Unloaded rock mass critical instability time prediction method and device based on Zhairai method
By acquiring monitoring data on rock mass creep deformation using the Saito method and calculating the creep instability time under unloading conditions, the problem of predicting creep in unloaded rock masses was solved, enabling accurate prediction of creep deformation in unloaded rock masses and ensuring the stability of the project.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGZHOU URBAN PLANNING & DESIGN SURVEY RES INST
- Filing Date
- 2025-12-10
- Publication Date
- 2026-05-08
AI Technical Summary
Existing technologies cannot accurately predict the time of rock mass creep instability and failure under unloading conditions, which leads to creep deformation risks in underground engineering and slope engineering, affecting the stability of the project.
Using the Saito method, by acquiring data on the monitoring range and accelerated creep stage of rock mass creep deformation, the time of rock mass creep instability failure, the first difference, and the second difference are calculated, a numerical table is established, and prediction is made in combination with field monitoring data.
It enables effective prediction of creep deformation and failure of unloaded rock masses, reduces the consequences of instability and failure, and ensures the smooth construction of underground engineering and slope engineering.
Smart Images
Figure CN121997532A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of data processing technology, and in particular to a method and apparatus for predicting the critical instability time of unloaded rock masses based on the Saito method. Background Technology
[0002] After excavation and unloading of underground engineering projects and slopes, the rock mass does not immediately become unstable and fail, exhibiting creep deformation. Creep deformation is one of the important mechanical properties of unloaded rock masses, so all excavation and unloading projects are closely related to the creep characteristics of unloaded rock masses. Currently, there are a large number of underground engineering projects such as rail transit, highway tunnels, and deep-sea tunnels, as well as artificially excavated slopes. After excavation and unloading, the rock mass does not immediately become unstable and fail. Over time, creep deformation instability or collapse may occur, with the surrounding rock exhibiting a clear characteristic of slow deformation over time. This is especially true for deeply buried underground caverns, where creep deformation is very pronounced, and the amount of deformation is much greater than the instantaneous deformation. The stability of unloaded rock masses in underground engineering projects and excavated slopes is crucial to the overall stability of the project; therefore, predicting the time point of creep instability and failure of rock masses under unloading conditions is also very important.
[0003] Currently, there is a wealth of research on prediction and forecasting techniques for unloaded rock mass landslides, including the Saito method, grey prediction model, Fukuzono model, Verhulst model, BP neural network model, fuzzy analysis method, and collaborative prediction model. These theories can accurately predict various types of landslides, but their drawback is that they are not applicable to the prediction of creep instability and failure of rock masses under unloading conditions. While there is extensive research both domestically and internationally on the deformation mechanisms of unloaded rock masses, there are relatively few techniques for predicting creep in unloaded rock masses. Therefore, there is an urgent need for a simple technique to predict creep instability and failure of unloaded rock masses in underground engineering projects, slopes, and other applications. Summary of the Invention
[0004] This application provides a method and apparatus for predicting the critical instability time of unloaded rock mass based on the Saito method. It can obtain the creep instability failure time, first difference, and second difference of rock mass under excavation unloading conditions based on the monitoring range of rock mass creep deformation and accelerated creep stage data, and further obtain a numerical table. Thus, it is possible to compare the current field monitoring data with the obtained numerical table to obtain the field instability failure time. It can effectively predict the creep deformation failure of unloaded rock mass in underground engineering and slopes, indirectly reducing the consequences of unloaded rock mass instability failure and ensuring the smooth construction of the entire underground engineering and excavation slope engineering.
[0005] In a first aspect, embodiments of this application provide a method for predicting the critical instability time of unloaded rock masses based on the Saito method, the method comprising: Obtain the monitoring range of rock mass creep deformation and obtain data on the accelerated creep stage; Based on the data processing of the accelerated creep stage, the time of rock mass creep instability failure, the first difference, and the second difference were obtained under the excavation unloading conditions. Numerical tables were obtained by processing the first difference, the second difference, and the time of rock mass creep instability and failure; Obtain on-site monitoring data, and determine the on-site instability and failure time based on the on-site monitoring data and numerical tables.
[0006] Furthermore, the monitoring scope for rock mass creep deformation includes: potential sliding zones, main sliding sections, trailing edge tensile cracks, slope crest platforms, and slope toes.
[0007] Furthermore, the accelerated creep stage data includes: initial time point, first time point, second time point, change time, and instantaneous deformation rate.
[0008] Furthermore, the method also includes: The displacement-time curve was obtained based on the on-site monitoring data; The initial moment of entering the acceleration phase is determined based on the displacement-time curve.
[0009] Furthermore, the method also includes: Based on the on-site monitoring data, obtain the displacement change of each monitoring point and the total number of monitoring points during the stable deformation stage. The instantaneous deformation rate is calculated based on the displacement change of each monitoring point during the stable deformation stage and the total number of monitoring points.
[0010] Furthermore, the method also includes: By performing two derivatives of the Saito formula, the creep deformation acceleration under unloaded stress conditions was obtained; The creep deformation acceleration under unloaded stress conditions is obtained by multiplying the creep deformation acceleration under preset constant and unloaded stress conditions. By integrating the creep deformation acceleration under unloading stress conditions, the relationship between the creep deformation rate and failure time of the rock mass under unloading conditions is obtained.
[0011] Furthermore, the method also includes: Based on the relationship between the rock mass creep deformation rate and failure time at the first time point, the second time point, and the unloading condition, the following calculations were performed: the deformation amount from the initial time point of entering the accelerated creep deformation stage to the first time point after a change in time; the deformation amount from the first time point to the second time point after a change in time; and the time from the initial time point of entering the accelerated creep deformation stage to the rock mass creep instability failure under the unloading condition.
[0012] Secondly, embodiments of this application provide a device for predicting the critical instability time of unloaded rock mass based on the Saito method, the device comprising: The acquisition module is used to acquire the monitoring range of rock mass creep deformation and obtain data on the accelerated creep stage; The calculation module is used to obtain the time of rock mass creep instability failure, the first difference, and the second difference under excavation unloading conditions based on the data processing of the accelerated creep stage. The processing module is used to process the first difference, the second difference, and the time of rock mass creep instability and failure to obtain a numerical table; The prediction module is used to acquire on-site monitoring data and determine the on-site instability and failure time based on the on-site monitoring data and numerical tables.
[0013] Thirdly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the steps of a method for predicting the critical instability time of unloaded rock mass based on the Saito method as described in any of the above embodiments.
[0014] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of a method for predicting the critical instability time of unloaded rock mass based on the Saito method as described in any of the above embodiments.
[0015] In summary, compared with the prior art, the beneficial effects of the technical solution provided in this application include at least the following: This application provides a method for predicting the critical instability time of unloaded rock mass based on the Saito method. This method can obtain the creep instability failure time, first difference, and second difference of rock mass under excavation unloading conditions based on the monitoring range of rock mass creep deformation and accelerated creep stage data. Furthermore, it generates a numerical table, allowing for comparison between current field monitoring data and the obtained numerical table to determine the on-site instability failure time. This method effectively predicts creep deformation failure of unloaded rock masses in underground engineering and slope engineering, indirectly reducing the consequences of unloaded rock mass instability failure and ensuring the smooth construction of the entire underground engineering and excavation slope engineering. Attached Figure Description
[0016] Figure 1 A flowchart illustrating a method for predicting the critical instability time of unloaded rock mass based on the Saito method, provided as an exemplary embodiment of this application.
[0017] Figure 2 Provided as an exemplary embodiment of this application and Graph of the function.
[0018] Figure 3 This is a structural diagram of a device for predicting the critical instability time of unloaded rock mass based on the Saito method, provided as an exemplary embodiment of this application. Detailed Implementation
[0019] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.
[0020] Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this application.
[0021] Please see Figure 1 This application provides a method for predicting the critical instability time of unloaded rock masses based on the Saito method. The method specifically includes the following steps: Step S1: Obtain the monitoring range of rock mass creep deformation to obtain data on the accelerated creep stage.
[0022] In some embodiments, the monitoring range for rock mass creep deformation includes: potential slip zone, main slip section, trailing edge tensile crack, slope crest platform, and slope toe.
[0023] In some embodiments, the accelerated creep stage data includes: initial time point, first time point, second time point, change time, and instantaneous deformation rate.
[0024] The monitoring scope and monitoring points for rock mass creep deformation are deployed by specialized personnel, following the principles of prioritizing key areas, overall control, three-dimensional monitoring, and dynamic optimization. The system focuses on covering critical areas such as potential slip zones, main slip sections, rear-edge tensile cracks, slope crest platforms, and slope toes. Through this systematic deployment, high-precision monitoring of rock mass creep deformation can be achieved, enabling real-time perception of rock mass deformation trends and stability. This provides reliable data support for early identification of rock mass deformation and warning of potential risks, further supporting timely engineering decisions and the formulation of prevention and control measures, effectively ensuring the safety of underground engineering construction and the stability of the geological environment in the construction area.
[0025] Step S2: Based on the data processing of the accelerated creep stage, the time of rock mass creep instability failure, the first difference, and the second difference are obtained under the excavation unloading conditions.
[0026] In particular, this application addresses the issue that the early warning method for the instability and failure time of slopes during the accelerated creep deformation stage proposed by scholar Saito is not applicable to creep deformation early warning in underground engineering and slopes under excavation and unloading conditions. This method is improved by using the following formula to predict the creep instability and failure time of rock mass under excavation and unloading conditions. :
[0027] in, At the initial time point, As the first time point, For the second time point, For the time of change; The moment when the accelerated creep deformation stage begins After Arrival Time The amount of deformation over time; For time points After Arrival Time The amount of deformation over time; The first difference is, that is to The slope of the secant line for the displacement change over time and the initial time point of the accelerated creep phase. Instantaneous deformation rate The difference; The second difference is, that is to The slope of the secant line for the displacement change over time and the initial time point of the accelerated creep phase. Instantaneous deformation rate The difference; The time point for entering the accelerated creep deformation stage Time to rock mass creep instability and failure under unloading conditions.
[0028] Step S3: Obtain a numerical table based on the first difference, the second difference, and the time of rock mass creep instability and failure.
[0029] In some embodiments, the method further includes: Based on the on-site monitoring data, obtain the displacement change of each monitoring point and the total number of monitoring points during the stable deformation stage. The instantaneous deformation rate is calculated based on the displacement change of each monitoring point during the stable deformation stage and the total number of monitoring points.
[0030] When the displacement-time curve is stable and the acceleration fluctuation is minimal, this stage can be determined as the stable deformation stage. During the stable deformation stage, the average displacement change per unit time can be calculated using data such as the displacement change at each monitoring point over the time elapsed and the total number of monitoring points. This average displacement change is the instantaneous deformation rate, which can be calculated using the following formula:
[0031] in, The time elapsed during the stable deformation stage of the monitoring point The displacement change is denoted by n, where n is the total number of monitoring points. The time period for this change can be any time interval, selected according to the user's needs.
[0032] In some embodiments, the method further includes: By performing two derivatives of the Saito formula, the creep deformation acceleration under unloaded stress conditions was obtained; The creep deformation acceleration under unloaded stress conditions is obtained by multiplying the creep deformation acceleration under preset constant and unloaded stress conditions. By integrating the creep deformation acceleration under unloading stress conditions, the relationship between the creep deformation rate and failure time of the rock mass under unloading conditions is obtained.
[0033] Among them, Saito method for determining the in-situ instability and failure time of slope creep. The determination mainly focuses on non-unloading stress conditions, and is insufficient for early warning of instability and failure time of underground engineering and slopes under excavation unloading conditions. Considering that the creep deformation rate of rock mass under unloading stress conditions is faster than under loading stress conditions, and that there is an iso-accelerated creep stage, there are... ,in, , These represent the creep deformation acceleration under unloaded stress conditions and the creep deformation acceleration under unloaded stress conditions, respectively. A constant ( ).
[0034] To simplify the improvement of Saito's formula, the deformation acceleration is expressed in terms of creep change, i.e. ;in, , These represent the creep deformation acceleration under unloaded stress conditions and the creep deformation acceleration under unloaded stress conditions, respectively.
[0035] Saito believes that the failure time of creeping soil is related to its strain rate, and the instability failure time can be predicted by the following formula:
[0036] in, To accelerate the initial time point for creep deformation monitoring; To observe the amount of deformation Time; Instability and failure time; It is a constant.
[0037] Taking the derivative of Saito's formula twice yields the following:
[0038] Where b is a constant.
[0039] but:
[0040] make Integrating both sides of the above equation, we get:
[0041] Among them, when hour, ,and .
[0042] Then the relationship between the rock mass creep deformation rate and failure time under unloading conditions is obtained:
[0043] Where c is a constant.
[0044] In some embodiments, the method further includes: Based on the relationship between the rock mass creep deformation rate and failure time at the first time point, the second time point, and the unloading condition, the following calculations were performed: the deformation amount from the initial time point of entering the accelerated creep deformation stage to the first time point after a change in time; the deformation amount from the first time point to the second time point after a change in time; and the time from the initial time point of entering the accelerated creep deformation stage to the rock mass creep instability failure under the unloading condition.
[0045] Among them, when When we get the following formula:
[0046] when When we get the following formula:
[0047] make , and ,from arrive Time period The change in internal displacement is ,from arrive Time period The change in internal displacement is ,but , Substituting the two equations above and performing division, we get:
[0048] in, The initial time point for entering the accelerated creep deformation stage After arrive The amount of deformation over time; for After arrive The amount of deformation over time; To enter the accelerated creep deformation stage Time to rock mass creep instability and failure under unloading conditions.
[0049] For ease of description, let ;in, for to The slope of the secant line for the displacement change over time and the starting point of the accelerated creep stage Instantaneous deformation rate The difference; for to The slope of the secant line for the displacement change over time and the starting point of the accelerated creep stage Instantaneous deformation rate The difference.
[0050] In some embodiments, the method further includes: The displacement-time curve was obtained based on the on-site monitoring data; The initial moment of entering the acceleration phase is determined based on the displacement-time curve.
[0051] This system allows for the acquisition of on-site monitoring data based on user needs, generating a displacement-time curve. The point where the slope of the displacement-time curve abnormally increases is the initial point of entry into the acceleration phase. Through actual on-site monitoring data and precise graphical analysis, the initial point of entry can be quickly determined, avoiding the waste of resources from comparing multiple data sets and improving data processing efficiency.
[0052] In some embodiments, data processing software is further used to draw... - The function graph, i.e., the displacement-time curve; list each one. Values and their corresponding The values are used to obtain a numerical table.
[0053] Among them, the improved Saito formula can quickly predict the time of instability and failure under accelerated creep deformation and failure modes of unloaded rock masses such as underground engineering and excavated slopes, which greatly improves the prediction efficiency and enriches the prediction methods of unloaded rock mass creep.
[0054] Step S4: Obtain on-site monitoring data and determine the on-site instability and failure time based on the on-site monitoring data and numerical table.
[0055] Furthermore, based on on-site monitoring data and numerical tables, during the accelerated creep stage, the displacement change over two equal time intervals can be used to determine the on-site instability and failure time.
[0056] In some embodiments, and The graph of the function is as follows Figure 2 As shown in Table 1 below, the numerical values are presented in the table.
[0057] Table 1
[0058] In some embodiments, the specific calculation process can be as follows: For an underground cavern under accelerated failure modes such as creep, based on field monitoring data, the deformation rate during the steady creep stage is determined to be 0.5 mm / d, the time to enter the accelerated creep stage is 120 days, the average deformation rate during the first 10 days of the accelerated creep stage is 0.85 mm / d, and the deformation rate during the second 10 days is 1.68 mm / d; then... It equals 3.37. Looking up the values in the table above, we can see that... If it equals 8.8, then This equates to 88 days, meaning that after entering the accelerated creep phase, instability and failure occur after 88 days.
[0059] The above embodiments provide a method for predicting the critical instability time of unloaded rock mass based on the Saito method. This method can obtain the creep instability failure time, first difference, and second difference of rock mass under excavation unloading conditions based on the monitoring range of rock mass creep deformation and the data of accelerated creep stage. It further obtains a numerical table, which can be compared with the current field monitoring data and the obtained numerical table to obtain the field instability failure time. This method can effectively predict the creep deformation failure of unloaded rock mass in underground engineering and slopes, indirectly reducing the consequences of unloaded rock mass instability failure and ensuring the smooth construction of the entire underground engineering and excavation slope engineering.
[0060] Please see Figure 3 Another embodiment of this application provides a device for predicting the critical instability time of unloaded rock mass based on the Saito method. The device includes: The acquisition module 101 is used to acquire the monitoring range of rock mass creep deformation and obtain data of the accelerated creep stage.
[0061] The calculation module 102 is used to obtain the time of rock mass creep instability failure, the first difference, and the second difference under the excavation unloading conditions based on the data processing of the accelerated creep stage.
[0062] The processing module 103 is used to process the first difference, the second difference, and the time of rock mass creep instability and failure to obtain a numerical table.
[0063] The prediction module 104 is used to acquire on-site monitoring data and obtain the on-site instability and failure time based on the on-site monitoring data and numerical tables.
[0064] The specific limitations of the device for predicting the critical instability time of unloaded rock mass based on the Saito method provided in this embodiment can be found in the embodiment of the method for predicting the critical instability time of unloaded rock mass based on the Saito method described above, and will not be repeated here. Each module in the above-mentioned device for predicting the critical instability time of unloaded rock mass based on the Saito method can be implemented entirely or partially through software, hardware, or a combination thereof. Each module can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.
[0065] This application provides a computer device that may include a processor, memory, network interface, and database connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it causes the processor to perform the steps of a method for predicting the critical instability time of unloaded rock masses based on the Saito method, as described in any of the above embodiments.
[0066] The working process, working details, and technical effects of the computer equipment provided in this embodiment can be found in the embodiment above regarding a method for predicting the critical instability time of unloaded rock mass based on the Saito method, and will not be repeated here.
[0067] This application provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps of a method for predicting the critical instability time of unloaded rock mass based on the Saito method, as described in any of the above embodiments. The computer-readable storage medium refers to a data storage medium, which may include, but is not limited to, floppy disks, optical disks, hard disks, flash memory, USB flash drives, and / or memory sticks. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices.
[0068] The working process, working details and technical effects of the computer-readable storage medium provided in this embodiment can be found in the embodiment above regarding a method for predicting the critical instability time of unloaded rock mass based on the Saito method, and will not be repeated here.
[0069] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0070] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0071] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A method for predicting the critical instability time of unloaded rock mass based on the Saito method, characterized in that, The method includes: Obtain the monitoring range of rock mass creep deformation and obtain data on the accelerated creep stage; Based on the data processing of the accelerated creep stage, the time of rock mass creep instability failure, the first difference, and the second difference are obtained under the excavation unloading conditions; A numerical table is obtained by processing the first difference, the second difference, and the time of rock mass creep instability and failure; Obtain on-site monitoring data, and determine the on-site instability and failure time based on the on-site monitoring data and numerical table.
2. The method for predicting the critical instability time of unloaded rock mass based on the Saito method according to claim 1, characterized in that, The monitoring scope for rock mass creep deformation includes: potential sliding zone, main sliding section, rear edge tensile crack, slope top platform and slope toe.
3. The method for predicting the critical instability time of unloaded rock mass based on the Saito method according to claim 2, characterized in that, The accelerated creep stage data includes: initial time point, first time point, second time point, change time, and instantaneous deformation rate.
4. The method for predicting the critical instability time of unloaded rock mass based on the Saito method according to claim 3, characterized in that, The method further includes: The displacement-time curve was obtained based on the on-site monitoring data; The initial moment of entering the acceleration phase is determined based on the displacement-time curve.
5. The method for predicting the critical instability time of unloaded rock mass based on the Saito method according to claim 4, characterized in that, The method further includes: Based on the on-site monitoring data, obtain the displacement change of each monitoring point and the total number of monitoring points during the stable deformation stage. The instantaneous deformation rate is calculated based on the displacement change of each monitoring point during the stable deformation stage and the total number of monitoring points.
6. The method for predicting the critical instability time of unloaded rock mass based on the Saito method according to claim 5, characterized in that, The method further includes: By performing two derivatives of the Saito formula, the creep deformation acceleration under unloaded stress conditions was obtained; The creep deformation acceleration under unloading stress condition is obtained by multiplying the preset constant and the creep deformation acceleration under the unloading stress condition. By integrating the creep deformation acceleration under the unloading stress condition, the relationship between the rock mass creep deformation rate and failure time under the unloading condition is obtained.
7. The method for predicting the critical instability time of unloaded rock mass based on the Saito method according to claim 6, characterized in that, The method further includes: Based on the relationship between the rock mass creep deformation rate and failure time at the first time point, the second time point, and the unloading condition, the following calculations were performed: the deformation amount from the initial time point of entering the accelerated creep deformation stage to the first time point after a change in time; the deformation amount from the first time point to the second time point after a change in time; and the time from the initial time point of entering the accelerated creep deformation stage to the rock mass creep instability failure under the unloading condition.
8. A device for predicting the critical instability time of unloaded rock mass based on the Saito method, characterized in that, The device includes: The acquisition module is used to acquire the monitoring range of rock mass creep deformation and obtain data on the accelerated creep stage; The calculation module is used to process the data of the accelerated creep stage to obtain the time of rock mass creep instability failure, the first difference and the second difference under the excavation unloading conditions; The processing module is used to process the first difference, the second difference, and the time of rock mass creep instability and failure to obtain a numerical table; The prediction module is used to acquire on-site monitoring data and determine the on-site instability and failure time based on the on-site monitoring data and numerical tables.
9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for predicting the critical instability time of unloaded rock mass based on the Saito method as described in any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for predicting the critical instability time of unloaded rock mass based on the Saito method as described in any one of claims 1 to 7.