Passive restraint stress testing method and system for a uhpc-confined concrete column

Abstract

The application discloses a kind of UHPC constrained concrete column passive constraint stress test method and system, specifically related to the technical field of the performance of solid material for testing mechanical stress, to solve the problem that existing test means is difficult to accurately obtain the non-uniform passive constraint stress full-field information generated by super high performance concrete to core concrete column under the premise of not relying on simplified mechanical model assumption;By fulling film pressure sensor at the interface of super high performance concrete sleeve and core concrete column, axial load is applied and interface pressure signal is collected to generate passive constraint stress nephogram, the ring direction unevenness and its attenuation mode along the axial direction are extracted from the nephogram, the gradient divergence field is calculated for the attenuation mode, and the zero-value crossing section is determined by the gradient divergence from the negative value area to the positive value area to determine the convergence-divergence fractal boundary, and the effective constraint area distribution atlas is constructed based on the fractal boundary.

Description

Technical Field

[0001] This invention relates to the technical field of testing the properties of solid materials by applying mechanical stress, and more specifically, to a method and system for testing the passive restraint stress of UHPC-confined concrete columns. Background Technology

[0002] In engineering applications of ultra-high performance concrete (UHPC) reinforcement of existing concrete columns, utilizing UHPC sleeves or outer cladding to passively constrain the core concrete column is a key technical means to improve its load-bearing capacity and ductility. Accurate testing of the passive constraint stress on the core concrete is a fundamental prerequisite for revealing the collaborative working mechanism between UHPC and concrete, establishing a reliable constitutive model of UHPC-constrained concrete, and ultimately forming a scientific design method. In existing technologies, the testing methods for this passive constraint stress typically borrow from those used for conventional steel-tube concrete or fiber-reinforced polymer (FRP) confined concrete, mainly relying on pre-embedded traditional point sensors within the core concrete or indirect calculations based on strain data from the outer surface of the UHPC reinforcement layer using theoretical models.

[0003] However, the existing testing methods have significant shortcomings. Point sensors embedded in the core concrete can only acquire local stress information at the measurement point location, making it difficult to reflect the non-uniform distribution characteristics of the overall stress field of the core concrete under the passive constraint of UHPC. At the same time, the accuracy of the method based on the data of the outer surface of the reinforcement layer is highly dependent on the simplified assumptions of the mechanical model used regarding the hardening shrinkage of UHPC, the creep of the core concrete, and the complex interaction between the two. As a result, the calculated results deviate from the actual state of the passive constraint stress, making it impossible to accurately and reliably obtain the passive constraint stress of the UHPC-confined concrete column. This, in turn, affects the in-depth understanding of the UHPC reinforcement mechanism and the accurate establishment of the bearing capacity calculation theory. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art, the present invention provides a passive restraint stress testing method and system for UHPC-confined concrete columns to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for testing the passive confinement stress of a UHPC-confined concrete column includes the following steps:

[0007] S1: Fabricate a concrete column specimen containing an ultra-high performance concrete sleeve, and fully insert thin-film pressure sensors at the interface between the ultra-high performance concrete sleeve and the core concrete column.

[0008] S2: Apply axial load to the concrete column specimen and simultaneously acquire the interface pressure signal output by the membrane pressure sensor;

[0009] S3: Generate contour maps of the passive constraint stress distribution along the circumferential and axial directions of the column based on the interface pressure signal;

[0010] S4: Select multiple monitoring sections along the column axis, and extract the non-uniformity of passive constraint stress distribution along the circumferential direction on each monitoring section based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis.

[0011] S5: Calculate the gradient field for the decay mode of non-uniformity along the column axis, calculate the divergence of the gradient field to obtain the gradient divergence distribution, and determine the zero-value crossing section of the gradient divergence from the negative value region to the positive value region as the convergent-divergent fractal boundary.

[0012] S6: Based on convergent-divergent fractal boundaries, construct the distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column.

[0013] Furthermore, concrete column specimens containing ultra-high performance concrete sleeves were fabricated, and thin-film pressure sensors were fully arranged at the interface between the ultra-high performance concrete sleeve and the core concrete column, including:

[0014] First, a core concrete column is poured and cured to the predetermined age. Then, a thin-film pressure sensor array that can sense two-dimensional stress state is fully covered on the outer surface of the core concrete column. Next, a formwork is erected around the core concrete column covered with the thin-film pressure sensor array and ultra-high performance concrete is poured. After hardening, a concrete column specimen is formed with thin-film pressure sensors fully covering the interface between the ultra-high performance concrete sleeve and the core concrete column.

[0015] Furthermore, an axial load was applied to the concrete column specimen, and the interfacial pressure signal output by the membrane pressure sensor was simultaneously acquired, including:

[0016] The concrete column specimen was placed on a compression testing machine. The leads of the thin-film pressure sensor array were connected to a multi-channel data acquisition instrument. The compression testing machine was started to apply an axial monotonic static load to the concrete column specimen. During the loading process, the interface pressure signals of all sensing units in the thin-film pressure sensor array were synchronously and continuously acquired by the multi-channel data acquisition instrument at a preset frequency until the concrete column specimen entered the descending segment of the load-displacement curve and then the loading and acquisition were stopped.

[0017] Furthermore, based on the interface pressure signal, contour maps of the passive constraint stress distribution along the circumferential and axial directions of the column are generated, including:

[0018] The interface pressure signal collected by each sensing unit is converted into the passive constraint stress value at the location of the sensing unit. Based on the spatial coordinates of the sensing units in the thin-film pressure sensor array at the interface between the ultra-high performance concrete sleeve and the core concrete column, the passive constraint stress values ​​at the locations of all sensing units are mapped to a two-dimensional spatial grid. The passive constraint stress values ​​on the two-dimensional spatial grid are spatially interpolated to generate a cloud map of the passive constraint stress distribution along the circumference and axial direction of the column.

[0019] Furthermore, multiple monitoring sections are selected along the column axis, and the non-uniformity of the passive constraint stress distribution along the circumferential direction on each monitoring section is extracted based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis, including:

[0020] In the cloud map of the passive constraint stress distribution along the circumferential and axial directions of the column, multiple monitoring sections are selected at equal intervals along the column axis. The sequence of passive constraint stress distribution along the circumferential direction on each monitoring section is extracted. The ratio of the standard deviation to the mean of the passive constraint stress distribution sequence along the circumferential direction on each monitoring section is calculated as the non-uniformity. The non-uniformities of all monitoring sections are arranged sequentially according to the axial position of the column to obtain the attenuation mode of non-uniformity along the column axis.

[0021] Furthermore, before calculating the ratio of the standard deviation to the mean as the non-uniformity, outlier data points in the sequence of passive constraint stress distributed along the circumferential direction that deviate from the mean by more than a preset deviation threshold are removed. The ratio of the standard deviation to the mean of the sequence of passive constraint stress distributed along the circumferential direction after removing outlier data points is then used as the non-uniformity.

[0022] Furthermore, the gradient field is obtained for the attenuation mode of the inhomogeneity along the column axis, and the gradient divergence distribution is obtained by calculating the divergence of the gradient field. The zero-value crossing section of the gradient divergence from the negative region to the positive region is determined as the convergent-divergent fractal boundary, including:

[0023] In the attenuation mode of non-uniformity along the column axis, the non-uniformity of adjacent monitoring sections is subjected to first-order difference to obtain the gradient value at each monitoring section location. The gradient values ​​at all monitoring section locations are arranged sequentially according to the column axis to form a gradient field. The gradient values ​​of adjacent monitoring sections in the gradient field are subjected to first-order difference to obtain the divergence value at each monitoring section location. The divergence values ​​at all monitoring section locations are arranged sequentially according to the column axis to obtain the gradient divergence distribution. In the gradient divergence distribution, the zero-value crossing section corresponding to the divergence value changing from negative to positive is identified, and the zero-value crossing section is determined as the convergence-divergence fractal boundary.

[0024] Furthermore, before performing first-order difference on the gradient values ​​of adjacent monitoring sections in the gradient field, cubic spline interpolation is performed on the gradient values ​​at each monitoring section location in the gradient field to obtain a densified gradient field. First-order difference is performed on the gradient values ​​at adjacent interpolation points in the densified gradient field to obtain the divergence value at each interpolation point location. The divergence values ​​at all interpolation point locations are arranged sequentially according to the axial position of the column to obtain the gradient divergence distribution.

[0025] Furthermore, based on convergent-divergent fractal boundaries, a distribution map of the effective confinement region of the ultra-high performance concrete sleeve for the core concrete column is constructed, including:

[0026] Using the position of the convergent-divergent fractal boundary along the column axis as the dividing line, the interface between the ultra-high performance concrete sleeve and the core concrete column is divided into an effective constraint zone and an ineffective constraint zone along the column axis. The position of the convergent-divergent fractal boundary and the range of the effective constraint zone are superimposed on the cloud map of the passive constraint stress distribution along the column circumference and axis to generate a distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column.

[0027] On the other hand, the present invention provides a passive restraint stress testing system for UHPC-confined concrete columns, comprising the following modules:

[0028] The specimen fabrication module is used to fabricate concrete column specimens containing ultra-high performance concrete sleeves, and thin-film pressure sensors are fully arranged at the interface between the ultra-high performance concrete sleeve and the core concrete column.

[0029] The loading acquisition module is used to apply axial load to the concrete column specimen and simultaneously acquire the interface pressure signal output by the membrane pressure sensor;

[0030] The cloud map generation module is used to generate cloud maps of the passive constraint stress distribution along the circumferential and axial directions of the column based on the interface pressure signal.

[0031] The feature extraction module is used to select multiple monitoring sections along the column axis, and extract the non-uniformity of the passive constraint stress distribution along the circumferential direction on each monitoring section based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis.

[0032] The boundary identification module is used to obtain the gradient field of the decay mode of non-uniformity along the column axis, obtain the gradient divergence distribution by calculating the divergence of the gradient field, and determine the zero-value crossing section of the gradient divergence from the negative value region to the positive value region as the convergent-divergent fractal boundary.

[0033] The map construction module is used to construct a distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column based on the convergent-divergent fractal boundary.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1. By fully distributing thin-film pressure sensors at the interface between the ultra-high performance concrete sleeve and the core concrete column, two-dimensional pressure signals at the interface are directly acquired, and a full-field cloud map of the passive constraint stress distribution along the circumferential and axial directions of the column is generated. This avoids the limitation of point sensors that can only acquire local stress information, and also eliminates the reliance on simplified assumptions of mechanical models in traditional indirect deduction methods. The interface pressure signals collected during the test are entirely derived from the measured contact stress at the interface between the ultra-high performance concrete sleeve and the core concrete column. No simplified assumptions are introduced regarding the hardening shrinkage of ultra-high performance concrete, creep of core concrete, or complex interactions at the interface. The generated passive constraint stress cloud map can truly reflect the non-uniform distribution characteristics of the constraint stress on the core concrete column.

[0036] 2. By extracting circumferential non-uniformity and its attenuation mode along the axial direction from the passive constraint stress cloud map, and further calculating the gradient divergence field of the attenuation mode to determine the convergence-divergence fractal boundary, structural characteristic quantities characterizing the transmission and diffusion of constraint stress were extracted from the measured data. The convergence-divergence fractal boundary divides the constraint effect of the ultra-high performance concrete sleeve on the core concrete column into an end effect-dominant region and a uniform constraint region along the axial direction. The effective constraint region distribution map constructed in this way intuitively presents the spatial correspondence between the effective range of the sleeve constraint effect and the stress distribution state, providing a measured criterion for accurately evaluating the constraint effectiveness of the ultra-high performance concrete sleeve. This allows the test results of passive constraint stress to no longer be limited to a single stress value level, but to rise to a spatial distribution understanding reflecting the constraint mechanism. Attached Figure Description

[0037] Figure 1 This is a flowchart of a passive restraint stress testing method for UHPC-confined concrete columns according to the present invention;

[0038] Figure 2 This is a schematic diagram of the passive restraint stress testing system for UHPC-confined concrete columns according to the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0040] Example 1: Figure 1 This invention provides a method for testing the passive confinement stress of a UHPC-confined concrete column, which includes the following steps:

[0041] S1: Fabricate a concrete column specimen containing an ultra-high performance concrete sleeve, and fully insert thin-film pressure sensors at the interface between the ultra-high performance concrete sleeve and the core concrete column.

[0042] S2: Apply axial load to the concrete column specimen and simultaneously acquire the interface pressure signal output by the membrane pressure sensor;

[0043] S3: Generate contour maps of the passive constraint stress distribution along the circumferential and axial directions of the column based on the interface pressure signal;

[0044] S4: Select multiple monitoring sections along the column axis, and extract the non-uniformity of passive constraint stress distribution along the circumferential direction on each monitoring section based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis.

[0045] S5: Calculate the gradient field for the decay mode of non-uniformity along the column axis, calculate the divergence of the gradient field to obtain the gradient divergence distribution, and determine the zero-value crossing section of the gradient divergence from the negative value region to the positive value region as the convergent-divergent fractal boundary.

[0046] S6: Based on convergent-divergent fractal boundaries, construct the distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column.

[0047] In specific implementation step S1, the core concrete column is first poured and cured to the predetermined age. The core concrete column is made of ordinary concrete with a strength grade of C40. The cross-sectional dimensions of the core concrete column are, for example, 300 mm × 300 mm, and the column height is, for example, 1200 mm. The pouring of the core concrete column is completed in a steel mold. After pouring, it is covered and moisturized for 28 days under standard curing conditions of temperature 20 ± 2 degrees Celsius and relative humidity not less than 95% to form the core concrete column. After curing to the predetermined age, the core concrete column is demolded from the steel mold, and the outer surface of the core concrete column is roughened. The roughening process is carried out by using an electric hammer to evenly create an uneven surface with a depth of, for example, 3 mm to 5 mm, on the four sides of the core concrete column to enhance the mechanical interlocking between the subsequently attached thin-film pressure sensor array and the ultra-high performance concrete and the outer surface of the core concrete column. After the roughening process is completed, a high-pressure air gun is used to remove the dust and debris from the outer surface of the core concrete column.

[0048] An array of thin-film pressure sensors capable of sensing two-dimensional stress states is fully covered on the outer surface of the core concrete column. The thin-film pressure sensor array employs a flexible matrix-type thin-film pressure sensor based on the piezoresistive principle. This flexible matrix-type sensor consists of multiple sensing units arranged in rows and columns. Each sensing unit senses the normal pressure acting on its surface and converts this pressure into a change in resistance, thereby obtaining the two-dimensional stress state. Before covering, the flexible matrix-type thin-film pressure sensors are cut to the unfolded dimensions of the four sides of the core concrete column, ensuring complete coverage of all four sides. The unfolded coverage area is, for example, 1200 mm in length and 1200 mm in width. During covering, an epoxy resin adhesive layer is evenly applied to the roughened outer surface of the core concrete column. The cut flexible matrix-type thin-film pressure sensors are then smoothly and evenly covered onto each of the four sides of the core concrete column. During the covering process, rubber rollers are used to evenly roll the flexible matrix-type thin-film pressure sensors from the center to the edges to remove air bubbles and ensure a tight fit between the sensors and the outer surface of the core concrete column. At the corners where two adjacent sides meet, the flexible matrix thin-film pressure sensor is bent along the corner line and continued to be attached, forming a continuous, uninterrupted two-dimensional sensing surface covering the core concrete column. After attachment, it is left to stand at room temperature for 24 hours to allow the epoxy resin adhesive layer to cure. Subsequently, the leads of the flexible matrix thin-film pressure sensor are led out from the top of the core concrete column. The number of leads corresponds to the number of rows and columns of the sensing unit, and the lead length is reserved, for example, 1500 mm, to allow for subsequent connection to an external multi-channel data acquisition instrument after passing through the top of the ultra-high performance concrete sleeve. A polytetrafluoroethylene (PTFE) protective sleeve is fitted along the lead path, with one end of the protective sleeve located at the root of the attached flexible matrix thin-film pressure sensor lead and the other end extending above the top of the core concrete column, to prevent the lead from being contaminated by the slurry or short-circuiting during subsequent ultra-high performance concrete pouring.

[0049] Next, formwork is erected around the core concrete column covered with a thin-film pressure sensor array, and ultra-high performance concrete is poured. Wooden formwork is used, with an inner cavity cross-section of, for example, 400 mm × 400 mm and a height of, for example, 1400 mm. A high-density foam pad with a thickness of, for example, 50 mm is sealed at the bottom of the wooden formwork, and a release agent is applied to the inside of the wooden formwork. The core concrete column covered with the thin-film pressure sensor array, with its leads already encased in a PTFE protective sleeve, is vertically hoisted into the center of the wooden formwork. A concrete pad with a height of, for example, 50 mm is placed between the bottom of the core concrete column and the bottom of the wooden formwork to suspend the core concrete column in mid-air. The distance from each of the four sides of the core concrete column to the inner wall of the wooden formwork is 50 mm, thus forming a 50 mm thick annular pouring cavity around the core concrete column. The ultra-high performance concrete used for pouring is steel fiber-reinforced ultra-high performance concrete with a compressive strength of not less than 150 MPa and a tensile strength of not less than 8 MPa. The mix proportion of the steel fiber-reinforced ultra-high performance concrete is as follows: 910 kg / m³ silicate cement, 230 kg / m³ silica fume, 980 kg / m³ quartz sand, 180 kg / m³ quartz powder, 22 kg / m³ high-efficiency water-reducing agent, 175 kg / m³ water, and 2% copper-plated microfiber steel fibers by volume. The copper-plated microfiber steel fibers have a length of, for example, 13 mm and a diameter of, for example, 0.2 mm. The steel fiber-reinforced ultra-high performance concrete mixture is poured into the annular pouring cavity from the top of the wooden formwork. During the pouring process, an immersion vibrator is used to alternately vibrate the annular pouring cavity from the four corners for short periods. Each vibration time does not exceed 5 seconds, and the insertion depth of the vibrator does not exceed two-thirds of the depth of the annular pouring cavity to avoid the vibrator touching the flexible matrix thin-film pressure sensor. After pouring the concrete to the top level with the wooden formwork, a moisturizing film was placed over the top of the wooden formwork. The wooden formwork was removed after 48 hours of room temperature and humidity curing. After removing the wooden formwork, the surface of the ultra-high performance concrete sleeve was covered with a moisturizing film and cured at room temperature and humidity for another 28 days. This resulted in a hardened ultra-high performance concrete column specimen with a layer of thin-film pressure sensors at the interface between the ultra-high performance concrete sleeve and the core concrete column. The ultra-high performance concrete sleeve was 50 mm thick, and a dense array of flexible matrix-type thin-film pressure sensors were embedded at the interface between the ultra-high performance concrete sleeve and the core concrete column, with leads extending from the top of the ultra-high performance concrete sleeve.

[0050] In specific implementation step S2, the concrete column specimen is placed on a compression testing machine. The compression testing machine is an electro-hydraulic servo universal compression testing machine with a maximum loading capacity of no less than 5000 kN and a loading accuracy class of no less than 0.5. The concrete column specimen is the one formed in step S1, with thin-film pressure sensors distributed at the interface between the ultra-high performance concrete sleeve and the core concrete column. The thickness of the ultra-high performance concrete sleeve in the concrete column specimen is 50 mm, the cross-sectional dimensions of the core concrete column are 300 mm × 300 mm, and the column height is 1200 mm. The concrete column specimen is vertically hoisted above the lower loading plate of the compression testing machine. Steel pads, for example, 20 mm thick, are placed on the top and bottom surfaces of the concrete column specimen. The planar dimensions of the steel pads match the outer contour dimensions of the ultra-high performance concrete sleeve, and the steel pads ensure that the axial load is evenly transferred to the entire cross-section of the concrete column specimen. Adjust the upper loading plate of the pressure testing machine to move downwards until it contacts and centers with the steel pad on the top surface of the concrete column specimen. Centering is assisted by a laser centering instrument. The requirement for centering is that the line of action of the axial load coincides with the geometric center axis of the concrete column specimen to avoid the loading eccentricity from interfering with the distribution of passive constraint stress.

[0051] Connect the leads of the thin-film pressure sensor array to the multi-channel data acquisition instrument. The thin-film pressure sensor array is the flexible matrix thin-film pressure sensor that is attached to the outer surface of the core concrete column and encased in an ultra-high performance concrete sleeve in step S1. The leads of the flexible matrix thin-film pressure sensor have already emerged from the top of the ultra-high performance concrete sleeve. The multi-channel data acquisition instrument is a dynamic signal acquisition instrument that supports synchronous sampling. The number of channels of the multi-channel data acquisition instrument is not less than the total number of sensing units in the flexible matrix thin-film pressure sensor. Each lead of the flexible matrix thin-film pressure sensor is connected to one signal input channel of the multi-channel data acquisition instrument. The connection between the leads and the multi-channel data acquisition instrument uses a shielded cable terminal block. The terminal block is placed near the top of the ultra-high performance concrete sleeve and fixed with an insulating bracket to prevent the leads from being pulled loose during loading. After connection, channel calibration is performed. The channel calibration procedure is as follows: Under zero load conditions where no load has been applied to the pressure testing machine, all sensing units are zeroed and balanced. The output signal value of each sensing unit under zero load conditions is stored as its own zero offset value. Then, a known standard pressure value is applied to each sensing unit for calibration coefficient calibration. The standard pressure value is provided by a standard pressure calibrator, which applies standard pressure values, for example, at three levels: 100 kPa, 500 kPa, and 1000 kPa. Each sensing unit acquires its output signal value at each standard pressure value. The difference between the output signal value and the zero offset value is divided by the standard pressure value to obtain the calibration coefficient of each sensing unit. The calibration coefficient is stored in the multi-channel data acquisition instrument for converting subsequently acquired voltage signals into pressure values.

[0052] The compression testing machine is started to apply an axial monotonic static load to the concrete column specimen. The loading control method adopts a displacement control loading mode, with a loading rate of, for example, 0.2 mm / min. The displacement control loading mode avoids the sudden brittle failure that might occur with the force control mode near the peak load, and is beneficial for fully capturing the descending segment of the load-displacement curve. Simultaneously with the application of the axial monotonic static load by the compression testing machine, a multi-channel data acquisition instrument is triggered to synchronously acquire interface pressure signals. The interface pressure signal is the normal pressure value obtained by converting the resistance change output by each sensing unit in the flexible matrix thin-film pressure sensor after calibration. The unit of the interface pressure signal is kilopascals (kPa). The preset frequency is determined comprehensively based on the total number of sensing units, the maximum sampling rate of the multi-channel data acquisition instrument, and the expected duration of the loading. The preset frequency is determined by multiplying the expected duration of the loading by the preset frequency to obtain the number of data points for each sensing unit. The number of data points is not less than five times the total number of sensing units to ensure that the continuous change trend of passive constraint stress during the complete loading process is fully recorded. The preset frequency is set, for example, to 10 Hz. During the loading process, the loading actuator of the pressure testing machine continuously presses down at a uniform speed in displacement-controlled loading mode, while simultaneously observing the real-time signal waveform displayed on the multi-channel data acquisition instrument. If the signal amplitude of a certain sensing unit is found to exceed the upper limit of the range of the flexible matrix thin-film pressure sensor, the gain of that sensing unit is switched from the current level to an adjacent low-gain level through the software interface of the multi-channel data acquisition instrument. The gain value of the low-gain level is determined according to the correspondence table between gain level and range in the factory calibration data of the flexible matrix thin-film pressure sensor. The range after switching to the low-gain level covers the current output signal amplitude of the sensing unit to ensure that the interface pressure signal does not experience clipping distortion. The upper limit of the range of the flexible matrix thin-film pressure sensor is determined according to the selected sensor model, for example, a flexible matrix thin-film pressure sensor with an upper limit of 10 MPa is selected.

[0053] During loading, the real-time output of the load sensor and displacement sensor readings of the compression testing machine were continuously monitored. The load sensor reading represented the total axial load applied to the concrete column specimen by the compression testing machine, and the displacement sensor reading represented the axial compressive displacement of the concrete column specimen. A load-displacement curve was plotted in real time, with the displacement sensor reading on the x-axis and the load sensor reading on the y-axis. The criterion for determining the descending segment of the load-displacement curve was: when the load sensor reading continuously decreased from the peak load point on the load-displacement curve, and the continuous decrease in the load sensor reading exceeded 20% of the peak load, the concrete column specimen entered the descending segment of the load-displacement curve. After the concrete column specimen entered the descending segment of the load-displacement curve, the displacement-controlled loading mode was maintained until the load sensor reading dropped to 50% of the peak load, at which point the loading of the compression testing machine and the acquisition by the multi-channel data acquisition instrument were simultaneously stopped. After the acquisition stops, the interface pressure signal data of all sensing units stored in the multi-channel data acquisition instrument is exported as a data file. The interface pressure signal data includes the time-series pressure value of each sensing unit during the complete loading process, the corresponding timestamp, and the row and column number of each sensing unit in the flexible matrix thin film pressure sensor. The interface pressure signal data is used to generate a cloud map of the passive constraint stress distribution along the circumferential and axial directions of the column.

[0054] In specific implementation step S3, the interface pressure signal data file exported in step S2 is loaded into the data processing program. The interface pressure signal data file contains the time-series pressure values ​​of each sensing unit during the complete loading process, the corresponding timestamps, and the row and column numbers of each sensing unit in the flexible matrix thin-film pressure sensor. The data processing program reads the data line by line, extracting the row and column numbers of each sensing unit, as well as the interface pressure signal value corresponding to the timestamp at the end of the descending segment of the load-displacement curve. The end of the descending segment of the load-displacement curve is the time when the load sensor reading drops to 50% of the peak load in step S2. The extracted interface pressure signal values ​​at the end of the descending segment of the load-displacement curve for each sensing unit are used as input data to generate cloud maps showing the passive constraint stress distribution along the column's circumferential and axial directions. The interface pressure signal values ​​at the end of the descending segment of the load-displacement curve reflect the final stress state of the ultra-high performance concrete sleeve passively constraining the core concrete column.

[0055] The interface pressure signal collected by each sensing unit is converted into the passive constraint stress value at the location of that sensing unit. The interface pressure signal is the positive pressure value output by the sensing unit in the flexible matrix thin-film pressure sensor, and the unit of the interface pressure signal is kilopascal (kPa). The passive constraint stress value is the radial compressive stress value generated on the interface between the ultra-high performance concrete sleeve and the core concrete column, and the unit of the passive constraint stress value is megapascal (MPa). The specific conversion method is as follows: the interface pressure signal value of each sensing unit is multiplied by a conversion factor of 0.001 to obtain the passive constraint stress value at the location of that sensing unit. The conversion factor of 0.001 is the unit conversion factor from kilopascal to MPa. The conversion process retains the sign of the interface pressure signal; a positive value indicates a compressive state, and a negative value indicates a tensile state. Under the passive constraint condition of the ultra-high performance concrete sleeve, the passive constraint stress value is always positive. After conversion, the row number, column number, and the converted passive constraint stress value of each sensing unit are stored as a data triplet, in the form of, for example, row number, column number, and passive constraint stress value.

[0056] Based on the spatial coordinates of the sensing units in the thin-film pressure sensor array at the interface between the ultra-high-performance concrete sleeve and the core concrete column, a mapping relationship between the row and column numbers of each sensing unit and its spatial coordinates is established. In step S1, flexible matrix thin-film pressure sensors are attached to the four sides of the core concrete column. The cross-sectional dimensions of the core concrete column are, for example, 300 mm × 300 mm, and the column height is, for example, 1200 mm. The row and column arrangement of the flexible matrix thin-film pressure sensors is as follows: the row direction is along the column axis, and the column direction is along the column circumference. The total number of rows in the row direction is, for example, 48 rows, and the total number of columns in the column direction is, for example, 48 columns. The sensing units attached to one side cover the entire area of ​​that side. The four sides are sequentially and continuously attached, forming a continuous and uninterrupted sensing array in the circumferential direction. The axial height position of each sensing unit is determined based on the row number of the sensing unit, the total number of rows, and the height of the core concrete column. The determination method is: axial height equals the difference between the row number and 1, divided by the difference between the total number of rows and 1, multiplied by the column height. Row numbers start from 1, and the zero point of the axial height is defined at the bottom surface of the core concrete column. The circumferential angle position of each sensing unit is determined based on the column number of the sensing unit, the total number of columns, and the unfolded perimeter of the four sides of the core concrete column. For example, the unfolded perimeter is the cross-sectional perimeter of the core concrete column: 4 × 300 mm = 1200 mm. The circumferential angle position of each sensing unit is determined as follows: The arc length position of this sensing unit on the unfolded perimeter is calculated based on the column number and the total number of columns. The arc length position is equal to the difference between the column number and 1, divided by the difference between the total number of columns and 1, multiplied by the unfolded perimeter. The arc length position is then converted to a circumferential angle, which is equal to the arc length position divided by the cross-sectional perimeter of the core concrete column, multiplied by 360 degrees. The zero point of the circumferential angle is defined at the starting edge position of the side on which the flexible matrix thin-film pressure sensor is first attached on one of the four sides of the core concrete column. The circumferential angle increases counterclockwise along the circumference of the column. The spatial position coordinates of each sensing unit are uniquely determined by two dimensions: axial height and circumferential angle. These coordinates are stored as position coordinate pairs, i.e., axial height value and circumferential angle value. The unit of the axial height value is millimeters, and the unit of the circumferential angle value is degrees.

[0057] The passive constraint stress values ​​at all sensing unit locations are mapped to a two-dimensional spatial grid. The two-dimensional spatial grid is a rectangular grid region composed of a circumferential angle dimension and an axial height dimension. The circumferential angle dimension ranges from 0 degrees to 360 degrees, and the axial height dimension ranges from 0 mm at the bottom of the core concrete column to 1200 mm at the top. The grid resolution of the two-dimensional spatial grid is set, determined by a combination of the physical spacing of the sensing units of the flexible matrix thin-film pressure sensor and the desired smoothness of the contour map. For example, the grid resolution is set to one grid node per degree in the circumferential angle direction and one grid node per 1 mm in the axial height direction, resulting in a total of 360 × 1200 nodes in the two-dimensional spatial grid. For each sensing unit, based on its spatial coordinates (axial height and circumferential angle values), the nearest grid node with the corresponding axial height and circumferential angle values ​​is found in the two-dimensional spatial grid. The calculated passive constraint stress value for this sensing unit is then assigned to the found grid node. For the remaining mesh nodes in the two-dimensional spatial mesh that have not yet been assigned values, their passive constraint stress values ​​are marked as null values ​​to be filled by subsequent interpolation.

[0058] Spatial interpolation is performed on the passive constraint stress values ​​on a two-dimensional spatial mesh. Spatial interpolation employs a distance-inverse weighted interpolation method based on four pre-assigned mesh nodes. These four pre-assigned mesh nodes are the four nearest pre-assigned mesh nodes that surround the mesh node to be interpolated in both the circumferential angle and axial height dimensions. For each null mesh node to be interpolated, the four nearest pre-assigned mesh nodes are determined as follows: in the two-dimensional spatial mesh, the nearest pre-assigned mesh node along the direction of decreasing circumferential angle is designated as the first reference node; the nearest pre-assigned mesh node along the direction of increasing circumferential angle is designated as the second reference node; the nearest pre-assigned mesh node along the direction of decreasing axial height is designated as the third reference node; and the nearest pre-assigned mesh node along the direction of increasing axial height is designated as the fourth reference node. When the mesh node to be interpolated is located at the boundary of the two-dimensional spatial mesh, if no pre-assigned mesh node exists in a certain direction, a pre-assigned mesh node in the opposite direction is used to form a symmetrical interpolation. Calculate the Euclidean distances from the nodes of the mesh to be interpolated to the first, second, third, and fourth reference nodes. The Euclidean distance is calculated as follows: the square of the circumferential angle difference multiplied by the perimeter of the core concrete column section divided by 360 degrees, plus the square of the axial height difference, and then taking the square root. Take the reciprocal of each of the four Euclidean distances to obtain four reciprocal distance weights. Normalize these four reciprocal distance weights by dividing the reciprocal distance weight corresponding to the first reference node by the sum of the four reciprocal distance weights, the second reference node by the sum of the four reciprocal distance weights, the third reference node by the sum of the four reciprocal distance weights, and the fourth reference node by the sum of the four reciprocal distance weights. The sum of the four normalized reciprocal distance weights is 1. The passive constraint stress value of the first reference node is multiplied by the normalized inverse distance weight of the first reference node, the passive constraint stress value of the second reference node is multiplied by the normalized inverse distance weight of the second reference node, the passive constraint stress value of the third reference node is multiplied by the normalized inverse distance weight of the third reference node, and the passive constraint stress value of the fourth reference node is multiplied by the normalized inverse distance weight of the fourth reference node. These four products are then added together to obtain the passive constraint stress value of the mesh node to be interpolated. The interpolation process is performed one by one for all null mesh nodes until all mesh nodes on the two-dimensional spatial mesh are assigned passive constraint stress values.

[0059] A contour map of the passive constraint stress distribution along the column's circumference and axial direction is generated. The spatially interpolated 2D mesh data is converted into a graphical representation, with the horizontal axis representing the circumferential angle and the vertical axis representing the axial height. The passive constraint stress value of each mesh node is mapped to a color, for example, mapping the minimum passive constraint stress value to blue, the maximum passive constraint stress value to red, and passive constraint stress values ​​between the minimum and maximum values ​​to a continuous blue-cyan-green-yellow-red spectrum. In the contour map of the passive constraint stress distribution along the column's circumference and axial direction, the intensity of the color indicates the magnitude of the passive constraint stress; a darker color, closer to red, indicates a larger passive constraint stress value, and a lighter color, closer to blue, indicates a smaller passive constraint stress value. The creation of the contour map of the passive constraint stress distribution along the column's circumference and axial direction includes labeling the circumferential angle scale, the axial height scale, and the color scale. The labeling content demonstrates the 2D distribution characteristics of the passive constraint stress at the interface between the ultra-high performance concrete sleeve and the core concrete column.

[0060] In the specific implementation step S4, multiple monitoring sections are selected at equal intervals along the column axis in the cloud map of the passive constraint stress distribution along the column circumference and axial direction generated in step S3. The axial range of the column extends from 0 mm at the bottom axial height of the core concrete column to the top axial height, and the axial heights of the bottom and top surfaces of the core concrete column are consistent with the range of the axial height dimension of the two-dimensional spatial grid in step S3. The spacing of the equally spaced monitoring sections is determined as follows: based on the thickness of the ultra-high performance concrete sleeve, the cross-sectional dimensions of the core concrete column, and the expected severity of the axial variation of the passive constraint stress, a spacing value that can fully capture the axial variation characteristics of the non-uniformity is selected. For example, if the spacing value is set to 25 mm, a monitoring section is selected every 25 mm starting from the axial height of 0 mm, up to the top axial height, for example, a total of 49 monitoring sections are selected, each corresponding to an axial height position. The selected axial height positions are aligned with the grid nodes in the axial height dimension of the two-dimensional spatial grid. If there is no corresponding grid node for a certain axial height position, the axial height of the grid node closest to this axial height position is selected as the monitoring section. For each selected monitoring section, in the cloud map of the passive constraint stress distribution along the circumferential and axial directions of the column, the passive constraint stress values ​​of all grid nodes along the circumferential angle dimension from 0 degrees to 360 degrees at the axial height position of the monitoring section are extracted and arranged in order of ascending circumferential angle to form a sequence of passive constraint stress distribution along the circumferential direction on the monitoring section.

[0061] Before calculating the ratio of standard deviation to mean as the non-uniformity, outlier data points are removed from the circumferential distribution sequence of passive constraint stress for each monitoring section. The input for outlier removal is the circumferential distribution sequence of passive constraint stress, and the output is the circumferential distribution sequence of passive constraint stress after outlier removal. The criteria for identifying outliers are as follows: first, the mean and standard deviation of the circumferential distribution sequence of passive constraint stress are calculated; the upper limit of the preset deviation threshold is set to the sum of the mean and the standard deviation of the sequence; and the lower limit of the preset deviation threshold is set to the difference between the mean and the standard deviation of the sequence. The preset deviation threshold is based on the fact that, for the passive constraint stress data collected by the flexible matrix thin-film pressure sensor at the interface between the ultra-high performance concrete sleeve and the core concrete column, under the trend of the ultra-high performance concrete sleeve forming a uniform circumferential constraint on the core concrete column, each data point in the sequence of passive constraint stress along the circumferential distribution on the same monitoring section should fluctuate around the average value of the sequence within a certain range. The fluctuation amplitude is related to the pouring uniformity of the ultra-high performance concrete sleeve, the flatness of the flexible matrix thin-film pressure sensor, and the random distribution of the uneven rough surface formed by the roughening treatment of the outer surface of the core concrete column. Passive constraint stress values ​​that deviate from the average value of the sequence by more than three standard deviations are judged as abnormal data points caused by poor local contact of the sensor, transient electromagnetic interference, or local defects in the concrete. Such abnormal data points do not reflect the true statistical characteristics of the passive constraint stress distribution along the circumferential direction. Each passive constraint stress value in the circumferential distribution sequence is compared sequentially with the upper and lower limits of a preset deviation threshold. When a passive constraint stress value is greater than the upper limit or less than the lower limit, it is marked as an abnormal data point and removed from the circumferential distribution sequence. After removal, the number of data points in the circumferential distribution sequence is reduced accordingly. After removing abnormal data points, the circumferential distribution sequence of passive constraint stress at the monitoring section is obtained.

[0062] For each monitoring section, after removing outlier data points, the sequence of passive constraint stress distributed circumferentially is calculated. The ratio of the standard deviation of this sequence to the mean of the sequence is then used as the non-uniformity of the circumferential distribution of passive constraint stress on the monitoring section. The standard deviation is calculated using the sample standard deviation method: the square of the difference between each data point in the sequence and the mean of the sequence is calculated; the sum of these squares is then obtained; this sum is divided by the difference between the number of data points in the sequence and one; and the square root is taken to obtain the standard deviation. The mean is calculated as follows: the sum of all data points in the sequence is obtained; this sum is then divided by the number of data points in the sequence and one; and the mean is obtained. The non-uniformity of the passive constraint stress distribution along the circumference reflects the degree of non-uniformity in the circumferential distribution of the passive constraint stress provided by the ultra-high performance concrete sleeve to the core concrete column on the monitoring section. A larger value for the non-uniformity indicates a greater difference in passive constraint stress at different locations along the circumference. The process of removing outlier data points and calculating the non-uniformity of the passive constraint stress distribution along the circumference was performed on each selected monitoring section to obtain the non-uniformity value of the passive constraint stress distribution along the circumference for each monitoring section.

[0063] The non-uniformity of passive constraint stress along the circumferential direction at all monitored sections was arranged sequentially according to the axial position of the column to obtain the attenuation pattern of non-uniformity along the column axis. The arrangement was as follows: A data pair was formed by pairing the axial height position corresponding to each monitored section with the calculated non-uniformity value of the passive constraint stress along the circumferential direction. Each data pair contained both the axial height value and the non-uniformity value of the passive constraint stress along the circumferential direction. All data pairs for all monitored sections were arranged in ascending order of axial height value to form the attenuation pattern of non-uniformity along the column axis. The attenuation pattern of non-uniformity along the column axis is represented as a one-dimensional data sequence, where the x-axis represents the axial height and the y-axis represents the non-uniformity of the passive constraint stress along the circumferential direction. The attenuation pattern describes the trend of the circumferential non-uniformity of the passive constraint stress gradually decreasing along the axial direction from the end of the core concrete column to the middle of the core concrete column.

[0064] In the specific implementation step S5, the gradient field is obtained by first-order difference calculation of the attenuation mode of non-uniformity along the column axis obtained in step S4. The attenuation mode of non-uniformity along the column axis is input from step S4, and the data structure is a one-dimensional data sequence. The one-dimensional data sequence contains multiple data pairs arranged in ascending order of axial height value. Each data pair contains the axial height value and the non-uniformity of the passive constraint stress distribution along the circumferential direction. The unit of the axial height value is millimeters, and the non-uniformity of the passive constraint stress distribution along the circumferential direction is a dimensionless ratio. The first-order difference is calculated as: Gi = (Ui - U{i-1}) / |Hi - H{i-1}|; where Gi represents the gradient value at the i-th monitoring section position, Ui represents the non-uniformity of the passive constraint stress distribution along the circumferential direction for the i-th data pair, U{i-1} represents the non-uniformity of the passive constraint stress distribution along the circumferential direction for the (i-1)-th data pair, Hi represents the axial height value of the i-th data pair, H{i-1} represents the axial height value of the (i-1)-th data pair, and |Hi - H{i-1}| represents the absolute value of the difference between the axial height values ​​of the i-th and (i-1)-th data pairs. The gradient value is expressed in millimeters as the change in non-uniformity. For the first data pair in the non-uniformity attenuation mode along the column axis, since the preceding data pair does not exist, the gradient value at the location of the first data pair is assigned the gradient value of the second adjacent monitoring section interval adjacent to the first data pair, thus maintaining data continuity of the gradient field at the axial starting point. The gradient values ​​at each monitoring section location are arranged in ascending order of their corresponding axial height values ​​to form a gradient field, which is a one-dimensional data sequence with axial height values ​​as the abscissa and gradient values ​​as the ordinate.

[0065] Before obtaining the divergence value by performing first-order difference on the gradient values ​​of adjacent monitoring sections in the gradient field, cubic spline interpolation is performed on the gradient values ​​at each monitoring section location in the gradient field to obtain a refined gradient field. The input of cubic spline interpolation is multiple interpolation nodes arranged in the gradient field according to their axial height values. Each interpolation node contains the axial height value and the gradient value at that axial height value. The output of cubic spline interpolation is the refined gradient field obtained by inserting multiple interpolation points between the original axial height values ​​of each monitoring section. The boundary conditions of cubic spline interpolation are set to natural boundary conditions. In this scenario, the natural boundary conditions mean that at the beginning of the gradient field's axial direction, the second derivative of the gradient value with respect to the axial height value is zero, and at the end of the gradient field's axial direction, the second derivative of the gradient value with respect to the axial height value is also zero. The setting of natural boundary conditions ensures that cubic spline interpolation does not introduce additional curvature constraints at both ends of the gradient field, and the interpolation curve extends naturally at both ends. The axial spacing between adjacent interpolation points in the encrypted gradient field is determined by combining the axial spacing of the original monitoring sections and the desired encryption density. For example, the axial spacing between adjacent interpolation points in the encrypted gradient field is set to 1 / 5 of the axial spacing of the original monitoring sections. When the axial spacing of the original monitoring sections is, for example, 25 mm, the axial spacing between adjacent interpolation points in the encrypted gradient field is, for example, 5 mm. The total number of interpolation points in the encrypted gradient field is determined by the number of original monitoring sections and the encryption density. The total number of interpolation points is equal to the difference between the number of original monitoring sections minus one, multiplied by the encryption density multiple, and then added by one. The piecewise construction method of cubic spline interpolation is as follows: Between every two adjacent interpolation nodes, a cubic polynomial is constructed. The function value of the cubic polynomial at the left endpoint of this adjacent interpolation node interval is equal to the gradient value at the left endpoint. The function value of the cubic polynomial at the right endpoint of this adjacent interpolation node interval is equal to the gradient value at the right endpoint. The first derivative of the cubic polynomial at the left endpoint of this adjacent interpolation node interval is equal to the first derivative of the cubic polynomial at the left endpoint of the adjacent interval to the left. The first derivative of the cubic polynomial at the right endpoint of this adjacent interpolation node interval is equal to the first derivative of the cubic polynomial at the right endpoint of the adjacent interval to the right. The coefficients of the cubic polynomials in all adjacent interpolation node intervals are determined by solving a tridiagonal linear equation system including boundary conditions. After solving, the cubic polynomial in each interpolation node interval is obtained. Within the interpolation node interval, the gradient value at the interpolation point is obtained by sampling at equal intervals according to the axial spacing between adjacent interpolation points in the refined gradient field.

[0066] The first-order difference is performed on the gradient values ​​at adjacent interpolation points in the encrypted gradient field to obtain the divergence value at each interpolation point. In this scenario, the divergence value is defined as a measure of the rate of change of the gradient value along the axial direction in the gradient field. A negative divergence value indicates that the gradient value decreases along the axial direction, while a positive divergence value indicates that the gradient value increases along the axial direction. The first-order difference is calculated as: Dj = (Gj - G{j-1}) / |Hj - H{j-1}|; where Dj represents the divergence value at the j-th interpolation point, Gj represents the gradient value at the j-th interpolation point, G{j-1} represents the gradient value at the (j-1)-th interpolation point, Hj represents the axial height value at the j-th interpolation point, H{j-1} represents the axial height value at the (j-1)-th interpolation point, and |Hj - H{j-1}| represents the absolute value of the difference between the axial height values ​​at the j-th and (j-1)-th interpolation points. The unit of the divergence value is the change in gradient value per millimeter. For the first interpolation point in the encrypted gradient field, since the preceding interpolation point does not exist, the divergence value at the location of the first interpolation point is assigned the divergence value of the interval between the second and third adjacent interpolation points, thus maintaining data continuity of the gradient divergence distribution at the axial starting point. The divergence values ​​at each calculated interpolation point are arranged in ascending order of their corresponding axial height values ​​to obtain the gradient divergence distribution, which is a one-dimensional data sequence with axial height as the x-axis and divergence as the y-axis.

[0067] In a gradient divergence distribution, the zero-value crossing section corresponding to the change from negative to positive divergence values ​​is identified, and this zero-value crossing section is defined as the convergent-divergent fractal boundary. The identification method is as follows: starting from the second divergence value in the gradient divergence distribution, the sign of each divergence value is compared sequentially with the sign of the previous divergence value. When the sign of the previous divergence value is negative and the sign of the next divergence value is positive, a zero-value crossing section exists within the axial interval between the two adjacent interpolation points. The zero-value crossing section is a plane perpendicular to the column axis, passing through the position where the divergence value becomes zero when the divergence value changes from negative to positive within the axial interval between the two adjacent interpolation points. The precise location of the zero-value crossing section is determined by linear interpolation. The linear interpolation is calculated as follows: Hzero = H{k-1} + [|D{k-1}| / (|D{k-1}| + |Dk|)] × |Hk - H{k-1}|; where Hzero represents the axial height of the zero-value crossing section, H{k-1} represents the axial height of the previous interpolation point among two adjacent interpolation points, Hk represents the axial height of the next interpolation point among two adjacent interpolation points, D{k-1} represents the divergence value of the previous interpolation point among two adjacent interpolation points, Dk represents the divergence value of the next interpolation point among two adjacent interpolation points, |D{k-1}| represents the absolute value of the divergence value of the previous interpolation point among two adjacent interpolation points, |Dk| represents the absolute value of the divergence value of the next interpolation point among two adjacent interpolation points, and |Hk - H{k-1}| represents the axial distance between two adjacent interpolation points. When multiple divergence values ​​in the gradient divergence distribution are identified as changing from negative to positive, the zero-value crossing section with the smallest axial height is selected as the convergent-divergent fractal boundary. This zero-value crossing section represents the axial boundary where the constraint stress diffusion mode of the ultra-high performance concrete sleeve on the core concrete column transitions from a negative divergence interval dominated by end effects to a positive divergence interval dominated by uniform constraint in the middle. The determined axial height values ​​of the convergent-divergent fractal boundary are stored and used to subsequently construct the distribution map of the effective constraint region of the ultra-high performance concrete sleeve on the core concrete column.

[0068] In the specific implementation step S6, the convergent-divergent fractal boundary determined in step S5 is used as the boundary criterion. The axial height value of the convergent-divergent fractal boundary is stored in step S5. The axial height value of the convergent-divergent fractal boundary represents the axial boundary position where the constraint stress diffusion mode of the ultra-high performance concrete sleeve on the core concrete column changes from the negative divergence interval dominated by end effects to the positive divergence interval dominated by uniform constraint in the middle. Taking the position of the convergent-divergent fractal boundary on the column axis as the boundary, the interface between the ultra-high performance concrete sleeve and the core concrete column is divided into an effective constraint zone and an ineffective constraint zone along the column axis. The division method is as follows: The interface region with an axial height value less than the axial height value of the convergent-divergent fractal boundary is defined as the non-effective constraint region. The non-effective constraint region is close to the end of the core concrete column. In the non-effective constraint region, the passive constraint stress distribution provided by the ultra-high performance concrete sleeve to the core concrete column is affected by the end stress concentration and interface friction effect. The non-uniformity of the passive constraint stress distribution along the circumferential direction decreases rapidly along the axial direction. The interface region with an axial height value greater than or equal to the axial height value of the convergent-divergent fractal boundary is defined as the effective constraint region. The effective constraint region extends from the convergent-divergent fractal boundary to the middle of the core concrete column. In the effective constraint region, the passive constraint stress provided by the ultra-high performance concrete sleeve to the core concrete column tends to be uniformly distributed. The non-uniformity of the passive constraint stress distribution along the circumferential direction decreases to a lower value range along the axial direction.

[0069] Obtain the contour maps of the passive constraint stress distribution along the circumference and axial direction of the column generated in step S3. These contour maps contain two-dimensional spatial grid data with the circumferential angle as the horizontal axis and the axial height as the vertical axis. Each grid node in the two-dimensional spatial grid data has a passive constraint stress value. Perform an overlay annotation operation on the contour maps of the passive constraint stress distribution along the circumference and axial direction of the column. The overlay annotation operation includes annotating the location of the convergent-divergent fractal boundary and the extent of the effective constraint region. The location of the convergent-divergent fractal boundary is marked as follows: On the vertical axis (axial height axis) of the contour map showing the distribution of passive constraint stress along the column's circumference and axial direction, at the position corresponding to the axial height value of the convergent-divergent fractal boundary, draw a horizontal solid line parallel to the horizontal axis (circumferential angle axis). This horizontal solid line extends from 0 degrees to 360 degrees. The color of the horizontal solid line is set to a color with high contrast to the background color of the contour map showing the distribution of passive constraint stress along the column's circumference and axial direction, such as black. The line width of the horizontal solid line is set to a value greater than the width of the grid lines in the contour map showing the distribution of passive constraint stress along the column's circumference and axial direction, for example, three times the width of the grid lines. A text label is attached next to the horizontal solid line, stating that it indicates the convergent-divergent fractal boundary. The font size and color of the text label are the same as the color of the horizontal solid line. The text label is located outside the vertical axis at the intersection of the horizontal solid line and the vertical axis, and the text label does not obscure the stress data in the contour map showing the distribution of passive constraint stress along the column's circumference and axial direction.

[0070] The effective constraint zone is marked as follows: The area from the convergence-divergence fractal boundary to the axial height of the top surface of the core concrete column in the cloud map showing the passive constraint stress distribution along the column's circumference and axial direction is covered and marked with a semi-transparent color block. The coverage of the semi-transparent color block extends from 0 degrees to 360 degrees in the circumferential angle dimension and from the convergence-divergence fractal boundary to the top surface of the core concrete column in the axial height dimension. The color of the semi-transparent color block is a single hue different from the color spectrum of the passive constraint stress distribution along the column's circumference and axial direction, such as light green. The transparency of the semi-transparent color block is set to a value that allows the stress color in the cloud map showing the passive constraint stress distribution along the column's circumference and axial direction to still be identifiable under the coverage of the semi-transparent color block, for example, a transparency of 40%. A text label is attached at the center of the area covered by the semi-transparent color block, indicating the effective constraint zone. The font color of the text label contrasts with the color of the semi-transparent color block; when the color of the semi-transparent color block is light green, the font color of the text label is dark green. In the contour maps showing the distribution of passive constraint stress along the column's circumference and axial direction, regions where the axial height value is lower than the axial height value of the convergent-divergent fractal boundary are designated as ineffective constraint areas. These ineffective constraint areas are visually distinguished from effective constraint areas by a semi-transparent color block overlay, contrasting with the uncovered original contour map representation of ineffective constraint areas. Through this semi-transparent color block overlay, the distribution characteristics of passive constraint stress along the column's circumference and axial direction in the contour maps, along with the spatial extent of the effective constraint areas, are simultaneously presented in the same map.

[0071] After completing the location annotation of the convergent-divergent fractal boundary and the extent annotation of the effective constraint zone, a distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column is generated. This distribution map is a composite image containing three pieces of information: first, a cloud map showing the distribution of passive constraint stress along the column's circumference and axial direction, represented by varying color depths at the interface between the ultra-high performance concrete sleeve and the core concrete column; second, the location of the convergent-divergent fractal boundary, indicated by horizontal solid lines and text labels; and third, the extent of the effective constraint zone, indicated by semi-transparent color blocks and text labels. The output format of the distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column is a digital image file, with the resolution matching that of the cloud map showing the distribution of passive constraint stress along the column's circumference and axial direction. The output of the distribution map of the effective confinement area of ​​the core concrete column by the ultra-high performance concrete sleeve includes image files and corresponding map description text. The map description text records the axial height value of the convergent-divergent fractal boundary, the axial height range of the effective confinement area, the axial height range of the ineffective confinement area, and the generation date. The axial height range of the effective confinement area extends from the axial height value of the convergent-divergent fractal boundary to the axial height value of the top surface of the core concrete column, while the axial height range of the ineffective confinement area extends from the axial height value of the bottom surface of the core concrete column to the axial height value of the convergent-divergent fractal boundary.

[0072] Example 2: Figure 2 A schematic diagram of a passive restraint stress testing system for UHPC-confined concrete columns is provided according to the present invention. The system includes the following modules:

[0073] The specimen fabrication module is used to fabricate concrete column specimens containing ultra-high performance concrete sleeves, and thin-film pressure sensors are fully arranged at the interface between the ultra-high performance concrete sleeve and the core concrete column.

[0074] The loading acquisition module is used to apply axial load to the concrete column specimen and simultaneously acquire the interface pressure signal output by the membrane pressure sensor;

[0075] The cloud map generation module is used to generate cloud maps of the passive constraint stress distribution along the circumferential and axial directions of the column based on the interface pressure signal.

[0076] The feature extraction module is used to select multiple monitoring sections along the column axis, and extract the non-uniformity of the passive constraint stress distribution along the circumferential direction on each monitoring section based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis.

[0077] The boundary identification module is used to obtain the gradient field of the decay mode of non-uniformity along the column axis, obtain the gradient divergence distribution by calculating the divergence of the gradient field, and determine the zero-value crossing section of the gradient divergence from the negative value region to the positive value region as the convergent-divergent fractal boundary.

[0078] The map construction module is used to construct a distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column based on the convergent-divergent fractal boundary.

[0079] The calculations involved in the embodiments are all dimensionless numerical calculations, and the preset parameters and thresholds in the calculations are set by those skilled in the art according to the actual situation.

[0080] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0081] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and inventive constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0082] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0083] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0084] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0085] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for testing the passive confinement stress of a UHPC-confined concrete column, characterized in that, Includes the following steps: S1: Fabricate a concrete column specimen containing an ultra-high performance concrete sleeve, and fully insert thin-film pressure sensors at the interface between the ultra-high performance concrete sleeve and the core concrete column. S2: Apply axial load to the concrete column specimen and simultaneously acquire the interface pressure signal output by the membrane pressure sensor; S3: Generate contour maps of the passive constraint stress distribution along the circumferential and axial directions of the column based on the interface pressure signal; S4: Select multiple monitoring sections along the column axis, and extract the non-uniformity of passive constraint stress distribution along the circumferential direction on each monitoring section based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis. S5: Calculate the gradient field for the decay mode of non-uniformity along the column axis, obtain the gradient divergence distribution by calculating the divergence of the gradient field, and determine the zero-value crossing section of the gradient divergence from the negative value region to the positive value region as the convergent-divergent fractal boundary. S6: Based on convergent-divergent fractal boundaries, construct the distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column.

2. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 1, characterized in that, Concrete column specimens containing ultra-high performance concrete sleeves were fabricated. Thin-film pressure sensors were fully embedded at the interface between the ultra-high performance concrete sleeve and the core concrete column, including: First, a core concrete column is poured and cured to the predetermined age. Then, a thin-film pressure sensor array that can sense two-dimensional stress state is fully covered on the outer surface of the core concrete column. Next, a formwork is erected around the core concrete column covered with the thin-film pressure sensor array and ultra-high performance concrete is poured. After hardening, a concrete column specimen is formed with thin-film pressure sensors fully covering the interface between the ultra-high performance concrete sleeve and the core concrete column.

3. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 1, characterized in that, An axial load was applied to the concrete column specimen, and the interfacial pressure signal output by the membrane pressure sensor was acquired simultaneously, including: The concrete column specimen was placed on a compression testing machine. The leads of the thin-film pressure sensor array were connected to a multi-channel data acquisition instrument. The compression testing machine was started to apply an axial monotonic static load to the concrete column specimen. During the loading process, the interface pressure signals of all sensing units in the thin-film pressure sensor array were synchronously and continuously acquired by the multi-channel data acquisition instrument at a preset frequency until the concrete column specimen entered the descending segment of the load-displacement curve and then the loading and acquisition were stopped.

4. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 1, characterized in that, Based on the interface pressure signal, contour maps of the passive constraint stress distribution along the circumferential and axial directions of the column are generated, including: The interface pressure signal collected by each sensing unit is converted into the passive constraint stress value at the location of the sensing unit. Based on the spatial coordinates of the sensing units in the thin-film pressure sensor array at the interface between the ultra-high performance concrete sleeve and the core concrete column, the passive constraint stress values ​​at the locations of all sensing units are mapped to a two-dimensional spatial grid. The passive constraint stress values ​​on the two-dimensional spatial grid are spatially interpolated to generate a cloud map of the passive constraint stress distribution along the circumference and axial direction of the column.

5. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 1, characterized in that, Multiple monitoring sections were selected along the column axis. Based on the cloud map, the non-uniformity of the passive constraint stress distribution along the circumferential direction on each monitoring section, as well as the attenuation mode of the non-uniformity along the column axis, were extracted, including: In the cloud map of the passive constraint stress distribution along the circumferential and axial directions of the column, multiple monitoring sections are selected at equal intervals along the column axis. The sequence of passive constraint stress distribution along the circumferential direction on each monitoring section is extracted. The ratio of the standard deviation to the mean of the passive constraint stress distribution sequence along the circumferential direction on each monitoring section is calculated as the non-uniformity. The non-uniformities of all monitoring sections are arranged sequentially according to the axial position of the column to obtain the attenuation mode of non-uniformity along the column axis.

6. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 5, characterized in that, Before calculating the ratio of standard deviation to mean as the non-uniformity, outlier data points in the sequence of passive constraint stress distributed along the circumferential direction that deviate from the mean by more than a preset deviation threshold are removed. The ratio of standard deviation to mean of the sequence of passive constraint stress distributed along the circumferential direction after removing outlier data points is then used as the non-uniformity.

7. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 1, characterized in that, The gradient field is obtained by calculating the attenuation mode of the inhomogeneity along the column axis. The gradient divergence distribution is obtained by calculating the divergence of the gradient field. The zero-value crossing section of the gradient divergence from the negative region to the positive region is determined as the convergent-divergent fractal boundary, including: In the attenuation mode of non-uniformity along the column axis, the non-uniformity of adjacent monitoring sections is subjected to first-order difference to obtain the gradient value at each monitoring section location. The gradient values ​​at all monitoring section locations are arranged sequentially according to the column axis to form a gradient field. The gradient values ​​of adjacent monitoring sections in the gradient field are subjected to first-order difference to obtain the divergence value at each monitoring section location. The divergence values ​​at all monitoring section locations are arranged sequentially according to the column axis to obtain the gradient divergence distribution. In the gradient divergence distribution, the zero-value crossing section corresponding to the divergence value changing from negative to positive is identified, and the zero-value crossing section is determined as the convergence-divergence fractal boundary.

8. The passive restraint stress testing method for a UHPC-confined concrete column according to claim 7, characterized in that, Before performing first-order difference on the gradient values ​​of adjacent monitoring sections in the gradient field, cubic spline interpolation is performed on the gradient values ​​at each monitoring section location in the gradient field to obtain the densified gradient field. First-order difference is performed on the gradient values ​​at adjacent interpolation points in the densified gradient field to obtain the divergence value at each interpolation point location. The divergence values ​​at all interpolation point locations are arranged sequentially according to the axial position of the column to obtain the gradient divergence distribution.

9. The passive restraint stress testing method for UHPC-confined concrete columns according to claim 1, characterized in that, Based on convergent-divergent fractal boundaries, a distribution map of the effective confinement region of the ultra-high performance concrete sleeve for the core concrete column is constructed, including: Using the position of the convergent-divergent fractal boundary along the column axis as the dividing line, the interface between the ultra-high performance concrete sleeve and the core concrete column is divided into an effective constraint zone and an ineffective constraint zone along the column axis. The position of the convergent-divergent fractal boundary and the range of the effective constraint zone are superimposed on the cloud map of the passive constraint stress distribution along the column circumference and axis to generate a distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column.

10. A passive restraint stress testing system for UHPC-confined concrete columns, used to implement the passive restraint stress testing method for UHPC-confined concrete columns as described in any one of claims 1-9, characterized in that, Includes the following modules: The specimen fabrication module is used to fabricate concrete column specimens containing ultra-high performance concrete sleeves, and thin-film pressure sensors are fully arranged at the interface between the ultra-high performance concrete sleeve and the core concrete column. The loading acquisition module is used to apply axial load to the concrete column specimen and simultaneously acquire the interface pressure signal output by the membrane pressure sensor; The cloud map generation module is used to generate cloud maps of the passive constraint stress distribution along the circumferential and axial directions of the column based on the interface pressure signal. The feature extraction module is used to select multiple monitoring sections along the column axis, and extract the non-uniformity of the passive constraint stress distribution along the circumferential direction on each monitoring section based on the cloud map, as well as the attenuation mode of the non-uniformity along the column axis. The boundary identification module is used to obtain the gradient field of the decay mode of non-uniformity along the column axis, obtain the gradient divergence distribution by calculating the divergence of the gradient field, and determine the zero-value crossing section of the gradient divergence from the negative value region to the positive value region as the convergent-divergent fractal boundary. The map construction module is used to construct a distribution map of the effective constraint area of ​​the ultra-high performance concrete sleeve on the core concrete column based on the convergent-divergent fractal boundary.

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