鋼纖維等材料構成之人工結構,近代隧道工法在隧道施工時持續監測隧道變形,待變形趨於穩定後方施作襯砌,因此襯砌原為美觀及提供額外防護而施作,理論上不會承受過多應力。然台灣近2/3以上隧道在營運後襯砌出現異常狀況,其中最常見類型即為變形及裂縫,故近年研究開始關注襯砌變位與裂縫,並將其視為隧道結構劣化和協助研判劣化肇因的重要指標。 The tunnel lining is an artificial structure composed of brick, stone, concrete or concrete and steel wire mesh, steel bar, steel fiber and other materials on the surface of the tunnel. The modern tunnel construction method continuously monitors the deformation of the tunnel during the construction of the tunnel. When the deformation becomes stable, the lining is applied Therefore, the lining was originally constructed for aesthetics and additional protection, and theoretically will not bear excessive stress. However, nearly two-thirds of the tunnels in Taiwan have abnormal conditions in the lining after operation. The most common types are deformation and cracks. Therefore, in recent years, research has begun to pay attention to lining displacement and cracks, which are regarded as tunnel structural deterioration and assist in the study of deterioration. An important indicator of the cause.
已知隧道變位解析方法大多針對監測斷面自身變形行為,然而近年隧道三維絕對變位監測資料的解析成果顯示除單一監測斷面上可見之向內擠壓或向外突出之二維變形行為外,監測斷面之間尚存在可觀之三維變形,以往考慮的斷面變形僅影響局部範圍內之襯砌裂縫,現地所觀察到延續數公尺至數十公尺的斜向、縱向等裂縫型態係由相鄰監測斷面的相對變位所引致。 Known tunnel displacement analysis methods are mostly aimed at the deformation behavior of the monitoring section itself. However, the analysis results of the three-dimensional absolute displacement monitoring data of the tunnel in recent years show that except for the two-dimensional deformation behavior that can be seen in a single monitoring section, which is compressed inward or protruded outward In addition, there is still considerable three-dimensional deformation between the monitored sections. The section deformation considered in the past only affects the lining cracks in a local area. Oblique and longitudinal cracks that continue from several meters to tens of meters are observed in the field. The state is caused by the relative displacement of adjacent monitoring sections.
已知隧道襯砌裂縫型態模擬係建立二維或三維的隧道數值模型,給予外力或變位條件,獲得隧道應變與應力分布。其採用連續體分析,以彈塑性組成律描述隧道襯砌,將進入塑性的部分視為襯砌材料破壞裂縫產 生。模擬結果可與現地隧道監測的地表沉陷量、隧道內空變位比較,或與室內隧道縮尺試驗監測的力-應變曲線相比,以進行數值模型驗證。換言之,已知技術多係透過隧道內複數點位在加載過程的應力-應變曲線,或位於隧道內或隧道上方幾處位置的變位來確認數值模型的正確性,發生隧道裂縫的位置則以數值模型中進入塑性區之網格代表,鮮少將其模擬結果與實際隧道之裂縫型態直接比對。 It is known that the tunnel lining crack pattern simulation system establishes a two-dimensional or three-dimensional numerical model of the tunnel, and gives the external force or displacement conditions to obtain the tunnel strain and stress distribution. It uses continuum analysis to describe the tunnel lining with the elastic-plastic composition law, and regards the part that enters the plasticity as the lining material damage crack Raw. The simulation results can be compared with the surface subsidence monitored by the on-site tunnel, the displacement of the tunnel space, or with the force-strain curve monitored by the indoor tunnel scale test for numerical model verification. In other words, the known technologies mostly use the stress-strain curve of multiple points in the tunnel during the loading process, or the displacement of several positions in or above the tunnel to confirm the correctness of the numerical model. The location of tunnel cracks is determined by In the numerical model, the grid representation entering the plastic zone rarely compares the simulation results directly with the crack pattern of the actual tunnel.
本發明之主要目的在於提供一種透過變位量推求隧道襯砌的應力變化之解析方法,其包括以下步驟:(S1)提供模擬模型,包含三維隧道單元、做為模型邊界之不同的複數個斷面,及其數量足以偵測隧道變形現象之測量變數與其特定斷面變化量所構成之變位模態;(S2)根據該些斷面之變位量測量值計算該隧道單元的相對變位量及該變位模態之組成量且得到襯砌的應力變化之值;(S3)比對襯砌應力變化與壁面的裂縫分布,視情況修正該相對變位量及變位模態之計算值以獲得與該裂縫分布相符之應力變化。 The main purpose of the present invention is to provide an analytical method for estimating the stress change of the tunnel lining through the displacement, which includes the following steps: (S1) Provide a simulation model, including three-dimensional tunnel elements, as a plurality of different sections of the model boundary , And the displacement mode constituted by the measured variables and their specific cross-sectional changes sufficient to detect the tunnel deformation phenomenon; (S2) Calculate the relative displacement of the tunnel unit based on the displacement measured values of the cross-sections And get the value of the stress change of the lining; (S3) compare the stress change of the lining with the crack distribution on the wall, and modify the calculated value of the relative displacement and the displacement mode as appropriate Obtain the stress change consistent with the crack distribution.
本發明之一種透過變位量推求隧道襯砌的應力變化之解析方法,其中,該壁面係襯砌壁面,該變位量係該襯砌壁面在不同時間之空間位置變化,斷面為隧道中做為變位量測標的之監測橫斷面,該斷面包含數量足以偵測隧道變形現象之複數個監測點,該隧道單元係以二隧道監測斷面為邊界之隧道範圍,該斷面之所有監測點在不同時間之空間位置變化的集合為斷面變位量,特定斷面變化量係變位模態,其為斷面剛體運動與斷面變形,該變位模態對應已知的變位量及襯砌應力變化,斷面剛體運動包含所有該監測點一致等量移動為平移變位模態,所有該監測點對斷面形心一致 等量旋轉為旋轉變位模態,斷面變形模態包含斷面監測點相對於該斷面形心放大或縮小之均勻變形變位模態,及相對於該斷面形心之變形為橢圓變形變位模態,相對於該斷面形心之變形為三角變形變位模態,相對於該斷面形心之變形為四邊變形變位模態,相對於該斷面形心之變形為五邊變形變位模態,乃至相對於該斷面形心之變形為多邊變形變位模態之複數種變形變位模態或稱為變形模態,且三維空間中隧道內通行方向為軸向,重力方向為垂直向,另一與軸向和垂直向正交之方向為側向,該三維空間中斷面剛體運動包含軸向平移,側向平移,垂直向平移與相對軸向旋轉,相對側向軸旋轉和相對垂直軸旋轉。 The present invention is an analytical method for estimating the stress change of the tunnel lining through the displacement, wherein the wall is the lining wall, the displacement is the change in the space position of the lining wall at different times, and the section is the tunnel as the change The monitoring cross section of the measurement target, the section contains a plurality of monitoring points enough to detect the deformation phenomenon of the tunnel. The tunnel unit is the tunnel range with the two tunnel monitoring sections as the boundary, and all the monitoring points of the section The set of changes in the spatial position at different times is the section displacement. The specific section change is the displacement mode, which is the rigid body motion and section deformation of the section. The displacement mode corresponds to the known displacement. And the lining stress change, the section rigid body movement includes all the monitoring points consistent and equal movement is the translational displacement mode, all the monitoring points are consistent with the section centroid Equivalent rotation is a rotational displacement mode. The cross-section deformation mode includes a uniform deformation and displacement mode where the monitoring point of the cross-section is enlarged or reduced relative to the cross-section centroid, and the deformation relative to the cross-section centroid is an ellipse The deformation mode is a triangular deformation mode with respect to the centroid of the section, a quadrilateral deformation mode with respect to the centroid of the section, and a deformation mode with respect to the centroid of the section The five-sided deformation mode, and even the multiple deformation modes of the polygonal deformation mode relative to the centroid of the section, or called the deformation mode, and the direction of passage in the tunnel in the three-dimensional space is the axis The direction of gravity is the vertical direction, and the other direction orthogonal to the axial and vertical direction is the lateral direction. The rigid body motion of the three-dimensional space interruption surface includes axial translation, lateral translation, vertical translation and relative axial rotation, relative Lateral axis rotation and relative vertical axis rotation.
本發明之一種透過變位量推求隧道襯砌的應力變化之解析方法,步驟S1包含以下步驟:(S10)建立初始模擬模型,且該模擬模型包含三維隧道單元,做為模型邊界之不同的複數個斷面,及其測量變數與變位模態;(S11)分別施加剛體運動變位模態之斷面變位量於該模擬模型邊界,得到該隧道單元相對剛體運動之應力變化;(S12)判斷該初始模擬模型之測量變數及應力變化是否均勻,若否,進入步驟S10,若是,進行步驟S13;(S13)分別施加變形變位模態之斷面變位量於該模擬模型邊界,得到隧道單元變形之應力變化;(S14)判斷該初始模擬模型之測量變數及應力變化是否均勻,若否,進入步驟S10,若是,進行步驟S15;及(S15)基於變位模態模擬結果建立模擬模型。 The present invention is an analytical method for estimating the stress change of the tunnel lining through displacement. Step S1 includes the following steps: (S10) An initial simulation model is established, and the simulation model includes three-dimensional tunnel elements as a plurality of different model boundaries Section, its measurement variables and displacement mode; (S11) Apply the section displacement of the rigid body movement displacement mode to the boundary of the simulation model to obtain the stress change of the tunnel element relative to the rigid body movement; (S12) Judge whether the measurement variables and stress changes of the initial simulation model are uniform, if not, go to step S10, if yes, go to step S13; (S13) respectively apply the cross-section displacement of the deformation displacement mode to the boundary of the simulation model to obtain The stress change of the tunnel element deformation; (S14) Determine whether the measured variables and stress changes of the initial simulation model are uniform, if not, go to step S10, if yes, go to step S15; and (S15) establish a simulation based on the displacement modal simulation result model.
本發明之一種透過變位量推求隧道襯砌的應力變化之解析方法,步驟S2包含以下步驟:(S20)取得該些斷面的變位之測量值;(S21)得到該些斷面的變位之測量值的變位模態組成量;(S22a)基於該變位模態組成量得到屬於斷面剛體運動的變位模態之組成量;(S23a)基於作為隧道單元邊界之該斷面剛體運動而得到該隧道單元之相對剛體運動組成量,且基於該組
成量排序該相對剛體運動種類;(S24a)歸零該模擬模型之測量變數,且施加該相對剛體運動之值於該模擬模型邊界,得到該隧道單元相對剛體運動之應力變化;及(S22b)基於該變位模態組成量得到屬於斷面的變形變位模態之組成量;(S23b)基於作為隧道單元邊界之斷面變形得到該隧道單元之變形組成量,且基於該組成量排序變形模態;(S24b)歸第4頁,共12頁(發明說明書)零該模擬模型之測量變數,且同時施加該變形模態之值於該模擬模型邊界,得到隧道單元變形之應力變化;(S25)判斷步驟S24a中該模擬模型之測量變數及應力變化是否均勻,若是,進行步驟S3,若否,進行步驟S24a,及判斷步驟S24b中該模擬模型之測量變數及應力變化是否均勻,若是,進行步驟S3,若否,進行步驟S24b。
The present invention is an analytical method for estimating the stress change of the tunnel lining through displacement. Step S2 includes the following steps: (S20) Obtain the measured values of the displacements of the sections; (S21) Obtain the displacements of the sections (S22a) Based on the displacement modal composition quantity of the measured value of the displacement mode composition quantity; (S22a) Based on the displacement modal composition quantity, the composition quantity of the displacement mode belonging to the section rigid body motion is obtained; (S23a) Based on the section rigid body as the boundary of the tunnel element Motion to obtain the relative rigid body motion composition of the tunnel unit, and based on the group
Sort the relative rigid body motion types quantitatively; (S24a) zero the measurement variables of the simulation model, and apply the value of the relative rigid body motion to the boundary of the simulation model to obtain the stress change of the tunnel element relative to the rigid body motion; and (S22b) Obtain the component quantities of the deformation deformation modes belonging to the section based on the component quantity of the displacement mode; (S23b) Obtain the component quantity of the tunnel element deformation based on the section deformation as the boundary of the tunnel element, and sort the deformation based on the component quantity Mode; (S24b) Go to
本發明之一種透過變位量推求隧道襯砌的應力變化之解析方法,步驟S3包含以下步驟:(S30)歸零該模擬模型之測量變數,施加該隧道單元邊界斷面變位之測量值於該模擬模型邊界,得到該隧道單元因斷面變位測量值引致之應力變化總量;(S31)判斷該初始模擬模型之測量變數及應力變化是否均勻,若是,進行步驟S32,若否,進行步驟S34;(S32)判斷襯砌應力超出強度位置與襯砌裂縫位置是否相符,若是,進行步驟S34,若否,進行步驟S33;(S33)取得分析結果襯砌應力接近強度且未超過者,折減六種相對剛體運動量值及多種變形模態對應之邊界變位量,並視情形調整邊界變位量輸入順序,迄襯砌應力超出強度位置與襯砌裂縫位置相符,之後進行步驟S30;及(S34)得到分析隧道單元襯砌應力增量及變位量。 The present invention is an analytical method for estimating the stress change of the tunnel lining through displacement. Step S3 includes the following steps: (S30) Zero the measurement variables of the simulation model, and apply the measurement value of the displacement of the boundary section of the tunnel unit to the Simulate the model boundary to obtain the total stress change of the tunnel unit due to the measured value of the section displacement; (S31) judge whether the measured variables and stress change of the initial simulation model are uniform, if yes, proceed to step S32, if not, proceed to step S34; (S32) Determine whether the lining stress exceeds the strength position and the lining crack position is consistent, if yes, proceed to step S34, if not, proceed to step S33; (S33) obtain the analysis result if the lining stress is close to the strength and does not exceed, reduce six types Relative rigid body motion value and boundary displacement corresponding to various deformation modes, and adjust the input sequence of boundary displacement according to the situation, so far the lining stress exceeds the strength position and the lining crack position is consistent, then step S30; and (S34) are analyzed. The stress increment and displacement of the tunnel unit lining.
上述「發明內容」並非用以限制所主張標的之範疇,本發明的各種分析檢定作業詳細概觀,在下述實施方式段落會做更進一步描述。 The above-mentioned "Summary of the Invention" is not intended to limit the scope of the claimed subject matter. A detailed overview of the various analysis and verification operations of the present invention will be further described in the following implementation mode paragraphs.
S1、S2、S3、S10、S11、S12、S13、S14、S15、S20、S21、S22a、S23a、S24a、S22b、S23b、S24b、S25、S30、S31、S32、S33、S34:步驟 S1, S2, S3, S10, S11, S12, S13, S14, S15, S20, S21, S22a, S23a, S24a, S22b, S23b, S24b, S25, S30, S31, S32, S33, S34: steps
圖1係本發明之三維坐標定義與隧道空間關係的示意圖。 Figure 1 is a schematic diagram of the relationship between the three-dimensional coordinate definition and the tunnel space of the present invention.
圖2係本發明之透過變位量推求隧道襯砌的應力變化之解析方法的流程圖。 Fig. 2 is a flowchart of the analytical method for estimating the stress change of the tunnel lining through displacement of the present invention.
圖3係任意隧道內複數個斷面變位量及隧道單元相對變位的示意圖。 Figure 3 is a schematic diagram of a plurality of section displacements and relative displacements of tunnel units in any tunnel.
圖4係步驟S1包含之進一步步驟的流程圖。 Figure 4 is a flowchart of further steps included in step S1.
第5頁,共12頁(發明說明書) Page 5 of 12 (Invention Specification)
圖5係隧道單元前後監測斷面的建構示意圖。 Figure 5 is a schematic diagram of the construction of the front and rear monitoring sections of the tunnel unit.
圖6係各種變位模態的示意圖,包含六種剛體運動變位模態及部分變形變位模態。 Figure 6 is a schematic diagram of various displacement modes, including six rigid body movement displacement modes and partial deformation displacement modes.
圖7係模擬模型中強制變位分佈的示意圖。 Figure 7 is a schematic diagram of the forced displacement distribution in the simulation model.
圖8係步驟S2包含之進一步步驟的流程圖。 Figure 8 is a flowchart of further steps included in step S2.
圖9係步驟S3包含之進一步步驟的流程圖。 Figure 9 is a flowchart of further steps included in step S3.
圖10係各種變位模態之測量變數導致襯砌裂縫型態之範例的示意圖。 Fig. 10 is a schematic diagram showing examples of lining crack patterns caused by measurement variables of various displacement modes.
圖11係隧道單元因前後監測斷面相對運動引致之襯砌裂縫的模擬與實際結果範例。 Figure 11 is an example of simulation and actual results of lining cracks caused by the relative movement of the front and rear monitoring sections of the tunnel unit.
為詳細說明本發明之技術內容、所達成的目的及功效,以下茲例舉實施例並配合圖式詳予說明。 In order to describe in detail the technical content, the achieved purpose and the effect of the present invention, the following examples are given in conjunction with the drawings for detailed description.
圖1係本發明之三維坐標定義與隧道空間關係的示意圖。 Figure 1 is a schematic diagram of the relationship between the three-dimensional coordinate definition and the tunnel space of the present invention.
圖2係本發明之透過變位量推求隧道襯砌的應力變化之解析方法的流程圖,其包括步驟S1至步驟S3。步驟S1中,提供模擬模型,且該模擬模型包含三維隧道單元、做為模型邊界之不同的複數個斷面及其數量足以偵 測隧道變形現象之測量變數與其特定斷面變化量所構成之變位模態。特定而言,步驟S1可建立與調整數值試驗模型,該三維模形可為三維隧道單元,且該壁面可為隧道的襯砌壁面。測量變數可為斷面變位量,進一步而言可為各種變位模態之變位量。圖3係取得不同之複數個監測斷面以供建立模擬模型、斷面變位量測量值等的示意圖。 Fig. 2 is a flow chart of the analytical method for estimating the stress change of the tunnel lining through the displacement of the present invention, which includes steps S1 to S3. In step S1, a simulation model is provided, and the simulation model includes a three-dimensional tunnel unit, a plurality of different sections as the boundary of the model, and the number is sufficient to detect The displacement mode formed by the measurement variable of the tunnel deformation phenomenon and its specific section change. Specifically, in step S1, a numerical test model can be established and adjusted. The three-dimensional model can be a three-dimensional tunnel unit, and the wall can be a lining wall of the tunnel. The measurement variable can be the displacement of the section, and furthermore, it can be the displacement of various displacement modes. Figure 3 is a schematic diagram of obtaining a plurality of different monitoring sections for the establishment of simulation models, measurement values of section displacements, etc.
步驟S2中,根據該些斷面之變位量測量值計算該隧道單元的相對變位量及該變位模態之組成量且得到隧道單元之該襯砌的應力變化之值。特定而言,步驟第6頁,共12頁(發明說明書)S2可解算該些監測斷面變位量之變位模態組成量,並根據該些變位模態組成量解算介於該些監測斷面間的隧道單元之相對變位量,進一步於該模擬模型邊界施加該變位量測量值及得到因該些相對變位量產生之應力變化。 In step S2, the relative displacement of the tunnel unit and the composition of the displacement mode are calculated according to the measured values of displacement of the sections, and the value of the stress change of the lining of the tunnel unit is obtained. In particular, step 6, page 6, a total of 12 pages (instruction manual) S2 can calculate the displacement modal composition of the monitored section displacements, and calculate the value between The relative displacements of the tunnel units between the monitoring sections are further applied to the simulation model boundary to measure the displacements and the stress changes due to the relative displacements are obtained.
步驟S3中,比對壁面應力變化與該襯砌的裂縫分布,視情況修正該相對變位量之計算值以獲得與該裂縫分布相符之應力變化。特定而言,步驟S3可根據襯砌應力變化均勻與否與隧道實際裂縫分布調整模擬模型,且求解得與裂縫分布相符之襯砌應力變化量。 In step S3, the wall stress change is compared with the crack distribution of the lining, and the calculated value of the relative displacement is corrected as appropriate to obtain a stress change consistent with the crack distribution. Specifically, in step S3, the simulation model can be adjusted according to whether the lining stress change is uniform or not and the actual crack distribution of the tunnel, and the lining stress change amount consistent with the crack distribution can be solved.
圖4係步驟S1包含之進一步步驟的流程圖。如圖4所示,步驟S1包含步驟S10至步驟S15。步驟S10中,可建立初始模擬模型,且該模擬模型包含三維隧道單元、做為模型邊界之不同的複數個斷面及其測量變數與變位模態。特定而言,數值模型之建立/調整應至少考慮隧道幾何形狀、結構及監測斷面佈置位置、網格尺寸等。測量變數及變位模態可例如為圖5中之相對軸向平移、相對側向平移、相對垂直向平移、相對軸向旋轉、相對側向軸旋轉、相對垂直軸旋轉、均勻變形變位模態、橢圓變形模態、三角變形模態、四邊變形模態、五邊變形模態等。 Figure 4 is a flowchart of further steps included in step S1. As shown in Fig. 4, step S1 includes step S10 to step S15. In step S10, an initial simulation model can be established, and the simulation model includes a three-dimensional tunnel unit, a plurality of different sections as the boundary of the model, and measurement variables and displacement modes. In particular, the establishment/adjustment of the numerical model should at least consider the tunnel geometry, structure, location of monitoring sections, grid size, etc. The measurement variables and displacement modes can be, for example, relative axial translation, relative lateral translation, relative vertical translation, relative axial rotation, relative lateral axis rotation, relative vertical axis rotation, uniform deformation displacement mode in Figure 5 State, ellipse deformation mode, triangle deformation mode, four-sided deformation mode, five-sided deformation mode, etc.
步驟S11中,可分別施加剛體運動變位模態之斷面變位量於該模 擬模型邊界,得到該隧道單元相對剛體運動之應力變化。特定而言,可於模型邊界施加變位模態之變位量,即將數值模型邊界之一(遠)端固定,另一(近)端施加模擬的單位變位值,之後讀取隧道襯砌變位的結果。詳細而言,本發明可取相鄰監測斷面為一隧道單元,將其中一端視為固定端強制使變位為零,即可計算該相鄰監測斷面之相對變位,並假設兩監測斷面間變位呈線性分布(圖5及圖7)。將隧道單元前後監測斷面之相對運動輸入數值模型以模擬襯砌裂縫,如已有多期變位與裂縫監測,則可利用前期監測結果再次檢核並修正數值模型,並用於預測未來變位與裂縫之發展趨勢(圖10及圖11)。 In step S11, the section displacement of the rigid body movement displacement mode can be applied to the mode The boundary of the pseudo-model is obtained, and the stress change of the tunnel element relative to the rigid body movement is obtained. Specifically, the displacement amount of the displacement mode can be applied to the model boundary, that is, one (distal) end of the numerical model boundary is fixed, and the other (near) end is applied with the simulated unit displacement value, and then the tunnel lining change is read Bit result. In detail, the present invention may take the adjacent monitoring section as a tunnel unit, and regard one end as a fixed end to force the displacement to zero, and then calculate the relative displacement of the adjacent monitoring section, and assume that the two monitoring sections The displacement between the planes is linearly distributed (Figure 5 and Figure 7). Input the relative movement of the monitored section before and after the tunnel unit into the numerical model to simulate the lining cracks. If there are multiple phases of displacement and crack monitoring, the previous monitoring results can be used to check and revise the numerical model again, and used to predict future displacements and The development trend of cracks (Figure 10 and Figure 11).
步驟S12中,可判斷該初始模擬模型之測量變數及應力變化是否均勻,若否,進入步驟S10,若是,進行步驟S13。特定而言,可對數值模型檢核隧道襯砌變位及隧道壁面與圍岩應力變化是否均勻。 In step S12, it can be judged whether the measured variables and stress changes of the initial simulation model are uniform, if not, go to step S10, if yes, go to step S13. Specifically, the numerical model can be used to check whether the deformation of the tunnel lining and the stress changes of the tunnel wall and surrounding rock are uniform.
步驟S13中,可施加變形變位模態之變位值於該模擬模型邊界,得到隧道單元變形之應力變化。特定而言,可將數值模型邊界的遠端以需求方式固定,且於近端施加例如均勻壓縮、橢圓、三角、四邊等變形變位模態之變位量,且讀取隧道壁面變位與襯砌應力變化的情況。 In step S13, the displacement value of the deformation displacement mode can be applied to the boundary of the simulation model to obtain the stress change of the tunnel element deformation. Specifically, the distal end of the boundary of the numerical model can be fixed in a required manner, and the proximal end can be applied to the proximal end such as uniform compression, ellipse, triangle, four-sided deformation and displacement mode displacement, and read the tunnel wall displacement and Changes in lining stress.
步驟S14中,可判斷該變形模態與施加於模擬模型邊界的條件是否吻合,若否,進入步驟S10,若是,進行步驟S2。特定而言,可對數值模型檢核隧道壁面變位及隧道襯砌與圍岩應力變化是否均勻。 In step S14, it can be judged whether the deformation mode is consistent with the condition imposed on the boundary of the simulation model, if not, go to step S10, if yes, go to step S2. Specifically, the numerical model can be used to check whether the tunnel wall displacement and the stress changes of the tunnel lining and surrounding rock are uniform.
圖8係步驟S2包含之進一步步驟的流程圖。如圖8所示,步驟S2包含步驟S20至步驟S21、步驟S22a至步驟S24a及步驟S22b至步驟S24b。步驟S20中,可取得該些斷面的變位之測量值,進一步而言,可基於高精度的隧道變位監測技術得到該些斷面變位之測量值。特定而言,可依據隧道監測斷面三維空間坐標測量值計算該隧道斷面變位測量值。 Figure 8 is a flowchart of further steps included in step S2. As shown in FIG. 8, step S2 includes step S20 to step S21, step S22a to step S24a, and step S22b to step S24b. In step S20, the measured values of the displacements of the sections can be obtained. Furthermore, the measured values of the displacements of the sections can be obtained based on the high-precision tunnel displacement monitoring technology. Specifically, the measured value of the tunnel section displacement can be calculated based on the measured value of the three-dimensional space coordinate of the tunnel monitoring section.
步驟S21中,可得到該些斷面的變位之測量值的變位模態組成量,進一步而言,可基於該斷面變位測量值得到變位模態組成量。特定而言,可依據監測斷面監測到的變位測量值而計算變位模態之組成量。 In step S21, the displacement modal composition of the measured value of the displacement of the sections can be obtained, and furthermore, the displacement modal composition of the measured value of the displacement of the section can be obtained. Specifically, the component quantity of the displacement mode can be calculated based on the displacement measurement value monitored by the monitoring section.
步驟S22a中,可基於該變位模態組成量得到屬於斷面剛體運動的變位模態之組成量。特定而言,可得到斷面變位測量值的變位模態組成中軸向平移,側向平移,垂直向平移與相對軸向旋轉,相對側向軸旋轉和相對垂直軸旋轉等六種變位模態對應的組成量之數值大小。 In step S22a, the composition quantity belonging to the displacement mode of the section rigid body motion can be obtained based on the displacement mode composition quantity. Specifically, there are six types of displacement modes including axial translation, lateral translation, vertical translation and relative axial rotation, relative lateral axis rotation and relative vertical axis rotation. The numerical value of the composition quantity corresponding to the bit mode.
步驟S23a中,可基於作為隧道單元邊界之該斷面剛體運動而得到該隧道單元之相對剛體運動組成量,且基於該組成量排序該相對剛體運動種第8頁,共12頁(發明說明書)類,進一步而言,可基於隧道單元邊界兩個斷面之剛體運動變位模態組成量得到該隧道單元之相對剛體運動模態組成量,且基於該組成量大小排序該相對剛體運動種類。特定而言,可得到以其中一斷面為基準之剛體運動量值,且將隧道單元之六個相對剛體運動變位之值依據大小排序。 In step S23a, the relative rigid body motion composition of the tunnel element can be obtained based on the section rigid body motion as the boundary of the tunnel element, and the relative rigid body motion types are sorted based on the composition. Page 8 of 12 (Invention Specification) Furthermore, the relative rigid body motion modal composition of the tunnel element can be obtained based on the rigid body motion displacement modal composition of the two sections of the tunnel element boundary, and the relative rigid body motion types can be sorted based on the composition value. Specifically, the rigid body movement value based on one of the sections can be obtained, and the displacement values of the six relative rigid body movement displacements of the tunnel unit are sorted according to the magnitude.
步驟S24a中,可歸零該模擬模型之測量變數,且施加該相對剛體運動之值於該模擬模型邊界,得到該隧道單元相對剛體運動之應力變化,進一步而言,可歸零該模擬模型之測量變數,且施加該隧道單元相對剛體運動模態組成量對應之變位值於該模擬模型邊界。特定而言,可歸零數值模型之變位,且於數值模型邊界施加相對剛體運動變位模態對應之變位值。即依據剛體運動變位模態的組成量,自佔有斷面變位測量值最大組成量之剛體運動變位模態開始,依序於數值模型邊界施加對應之變位值。 In step S24a, the measurement variables of the simulation model can be zeroed, and the value of the relative rigid body motion can be applied to the boundary of the simulation model to obtain the stress change of the tunnel element relative to the rigid body motion. Furthermore, the simulation model can be reset to zero Measure the variables, and apply the displacement value corresponding to the modal composition of the tunnel unit relative to the rigid body motion to the boundary of the simulation model. Specifically, the displacement of the numerical model can be zeroed, and the displacement value corresponding to the displacement mode of the relative rigid body motion is applied to the boundary of the numerical model. That is, according to the composition of the rigid body movement displacement mode, starting from the rigid body movement displacement mode that occupies the largest composition of the section displacement measurement value, the corresponding displacement value is applied to the numerical model boundary in sequence.
而於步驟S22b中,可基於該變位模態組成量得到屬於斷面的變形變位模態之組成量。特定而言,可得到斷面變位測量值的變位模態組成中相對於斷面形心放大或縮小之均勻變形模態,及相對於斷面形心之變形為 橢圓變形模態,相對於斷面形心之變形為三角變形模態,相對於斷面形心之變形為四邊變形模態,相對於斷面形心之變形為五邊變形模態,乃至相對於斷面形心之變形為多邊變形模態之複數種變位模態對應的組成量之數值大小。 In step S22b, the composition of the deformation and displacement mode belonging to the section can be obtained based on the composition of the displacement mode. Specifically, the uniform deformation mode that is enlarged or reduced with respect to the centroid of the section in the composition of the displacement mode from which the measured value of the section displacement can be obtained, and the deformation relative to the centroid of the section is The elliptical deformation mode is a triangular deformation mode relative to the cross-section centroid, the deformation relative to the cross-section centroid is a four-sided deformation mode, and the deformation relative to the cross-section centroid is a five-sided deformation mode, and even relative The deformation at the centroid of the section is the numerical magnitude of the composition corresponding to the multiple deformation modes of the polygonal deformation mode.
步驟S23b中,可基於作為隧道單元邊界之斷面變形得到該隧道單元之變形組成量,且基於該組成量排序變形模態,進一步而言,可基於隧道單元邊界兩個斷面之變形變位模態組成量得到該隧道單元之變形組成量,且基於該組成量大小排序該變形模態。特定而言,可得到該隧道單元複數種變形模態依據大小排序之成果。 In step S23b, the deformation composition of the tunnel element can be obtained based on the deformation of the section as the boundary of the tunnel element, and the deformation modes can be sorted based on the composition. Further, the deformation displacement of the two sections of the boundary of the tunnel element can be sorted. The modal composition quantity obtains the deformation composition quantity of the tunnel unit, and the deformation modalities are sorted based on the composition quantity. In particular, the results of the multiple deformation modes of the tunnel unit sorted by size can be obtained.
步驟S24b中,可歸零該模擬模型之測量變數,且同時施加該變形模態之值於該模擬模型邊界,得到隧道單元變形之應力變化,進一步而言,可歸零該模擬模型之測量變數,且施加該隧道單元變形模態組成量對應之變位值於該模擬模型邊界。特定而言,可歸零數值模型之變位,且基於該模擬模型邊界與該變形模態之組成量大小於該模擬模型邊界而施加對應該變形模態的變位量,從組成量最大之該變形模態開始,且向比例最小之該變形模態依序施加對應該變形模態的變位量於該模擬模型邊界。特定而言,可依據邊界與襯砌變形模態組成量於模型邊界施加對應變形模態之變位量,自現成比例最大變形模態開始,依序於模型邊界施加對應模態之變位量。 In step S24b, the measurement variables of the simulation model can be zeroed, and the value of the deformation mode can be applied to the boundary of the simulation model at the same time to obtain the stress change of the tunnel element deformation. Furthermore, the measurement variables of the simulation model can be zeroed , And apply the displacement value corresponding to the deformation modal composition of the tunnel element to the boundary of the simulation model. Specifically, the displacement of the numerical model can be reset to zero, and the displacement corresponding to the deformation mode is applied based on the composition of the simulation model boundary and the deformation mode at the simulation model boundary, from the largest composition The deformation mode starts, and the deformation amount corresponding to the deformation mode is sequentially applied to the boundary of the simulation model to the deformation mode with the smallest scale. Specifically, the displacement of the corresponding deformation mode can be applied to the model boundary according to the composition of the boundary and the lining deformation mode. Starting from the ready-to-scale maximum deformation mode, the displacement of the corresponding mode is sequentially applied to the model boundary.
以圓形隧道為例,進行第一次量測時,得到A、B兩斷面各監測點的絕對座標,斷面皆可藉由監測點的絕對座標計算出該斷面形心位置,並將第二期量測得到之監測值與一次之值相減,再將A斷面之監測值與B斷面之值相減,如此可獲得此兩次量測期間A斷面各監測點相對於B斷面各監 測點之變位情形,表示為(ui,vi,wi)AB,12。斷面變位可分離為剛體運動與變形,其中剛體運動又可分離為剛體平移運動與剛體旋轉運動兩類。 Taking a circular tunnel as an example, when the first measurement is performed, the absolute coordinates of each monitoring point on the A and B sections are obtained. The cross section can be calculated from the absolute coordinates of the monitoring point, and Subtract the monitored value obtained from the second measurement with the first value, and then subtract the monitored value of section A from the value of section B. In this way, the relative monitoring points of section A can be obtained during the two measurements. The displacement situation of each monitoring point on section B is expressed as ( ui , vi , wi )AB,12. Sectional displacement can be separated into rigid body motion and deformation, and rigid body motion can be separated into rigid body translational motion and rigid body rotational motion.
詳細而言,由分解變位之概念衍生出軸向單位平移,側向單位平移,垂直向平移與相對軸向旋轉,相對側向軸旋轉和相對垂直軸旋轉等六種剛體運動,加上均勻變形模態、橢圓變形模態、三角變形模態、四邊變形模態、五邊變形模態等複數種相對於斷面形心之多邊變形等複數種變形,針對此複數種變位型態分別給予不同的邊界條件,探討個別導致之隧道壁面應力變化及裂縫型態。剛體平移係在圍岩模型的前斷面均勻施加1單位長度的強制變位,即強制前斷面均勻地沿軸向(Y軸)、側向(X軸)或垂直向(Z軸)移動,側面假設線性漸變,使前、後兩斷面間變位連續分佈(圖7(a)以側向平移為例);剛體旋轉是前斷面分別繞X軸、Y軸及Z軸旋轉,側面亦假設線性漸變,連結前、後兩斷面(圖7(b)以繞Z軸旋轉為例);變形則是使前後兩斷面皆施加強制變位,側面變位均勻分佈(圖7(c)以橢圓變形為例),以及使前斷面施加強制變位,側面假設線性漸變,連結前、後兩斷面。邊界條件則設置於襯砌及圍岩模型之前、後斷面上。簡而言之,該壁面係襯砌壁面,該變位量係該襯砌壁面在不同時間之空間位置變化,斷面為隧道中做為變位量測標的之監測橫斷面,該斷面包含數量足以偵測隧道變形現象之複數個監測點,該隧道單元係以二隧道監測斷面為邊界之隧道範圍,該斷面之所有監測點在不同時間之空間位置變化的集合為斷面變位量,特定斷面變化量係變位模態,其為斷面剛體運動與斷面變形,該變位模態對應已知的變位量及襯砌應力變化,斷面剛體運動包含所有該監測點一致等量移動為平移變位模態,所有該監測點對斷面形心一致等量旋轉為旋轉變位模態,斷面變形變位模態包含斷面監測點相對於該斷面形心放大或縮小之均勻變形模態,及相對於該斷面形心之變 形為橢圓變形模態,相對於該斷面形心之變形為三角變形模態,相對於該斷面形心之變形為四邊變形模態,相對於該斷面形心之變形為五邊變形模態,乃至相對於該斷面形心之變形為多邊變形模態之複數種變位模態,且三維空間中隧道內通行方向為軸向,重力方向為垂直向,另一與軸向和垂直向正交之方向為側向,該三維空間中斷面剛體運動包含軸向平移,側向平移,垂直向平移與相對軸向旋轉,相對側向軸旋轉和相對垂直軸旋轉。 In detail, from the concept of decomposition and displacement, there are six rigid body movements, including axial unit translation, lateral unit translation, vertical translation and relative axial rotation, relative lateral axis rotation and relative vertical axis rotation, plus uniform Deformation mode, ellipse deformation mode, triangular deformation mode, four-sided deformation mode, five-sided deformation mode and other multiple deformations, such as multilateral deformation relative to the cross-section centroid, etc., respectively. Give different boundary conditions to explore the individual stress changes and crack patterns of the tunnel wall. The rigid body translation system uniformly applies a forced displacement of 1 unit length on the front section of the surrounding rock model, that is, forces the front section to move uniformly in the axial (Y-axis), lateral (X-axis) or vertical directions (Z-axis) , The lateral surface assumes a linear gradual change, so that the displacements between the front and rear sections are continuously distributed (Figure 7(a) takes the lateral translation as an example); the rigid body rotation means that the front section rotates around the X axis, Y axis, and Z axis. The side also assumes a linear gradual change, connecting the front and rear sections (Figure 7(b) takes the rotation around the Z axis as an example); the deformation is to force the front and rear sections to be forced displacement, and the lateral displacement is evenly distributed (Figure 7) (c) Take elliptical deformation as an example), and apply forced displacement on the front section, assuming a linear gradual change on the side, connecting the front and rear sections. The boundary conditions are set on the front and back sections of the lining and surrounding rock model. In short, the wall surface is the lining wall surface, the displacement is the spatial position change of the lining wall surface at different times, the cross section is the monitoring cross section used as the displacement measurement target in the tunnel, and the cross section contains the quantity Multiple monitoring points that are sufficient to detect tunnel deformation phenomena. The tunnel unit is the tunnel area bounded by the two tunnel monitoring sections. The collection of the spatial position changes of all monitoring points of the section at different times is the section displacement , The specific section change is the displacement mode, which is the section rigid body movement and section deformation. The displacement mode corresponds to the known displacement and lining stress change. The section rigid body motion includes all the monitoring points consistent Equivalent movement is the translational displacement mode, all the monitoring points are consistent with the cross-section centroid and rotate the same as the rotational displacement mode. The cross-sectional deformation displacement mode includes the enlargement of the monitoring point relative to the cross-section centroid Or reduced uniform deformation mode, and the change relative to the cross-section centroid The shape is an elliptical deformation mode, the deformation relative to the cross-section centroid is a triangular deformation mode, the deformation relative to the cross-section centroid is a four-sided deformation mode, and the deformation relative to the cross-section centroid is a five-sided deformation The modal, and even the multiple deformation modals of the polygonal deformation modal with respect to the centroid of the section, and the direction of passage in the tunnel in the three-dimensional space is the axial direction, the direction of gravity is the vertical direction, and the other is the same as the axial direction. The direction perpendicular to the orthogonal is the lateral direction. The rigid body motion of the three-dimensional space interruption surface includes axial translation, lateral translation, vertical translation and relative axial rotation, relative lateral axis rotation and relative vertical axis rotation.
在步驟S24a及步驟S24b之其中之一或兩者完成後,於步驟S25中,可判斷步驟S24a中該模擬模型之測量變數及應力變化是否均勻,若是,進行步驟S3,若否,進行步驟S24a,及判斷步驟S24b中該模擬模型之測量變數及應力變化是否均勻,若是,進行步驟S3,若否,進行步驟S24b。而步驟S22a至步驟S24a係在步驟S22b至步驟S24b之前、之後或同時進行。 After one or both of steps S24a and S24b are completed, in step S25, it can be determined whether the measured variables and stress changes of the simulation model in step S24a are uniform, if yes, go to step S3, if not, go to step S24a , And determine whether the measured variables and stress changes of the simulation model in step S24b are uniform, if yes, proceed to step S3, if not, proceed to step S24b. Steps S22a to S24a are performed before, after, or at the same time as steps S22b to S24b.
於步驟S30中,可歸零該模擬模型之測量變數,施加該隧道單元邊界斷面變位之測量值於該模擬模型邊界,得到該隧道單元因斷面變位測量值第11頁,共12頁(發明說明書)引致之應力變化總量。特定而言,可計算該斷面變位測量值造成的襯砌應力變化量值。 In step S30, the measurement variables of the simulation model can be zeroed, and the measured value of the displacement of the tunnel unit boundary section is applied to the boundary of the simulation model to obtain the measured value of the tunnel unit due to the displacement of the section. Page 11 of 12 The total amount of stress changes caused by pages (invention specification). Specifically, the lining stress change caused by the measured value of the section displacement can be calculated.
於步驟S31中,可判斷該初始模擬模型之測量變數及應力變化是否均勻,若是,進行步驟S32,若否,進行步驟S34。 In step S31, it can be judged whether the measured variables and stress changes of the initial simulation model are uniform, if yes, go to step S32, if not, go to step S34.
如上所述步驟S3可在不同情況中達到步驟S34。第一種情況,若步驟S31之結果為否,得到分析隧道單元襯砌應力增量及變位量結果。第二種情況,若步驟S31之結果為是,且步驟S32之襯砌應力超出強度位置與襯砌裂縫位置相符,得到分析隧道單元襯砌應力增量及變位量結果。第三種情況,若步驟S31之結果為是且步驟S32之結果為否,進行步驟S33,即可取得分析結果襯砌應力接近強度且未超過者,折減六種相對剛體運動量值及多種變形模態對應之邊界變位量、變形量輸入順序,迄襯砌應力超出強度 位置與襯砌裂縫位置相符,之後進行步驟S30。進一步而言,可取得應力超過該襯砌材料強度、接近或等於該襯砌材料的強度之壁面的空間位置,且折減複數個相對之該測量變數及對應該變位模態之斷面變位量的值,以折減過之變位模態斷面變位量施加於該模擬模型邊界,至襯砌應力小於該襯砌材料強度或襯砌應力大於該襯砌材料強度位置與襯砌裂縫位置相符為止。特定而言,可取得分析結果襯砌應力接近該襯砌材料的強度且未超過者,減少六個相對單位變位分量及變形模態對應之邊界變位量、變形量輸入數值,迄襯砌應力小於該襯砌材料強度或襯砌應力超出該襯砌材料的強度位置與襯砌裂縫位置相符。而測量變數導致襯砌裂縫型態之範例係如圖10所示。隧道單元因前後監測斷面相對運動引致之襯砌裂縫的模擬範例與實際案例比較結果係如圖11所示。 As described above, step S3 can reach step S34 in different situations. In the first case, if the result of step S31 is no, the result of analyzing the stress increment and displacement of the tunnel unit lining is obtained. In the second case, if the result of step S31 is yes, and the position of the lining stress exceeding the strength of step S32 matches the position of the lining crack, the result of analyzing the stress increment and displacement of the tunnel unit lining is obtained. In the third case, if the result of step S31 is yes and the result of step S32 is no, proceed to step S33 to obtain the analysis result that the lining stress is close to the strength and does not exceed it, and the six relative rigid body motion values and multiple deformation modes are reduced. The input sequence of boundary displacement and deformation corresponding to the state, so far the lining stress exceeds the strength The position matches the lining crack position, and then step S30 is performed. Furthermore, the space position of the wall surface where the stress exceeds the strength of the lining material and is close to or equal to the strength of the lining material can be obtained, and a plurality of relative measurement variables and the section displacement corresponding to the displacement mode can be reduced The value of is applied to the boundary of the simulation model with the reduced displacement modal section displacement, until the lining stress is less than the strength of the lining material or the lining stress is greater than the strength of the lining material and the position of the lining crack is consistent. Specifically, the analysis result can be obtained if the lining stress is close to the strength of the lining material and does not exceed the value, the six relative unit displacement components and the corresponding boundary displacement and deformation input values corresponding to the deformation mode are reduced. The location where the strength of the lining material or the lining stress exceeds the strength of the lining material is consistent with the location of the lining crack. An example of the lining crack pattern caused by measurement variables is shown in Figure 10. Figure 11 shows the comparison between the simulation example of the lining cracks caused by the relative movement of the front and rear monitoring sections of the tunnel unit and the actual case.
綜上所述,本發明能協助釐清隧道劣化的兩個重要指標即變位與裂縫的交互影響,輸入變位監測結果獲得引致之隧道襯砌應力、應變分布與裂縫型態,經實際監測資料檢核校正後,得到可描述案例隧道變位-裂縫機制的第12頁,共12頁(發明說明書)數值模型,可用於在長期監測下預測裂縫發展趨勢、模擬補強工法成效、評估隧道健全度和安全性等,對隧道維護管理最佳化提供實質建議。 To sum up, the present invention can help to clarify the two important indicators of tunnel deterioration, namely the interactive influence of displacement and cracks. Input the displacement monitoring results to obtain the induced stress, strain distribution and crack pattern of the tunnel lining. After verification and correction, a 12-page (invention manual) numerical model that can describe the tunnel displacement-crack mechanism of the case is obtained, which can be used to predict the development trend of cracks under long-term monitoring, simulate the effectiveness of reinforcement construction methods, evaluate tunnel soundness and Security, etc., provide substantial suggestions for the optimization of tunnel maintenance and management.
雖然本發明以具體實施例揭示如上,然其所揭示的具體實施例並非用以限定本發明,任何熟悉此技藝者,在不脫離本發明之精神和範圍內,當可作各種之更動與潤飾,其所作之更動與潤飾皆屬於本發明之範疇,本發明之保護範圍當視後附之申請專利範圍所界定者為準。 Although the present invention is disclosed as above in specific embodiments, the specific embodiments disclosed are not intended to limit the present invention. Anyone familiar with the art can make various changes and modifications without departing from the spirit and scope of the present invention. , The changes and modifications made by it all belong to the scope of the present invention, and the protection scope of the present invention shall be subject to those defined by the attached patent scope.
S1、S2、S3:步驟 S1, S2, S3: steps
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TW202001624A (en) | 2020-01-01 |
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