A pressurized recharge drainage device and method for tunnel reverse slope

Abstract

The application relates to the technical field of drainage in tunnel and underground engineering construction, and discloses a pressurized recharge drainage device and method for a tunnel reverse slope, which comprises a filter and precipitation water tank for collecting and pretreating tunnel accumulated water, and at least one anchor pipe recharge well unit. The anchor pipe recharge well unit comprises a recharge well, a recharge water pump and an anchor pipe arranged in the recharge well. The anchor pipe is hollow and is provided with water permeable holes on the pipe wall. The anchor pipe is fixed in the recharge well through an anchoring assembly, and the anchor pipe and the recharge well are filled with filter gravel. The water inlet end of the recharge water pump is connected with the filter and precipitation water tank, and the water outlet end is connected with the top end of the anchor pipe, so that the accumulated water in the filter and precipitation water tank is sent into the anchor pipe. The device has the advantages of compact structure, energy saving and environmental protection, and one effort brings multiple benefits while efficiently draining.

Description

Technical Field

[0001] This application relates to the field of drainage technology in tunnel and underground engineering construction, and in particular to a pressurized recharge drainage device and method for tunnel reverse slope. Background Technology

[0002] In tunnel and underground engineering construction, reverse slope drainage is a common and technically challenging engineering problem. Because the tunnel face elevation is lower than the exit, accumulated water cannot drain naturally by gravity and must be pumped out of the tunnel using a multi-stage pumping system. Traditional reverse slope drainage methods rely on multi-stage pumping stations and drainage pipes, which present the following problems: First, the system is complex, with numerous pumps, pipes, power distribution, and control systems occupying significant work and transportation space within the limited tunnel area, severely impacting parallel construction of other processes. Second, multi-stage pumps consume substantial amounts of electricity, and the dispersed nature of the pumps leads to heavy workloads for daily inspection, maintenance, and troubleshooting, resulting in high long-term operating costs. Third, directly discharging groundwater not only wastes valuable water resources but also requires the construction of external drainage treatment facilities, increasing project costs and contradicting modern green and energy-saving construction principles. Fourth, in tunnel sections with weak or highly deformable surrounding rock, laying fixed drainage pipes and pump foundations is extremely difficult and may be damaged by rock deformation, affecting rock stability and creating safety hazards. Therefore, there is an urgent need for a tunnel reverse slope drainage device that is simple in structure, energy-saving and environmentally friendly, and can adapt to complex geological conditions. Summary of the Invention

[0003] In view of the above-mentioned shortcomings and deficiencies of the prior art, this application provides a pressurized recharge drainage device and method for tunnel reverse slope, which solves the technical problems of existing reverse slope drainage devices, such as complex structure and large space occupation, high energy consumption and maintenance costs, serious waste of water resources, and difficulty in deployment in soft surrounding rock sections, which may affect the stability of the surrounding rock.

[0004] To achieve the above objectives, this application provides the following technical solution:

[0005] A pressurized recharge drainage device for tunnel reverse slope includes a filter sedimentation tank for collecting and pre-treating tunnel water and at least one anchor pipe recharge well unit.

[0006] The anchor pipe recharge well unit includes a recharge well, a recharge water pump, and an anchor pipe installed in the recharge well. The anchor pipe is hollow and has water-permeable holes on its pipe wall. The anchor pipe is fixed in the recharge well by an anchoring component. Filter gravel is filled between the anchor pipe and the recharge well.

[0007] The inlet of the recharge pump is connected to the filter sedimentation tank, and the outlet is connected to the top of the anchor pipe, so as to send the accumulated water in the filter sedimentation tank to the anchor pipe.

[0008] Preferably, the filtration and sedimentation tank includes a sedimentation tank and a clear water tank arranged sequentially along the water flow direction, and the sedimentation tank and the clear water tank are connected by an overflow outlet; the sedimentation tank is provided with a filter screen and a sand collection hopper, the filter screen is arranged horizontally, the sand collection hopper is located at the bottom of the sedimentation tank and directly below the filter screen, and the bottom of the sand collection hopper is provided with a first sand discharge outlet; the clear water tank is provided with an outlet connected to the inlet of the reinjection pump, and the bottom of the clear water tank is a slope structure sloping to one side, and a second sand discharge outlet is provided at the low point of the slope.

[0009] Preferably, the anchor pipe recharge well unit further includes a flushing pipe and a cleaning pump. The flushing pipe is coaxially disposed inside the anchor pipe, and multiple rotating nozzles are distributed along its axial direction. The top end of the flushing pipe extends to the outside of the anchor pipe and is connected to the outlet end of the cleaning pump. The inlet end of the cleaning pump is connected to the filter sedimentation tank.

[0010] Preferably, there are two anchor pipe recharge well units, and the recharge wells of the two anchor pipe recharge well units are respectively located at the arch foot on both sides of the tunnel;

[0011] It also includes a control component, which comprises a main recharge pipe, two branch recharge pipes, and a control unit;

[0012] One end of each of the two reinjection branch pipes is connected to the top of the anchor pipe of the two anchor pipe reinjection well units, and the other end is connected to one end of the reinjection main pipe through a tee fitting. The other end of the reinjection main pipe is connected to the outlet of the filter sedimentation tank. Each reinjection branch pipe is equipped with a flow regulating valve and a pressure sensor.

[0013] The control unit is electrically connected to the flow regulating valve and the pressure sensor, and is configured to: compare the pressure values ​​detected by the pressure sensors on the two reinjection branch pipes in real time, and dynamically adjust the opening of the flow regulating valve on the corresponding reinjection branch pipe according to the pressure value, so that the pressure difference between the two reinjection branch pipes is maintained within a preset range.

[0014] Preferably, the filter gravel material includes an inner ring reverse filter layer, a middle ring water guiding layer and an outer ring buffer layer, which are filled sequentially from the inside to the outside between the anchor pipe and the recharge well. A permeable isolation net is provided between the inner ring reverse filter layer and the outer wall of the anchor pipe, and a geotextile separation layer is provided between the inner ring reverse filter layer and the middle ring water guiding layer.

[0015] Preferably, the inner ring filter layer is made of quartz sand gravel with a particle size of 1~3mm and a filling thickness of 6~8cm;

[0016] The middle ring water-conducting layer is made of basalt gravel with a particle size of 8~12mm and a filling thickness of 10~12cm;

[0017] The outer ring buffer layer is made of graded sand and gravel mixture with a particle size of 5~20mm and a filling thickness of 12~15cm.

[0018] The permeable mesh is made of stainless steel with a pore size of 0.5mm;

[0019] The geotextile separator layer is a short-fiber needle-punched nonwoven geotextile with a basis weight ≥200g / m². 2 The fracture strength is ≥15kN / m.

[0020] A pressurized recharge drainage method for tunnel reverse slope, applied to any of the pressurized recharge drainage devices described above, comprising:

[0021] Collect the accumulated water in the tunnel face area and introduce it into a filter sedimentation tank for solid-liquid separation and sedimentation treatment;

[0022] The water level of the filter sedimentation tank is monitored in real time. When the water level reaches the preset high water level, the recharge pump is started to pressurize and transport the water treated by the filter sedimentation tank to the hollow inner cavity of the anchor pipe. The water seeps out through the permeable holes on the wall of the anchor pipe and is injected into the surrounding soil and rock to achieve pressurized recharge drainage. When the water level drops to the preset low water level, the recharge pump is stopped.

[0023] Preferably, during the pressurized recharge drainage process, the recharge flow rate and recharge pressure provided by the recharge pump are monitored in real time, and the corresponding recharge volume per unit pressure is calculated. The recharge volume per unit pressure is equal to the ratio of the recharge flow rate to the recharge pressure. The recharge pressure is dynamically adjusted based on the recharge volume per unit pressure, specifically including:

[0024] If the real-time value of the unit pressure reinjection volume continues to decrease within a preset time period and is lower than the preset permeability reduction threshold, the reinjection pressure will be increased in stages by 0.05~0.1MPa, and the increased reinjection pressure will not exceed the preset maximum safe pressure.

[0025] If the real-time value of the unit pressure reinjection volume continues to rise within a preset time period and exceeds the preset permeability increase threshold, or if abnormal seepage or slurry leakage is detected around the reinjection well, the reinjection pressure will be reduced by 0.1~0.2MPa, and the reduced reinjection pressure will not be lower than the preset minimum safe pressure.

[0026] Preferably, the step of dynamically adjusting the reinjection pressure based on the unit pressure reinjection volume further includes:

[0027] During the phased increase of reinjection pressure, if the real-time value of the reinjection volume per unit pressure rises and exceeds the permeability reduction threshold after the increase, the increase is paused and the current reinjection pressure is maintained to continue reinjection.

[0028] After reducing the reinjection pressure by 0.1~0.2MPa, if the real-time value of the unit pressure reinjection volume is lower than the permeability increase threshold and the abnormal seepage or slurry leakage disappears, then the reduced reinjection pressure is maintained and reinjection continues; otherwise, the reinjection pressure is further reduced by 0.05~0.1MPa until the minimum safe pressure is reached.

[0029] Preferably, it is characterized in that,

[0030] The hollow inner cavity of the anchor pipe is periodically flushed to remove any attached materials or blockages.

[0031] During the pressurized recharge and drainage process, periodic pulse disturbance operations are performed, as follows:

[0032] The current reinjection pressure value is used as the reference pressure P0;

[0033] Repeat the pulse disturbance cycle 2 to 4 times. The pulse disturbance cycle includes: within 30 to 60 seconds, increasing the reinjection pressure to 1.2 to 1.8 times P0, and the reinjection pressure after the increase shall not exceed the preset maximum safe pressure, and maintaining the increased reinjection pressure for 60 to 120 seconds; within 20 to 40 seconds, decreasing the reinjection pressure to 0.3 to 0.6 times P0.

[0034] The pressurized recharge drainage device for tunnel reverse slope provided in this application integrates a filter sedimentation tank, an anchor pipe recharge well unit, and a recharge pump. It replaces the traditional multi-stage pumping station and pipeline relay drainage with single-point centralized recharge, significantly simplifying the drainage system and reducing the space occupied by equipment within the tunnel. Simultaneously, by pressurizing and recharging accumulated water deep into the strata, it achieves in-situ water recycling, avoiding water waste and external treatment costs, and significantly reducing long-term operating energy consumption. Furthermore, the anchor pipes fixed within the recharge well unit by anchoring components can remain in the strata as a locking anchor structure after drainage, playing a long-term role in enhancing the stability of the tunnel arch foot, thus organically combining the drainage process with permanent structural reinforcement. This device achieves efficient drainage while also providing structural reinforcement, offering advantages such as compact structure, energy saving, environmental protection, and multiple benefits. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the arrangement of the pressurized recharge drainage device in this embodiment.

[0036] Figure 2 This is a schematic diagram of the anchor pipe in this embodiment.

[0037] Figure 3 This is a schematic diagram of the internal structure of the filtration and sedimentation tank in this embodiment.

[0038] Figure 4This is a top view of the layout of the two anchor pipe recharge well units in this embodiment.

[0039] Figure 5 This is a side view of the layout of the two anchor pipe recharge well units in this embodiment.

[0040] Figure 6 This is a schematic diagram showing the connection of the pipelines of the two anchor pipe recharge well units in this embodiment.

[0041] In the diagram: 1. Filter sedimentation tank; 2. Recharge well; 3. Filter gravel; 4. Anchor pipe; 5. Water permeable hole; 6. Sedimentation tank; 7. Clear water tank; 8. Overflow outlet; 9. Filter screen; 10. Sand collection hopper; 11. Flushing water supply main pipe; 12. Recharge main pipe; 13. Recharge branch pipe; 14. Flushing water supply branch pipe; 15. Working face. Detailed Implementation

[0042] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0043] In the description of this application, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0044] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0045] In tunnel engineering, when the excavation direction is downhill, the excavation front (i.e., the tunnel face) will be lower than the completed tunnel section, forming a so-called reverse slope condition. Under this condition, water seeping from the tunnel face and along the tunnel cannot drain by gravity and must be pumped out mechanically; this process is called reverse slope drainage. This condition not only brings high drainage energy consumption and complex pump and pipeline systems, but the pumping operation may also disturb the stability of the surrounding rock in key load-bearing parts of the tunnel, especially the arch foot areas connected to the foundation on both sides of the arch support structure. Therefore, how to achieve efficient and energy-saving drainage while simultaneously reinforcing the surrounding rock, especially the arch foot areas, has become an urgent problem to be solved in tunnel reverse slope drainage technology. This application addresses the above-mentioned technical problems by proposing a device and method that integrates drainage, recharge, and anchoring functions, aiming to achieve the dual goals of environmentally friendly drainage and structural safety reinforcement.

[0046] The pressurized recharge drainage device and method of this application have been successfully applied in tunnel reverse slope drainage projects such as the follow-up optimization project of the Hanjiang-Rongjiang-Lianjiang water system connection. In engineering practice, a water collection tank is set up at a certain distance behind the tunnel face, and anchor pipe recharge well units are deployed at the tunnel arch foot. The treated water is pressurized and recharged into the deep gravel layer by a recharge pump, effectively controlling the water level in the tunnel. At the same time, the anchor pipes play a locking and anchoring role, enhancing the stability of the arch foot. No obvious deformation or seepage has been observed in the engineering application, and the device operates stably, achieving the expected effects of water saving, reinforcement, and efficient drainage, thus verifying the feasibility and superiority of this application.

[0047] Example

[0048] See Figure 1-2 This embodiment provides a pressurized recharge drainage device for tunnel reverse slope, including a filter sedimentation tank 1 for collecting and pre-treating tunnel water accumulation, and at least one anchor pipe recharge well unit; the anchor pipe recharge well unit includes a recharge well 2, a recharge pump, and an anchor pipe 4 installed in the recharge well 2. The anchor pipe 4 is hollow and has water-permeable holes 5 on its pipe wall. The anchor pipe 4 is fixed in the recharge well 2 by an anchoring component. Filter gravel 3 is filled between the anchor pipe 4 and the recharge well 2; the inlet end of the recharge pump is connected to the filter sedimentation tank 1, and the outlet end is connected to the top end of the anchor pipe 4 to send the water accumulation in the filter sedimentation tank 1 into the anchor pipe 4.

[0049] During construction, the location of the recharge well 2 is first determined and drilled in a stable stratum area at a certain distance behind the tunnel face within the tunnel's reverse slope drainage section, at the arch foot. Then, the anchor pipe 4 is lowered into the recharge well 2. After the pipe is in place, the anchor pipe 4 is reliably locked to the surrounding rock of the recharge well 2 using anchoring components, forming a stable structure. Afterwards, filter gravel 3 is filled into the annular gap between the anchor pipe 4 and the recharge well 2.

[0050] The anchoring assembly can adopt conventional mechanical anchoring structures in the field, such as hydraulic anchors or wedge locking devices. Its function is to provide radial locking force after the anchor pipe 4 is installed in place, so that the outer wall of the anchor pipe 4 is tightly attached to the surrounding rock of the recharge well 2, thereby achieving reliable fixation of the anchor pipe 4 in the recharge well 2.

[0051] The filtration and sedimentation tank 1 can be made of corrosion-resistant and easily relocated PVC or steel plate material, and is installed in a low-lying area suitable for water collection behind the tunnel side ditch or the tunnel face 15. During construction, the accumulated water from the tunnel face 15 and the tunnel sidewall is introduced into the inlet of the filtration and sedimentation tank 1 through a simple drainage ditch or diversion pipe to achieve centralized collection and temporary storage of the accumulated water.

[0052] Recharge well 2 is located in a stable geological zone at a certain distance behind face 15, with the specific distance preferably controlled within the range of 10 to 30 meters. This location is outside the disturbance zone of face 15 and should be selected in a section where groundwater is underdeveloped or has good permeability to ensure recharge efficiency and safe operation of the equipment.

[0053] After filling the annular gap between the anchor pipe 4 and the recharge well 2 with filter gravel 3, the wellhead needs to be sealed with cement to prevent water from seeping along the well wall, ensure that the recharge water is injected into the target formation in a directional manner, and reduce the wetting effect on the shallow surrounding rock.

[0054] As the tunnel face 15 advances, the pressurized recharge drainage device in this embodiment needs to be moved forward accordingly, and the filtered sedimentation tank 1 and the new anchor pipe recharge well unit need to be rearranged. The recharge well 2 and the anchor pipe 4 within it that have already been constructed are permanently retained in their original positions. The anchor pipe 4 is not only mechanically locked by the anchoring components, but the filter gravel 3 filling its periphery also forms a lateral constraint on the anchor pipe 4 after compaction and permeation consolidation. This allows the anchor pipe 4 and the surrounding rock and soil to form an integral anchor body, which plays a long-term supporting role in enhancing the stability of the tunnel arch foot.

[0055] The pressurized recharge drainage device in this embodiment combines the drainage process with structural anchoring, achieving integrated drainage, irrigation, and anchoring. It directly recharges the water accumulated in the tunnel into the deep strata, avoiding the waste of water resources and additional treatment costs of traditional external drainage methods, and significantly improving the environmental friendliness and economy of construction. Furthermore, its compact structure and flexible layout greatly reduce the space occupied by traditional multi-stage pumping stations and pipelines in the tunnel. In addition, while efficiently draining water, it provides continuous structural reinforcement for the tunnel arch foot, enhances the stability of the surrounding rock, ensures the safety of construction, and achieves an effective unity of temporary drainage measures and permanent support functions.

[0056] See Figure 3The filtration and sedimentation tank 1 includes a sedimentation tank 6 and a clear water tank 7 arranged sequentially along the water flow direction. The sedimentation tank 6 and the clear water tank 7 are connected by an overflow port 8. The sedimentation tank 6 is equipped with a filter screen 9 and a sand collection hopper 10. The filter screen 9 is horizontally arranged, and the sand collection hopper 10 is located at the bottom of the sedimentation tank 6 and directly below the filter screen 9. The bottom of the sand collection hopper 10 is provided with a first sand discharge port. The clear water tank 7 is provided with an outlet connected to the inlet of the reinjection pump. The bottom of the clear water tank 7 is a slope structure sloping to one side, and a second sand discharge port is provided at the low point of the slope.

[0057] The sedimentation tank 1 filters and purifies the tunnel water, protecting subsequent reinjection equipment and ensuring long-term operational efficiency. The sedimentation tank 6 has an inlet on its top side wall, directly connected to the tunnel drainage ditch, enabling gravity-fed collection of water. The filter screen 9 inside the sedimentation tank 6 first coarsely filters the incoming water, intercepting larger solid debris (such as gravel and construction debris) to prevent them from entering subsequent processes and thus avoiding wear on the water pump or blockage of the permeable holes 5 of the anchor pipe 4. The intercepted material on the filter screen 9 needs to be manually cleaned periodically. Construction personnel can open the inspection port on the top of the sedimentation tank during drainage breaks or periodic maintenance and use cleaning tools (such as grab buckets and shovels) to manually remove and transport out the larger solid debris trapped on the screen surface.

[0058] The water flow, after being coarsely filtered by the filter screen 9, slows down in the sedimentation tank 6, creating conditions for gravity settling. Fine particles such as silt suspended in the water gradually settle into the sand collection hopper 10 at the bottom of the sedimentation tank 6, facilitating centralized cleaning. A first sand discharge valve is installed at the first sand discharge outlet at the bottom of the sand collection hopper 10, allowing for regular maintenance to maintain the effective volume and settling efficiency of the sedimentation tank 6.

[0059] The supernatant after initial sedimentation overflows through overflow port 8 into clear water tank 7, providing a stable water source for the reinjection pump. The slope at the bottom of clear water tank 7 utilizes gravity to automatically cause fine particles flowing into the tank to slide and collect at lower points. By periodically opening the second sand discharge valve at the second sand discharge outlet, this residual sediment can be completely discharged, further ensuring the purity of the water supplied to the reinjection pump and fundamentally preventing pump wear, efficiency reduction, and chemical and biological blockage of the anchor pipe 4 or permeable holes 5 caused by fine particles. Clear water tank 7 is equipped with a water level monitoring sensor to monitor the water level in the filtration sedimentation tank.

[0060] The filter sedimentation tank 1 in this embodiment greatly reduces the solid content of the reinjection water, effectively protects the reinjection pump and anchor pipe reinjection well unit, extends the service life of the equipment, and reduces maintenance costs. In addition, the stable supply of clean water ensures the constantness of the reinjection pressure, improves the reinjection efficiency and the reliability of control.

[0061] The anchor pipe recharge well unit also includes a flushing pipe and a cleaning pump. The flushing pipe is coaxially installed inside the anchor pipe 4. Multiple rotating nozzles are distributed along the axial direction of the flushing pipe. The top of the flushing pipe extends to the outside of the anchor pipe 4 and is connected to the outlet of the cleaning pump. The inlet of the cleaning pump is connected to the filter sedimentation tank 1.

[0062] In this embodiment, the flushing pipe and the anchor pipe 4 are detachably coaxially installed. Specifically, a flange is installed on the outer anchor head at the top of the anchor pipe 4. The top of the flushing pipe can be designed to connect to a dedicated interface or quick connector pre-reserved in the center of the flange, thereby achieving rapid fixation and alignment of the flushing pipe in the axial direction of the anchor pipe 4, ensuring stability of the flushing pipe during recharge or cleaning. When cleaning is required, the cleaning pump is turned on, and high-pressure water enters the flushing pipe, driving multiple rotating nozzles distributed along the axial direction of the flushing pipe to generate a high-speed rotating jet, which powerfully flushes and removes silt from the inner wall of the anchor pipe 4 and the permeable holes 5. After the recharge well 2 has completed its phase mission, the flushing pipe can be easily pulled out and recovered from the anchor pipe 4 simply by disassembling it at the flange, facilitating reuse in subsequent projects. The operation is simple, the connection is reliable, and it avoids the need for complex fixing mechanisms inside the anchor pipe 4.

[0063] The rotary nozzles are preferably non-powered rotary flushing nozzles that utilize fluid dynamics principles to achieve self-rotation. Specifically, examples include oblique-cut backwash nozzles or turbine-driven rotary nozzles. These nozzles have jet holes at specific angles on their sidewalls or ends. When high-pressure water passes through, the reaction force generated by the water flow drives the turbine to rotate, thereby causing the entire nozzle to slowly rotate around its axis, without the need for an external motor or transmission mechanism. In this embodiment, the rotary nozzles are arranged along the axial direction of the flushing pipe at equal intervals or in non-uniform segments according to the length of the anchor pipe 4, ensuring that the high-pressure water jet can cover the entire length of the inner wall of the anchor pipe 4, achieving rotary flushing without dead angles. The jet direction can be designed to be both forward and to the rear side to create a powerful flushing and agitation of deposits on the pipe wall (such as biofilm, chemical precipitates, and fine particle deposits).

[0064] This embodiment enables efficient, in-situ cleaning of anchor pipes 4 that are already embedded in the formation without disassembly. It removes blockages from the permeable holes 5 and the inside of the anchor pipe 4, restoring its permeability and recharge efficiency, extending its service life, and reducing replacement costs. Furthermore, the flushing pipe is recyclable and reusable, significantly saving material costs and construction complexity, aligning with green construction principles. The entire flushing process utilizes the filtered and settled water from the sedimentation tank 1 as the medium, achieving a closed-loop operation.

[0065] See Figures 4-5The system includes two anchor pipe recharge well units, with the recharge wells 2 of each unit located at the arch foot on both sides of the tunnel. It also includes a control assembly comprising a main recharge pipe 12, two branch pipes 13, and a control unit. One end of each branch pipe 13 is connected to the top of the anchor pipe 4 of the two anchor pipe recharge well units, and the other end is connected to one end of the main recharge pipe 12 via a tee fitting. The other end of the main recharge pipe 12 is connected to the outlet of the filter sedimentation tank 1. Each branch pipe 13 is equipped with a flow regulating valve and a pressure sensor. The control unit is electrically connected to the flow regulating valve and the pressure sensor and is configured to: compare the pressure values ​​detected by the pressure sensors on the two branch pipes 13 in real time, and dynamically adjust the opening of the flow regulating valve on the corresponding branch pipe according to the pressure values, so that the pressure difference between the two branch pipes remains within a preset range.

[0066] In this embodiment, each anchor pipe recharge well unit is equipped with a corresponding recharge water pump. The recharge water pump is installed in series on the corresponding recharge branch pipe 13. Its inlet end is connected to a tee fitting through the recharge branch pipe 13, and its outlet end is connected to the top of the anchor pipe 4 through the recharge branch pipe 13, thus forming an independent pressurized water supply circuit for each recharge well 2. On each recharge branch pipe 13, an on / off valve (such as an electric ball valve) is provided upstream or downstream of the recharge water pump to control the opening and closing of the recharge branch pipe, which facilitates the independent start-up, shutdown, maintenance, or isolation of a single recharge branch pipe from other pipelines.

[0067] One or more lateral interfaces are provided on the radial side wall of the flange of the outer anchor head of anchor pipe 4. The end of the recharge branch pipe 13 is connected to the lateral interface through a mating flange or quick connector, thereby realizing the physical separation and parallel operation of the recharge water supply path and the flushing pipe path. In addition, a ball valve check device is provided on the recharge branch pipe 13 to prevent backflow of recharge water.

[0068] See Figure 6 Each anchor pipe reinjection well unit has an independent flushing circuit. The top of the flushing pipe of each of the two anchor pipe reinjection well units is connected to a flushing water supply branch pipe 14. The other ends of the two flushing water supply branch pipes 14 converge into a flushing water supply main pipe 11 via a tee fitting. This flushing water supply main pipe 11 is ultimately connected in parallel with the reinjection main pipe 12 via another tee fitting, and both are connected to the outlet of the filter sedimentation tank 1. A cleaning pump is installed on each flushing water supply branch pipe 14 to provide an independent and controllable high-pressure cleaning water source for the corresponding flushing pipe.

[0069] The control unit is electrically connected to all on / off valves, the reinjection water pump, the cleaning pump, and the flow regulating valve and pressure sensor on the reinjection branch pipe 13. The control unit has a preset automatic cleaning program. When the preset cleaning cycle is reached or a manual cleaning command is received, the control unit first automatically closes the on / off valve and the reinjection water pump on the target reinjection branch pipe 13, cutting off the reinjection water flow in that path. Then, it starts the cleaning pump on the corresponding flushing water supply branch pipe. The cleaning pump pumps high-pressure clean water into the cleaning water supply branch pipe, delivering it to the center interface of the flange at the top of the anchor pipe 4, and then into the flushing pipe, continuously and comprehensively flushing the inner wall of the anchor pipe 4 and the permeable holes 5 automatically. The flushing time follows the preset program. After completion, the control unit automatically stops the cleaning pump and reopens the on / off valve and the reinjection water pump on the reinjection branch pipe 13, restoring the pressurized reinjection mode.

[0070] In this embodiment, two anchor pipe recharge well units are symmetrically arranged at the arch foot on both sides of the tunnel. The fundamental purpose is to adapt to the stress characteristics of the tunnel structure and achieve a balanced and coordinated drainage and reinforcement. The arch foot is a key stress-bearing part of the tunnel lining. Symmetrical reinforcement of the surrounding rock on both sides can effectively improve the stress state of the structure and avoid uneven settlement or eccentric pressure.

[0071] To achieve this balance, this embodiment implements coordinated control of the two anchor pipe recharge well units. The control unit compares the pressure values ​​on the two recharge branch pipes 13 in real time. If the difference exceeds a preset range, it indicates that the recharge resistance of the two anchor pipe recharge well units is unbalanced (possibly due to differences in formation permeability or local blockage). At this time, the control unit dynamically adjusts the opening of the flow regulating valve on the corresponding recharge branch pipe 13, appropriately reducing the flow rate on the side with higher resistance to reduce pressure, or appropriately increasing the flow rate on the side with lower resistance to increase pressure, thereby restoring the pressure balance on both sides and ensuring that the two anchor pipe recharge well units always operate under balanced conditions.

[0072] The above-mentioned linkage control achieves dual technical advantages. First, in terms of drainage, it avoids excessive concentration of flow and pressure in a single recharge well 2, thereby reducing the risk of blockage and load intensity of a single recharge well 2, and ensuring the stability and efficiency of drainage. In terms of reinforcement, it promotes the synchronous and balanced penetration and reinforcement effect of recharge water on the surrounding rock of the arch foot on both sides, providing symmetrical lateral constraints for the tunnel structure, maximizing the synergistic enhancement effect of the anchorage, and thus significantly improving the overall stability of the tunnel during the construction and operation periods.

[0073] The filter gravel 3 includes an inner ring filter layer, a middle ring water-conducting layer and an outer ring buffer layer, which are filled from the inside to the outside between the anchor pipe 4 and the recharge well 2. A permeable isolation net is provided between the inner ring filter layer and the outer wall of the anchor pipe 4, and a geotextile separation layer is provided between the inner ring filter layer and the middle ring water-conducting layer.

[0074] In this embodiment, the filter gravel 3 adopts a layered structure with progressively increasing particle size from the inside out. This structure simultaneously achieves multiple functions of reverse filtration protection, efficient water conduction, and pressure buffering through gradient gradation. Specifically, the inner ring reverse filtration layer is closely attached to the anchor pipe 4, and its particle size is smaller than the permeable pore size of the anchor pipe. It can effectively intercept reinjection water and fine particles migrating from the formation, preventing them from entering subsequent layers or formations, thus playing a core reverse filtration role. The middle ring water conduction layer, with its larger particle size and irregular particle shape, forms a continuous and interconnected pore structure, constituting a low-resistance main seepage channel, ensuring that the reinjection water can quickly and smoothly diffuse to the surroundings, guaranteeing infiltration efficiency. The outer ring buffer layer is located on the outermost side, and its continuously graded larger particles form a transition zone with good deformation adaptability, which can dissipate and buffer reinjection pressure pulses, avoiding direct impact of high-pressure water on the original formation structure, and playing a role in protecting formation stability.

[0075] In addition, a permeable isolation net is set between the inner ring filter layer and the outer wall of the anchor pipe 4, directly covering all the permeable holes 5. Its core function is to prevent the fine gravel particles of the inner ring filter layer from entering the anchor pipe 4 and causing blockage. The geotextile separation layer laid between the inner ring filter layer and the middle ring water-conducting layer strictly separates the filter materials of different particle sizes to prevent them from mixing under long-term seepage or vibration, thereby ensuring the long-term effectiveness of the filtration and water-conducting functions of each level.

[0076] Through careful material selection and structural design, the filter gravel 3 in this embodiment prevents the loss of fine formation particles and protects the formation structure while maintaining a highly permeable recharge channel. It also effectively prevents the filter material itself from invading the anchor pipe 4 system in the reverse direction. This significantly extends the service life of the recharge well 2, improves the efficiency and reliability of the recharge process, and ensures the protection of the surrounding rock and soil, achieving a balance between efficient drainage, long-term operation and formation safety.

[0077] Furthermore, during the automatic cleaning process, the high-pressure water flow drives the rotating nozzles on the flushing pipe to generate a high-speed rotating jet. This jet not only effectively removes deposits from the inner wall of the anchor pipe 4, but its powerful flow can also penetrate the permeable holes 5, disturbing and backflushing the permeable isolation net and the surface of the inner ring filter layer that are tightly attached to the pipe wall. This backflushing helps to shake off the fine particles that are clogging the outside of the permeable isolation net and the near area of ​​the inner ring filter layer, thereby locally restoring the permeability of the area without disturbing the structural integrity of the outer middle ring water guiding layer and the outer ring buffer layer.

[0078] The inner ring filter layer uses quartz sand and gravel with a particle size of 1-3mm and a filling thickness of 6-8cm; the middle ring water-conducting layer uses basalt gravel with a particle size of 8-12mm and a filling thickness of 10-12cm; the outer ring buffer layer uses graded sand and gravel mixture with a particle size of 5-20mm and a filling thickness of 12-15cm; the permeable isolation net is made of stainless steel with a pore size of 0.5mm; the geotextile separation layer is made of short-fiber needle-punched nonwoven geotextile with a basis weight ≥200g / m². 2 The fracture strength is ≥15kN / m.

[0079] To precisely control the radial thickness of the inner ring filter layer, the middle ring water guiding layer, and the outer ring buffer layer, a layered positioning backfilling process is adopted during construction. For example, when filling the inner ring filter layer, a removable radial positioning support is evenly arranged circumferentially within the annular gap between the outer wall of anchor pipe 4 and the well wall. The radial dimension of the support is strictly set according to the design thickness (6~8cm). This is used as a reference during filling and is supplemented by calibration with measuring ropes to ensure the formation of a uniform, continuous filter layer with the required thickness.

[0080] This embodiment also provides a pressurized recharge drainage method for tunnel reverse slope, applied to the above-mentioned pressurized recharge drainage device, including:

[0081] S1. Collect the accumulated water in area 15 of the tunnel face and introduce it into the filter sedimentation tank 1 for solid-liquid separation and sedimentation treatment.

[0082] S2. Monitor the water level of the filter sedimentation tank 1 in real time. When the water level reaches the preset high water level, start the recharge pump to pressurize and transport the water treated by the filter sedimentation tank 1 to the hollow cavity of the anchor pipe 4. The water will seep out through the permeable holes 5 on the wall of the anchor pipe 4 and be injected into the surrounding soil and rock to achieve pressurized recharge drainage. When the water level drops to the preset low water level, stop the recharge pump.

[0083] The control unit is electrically connected to the water level monitoring sensor and the recharge pump, and automatically realizes the start and stop cycle of recharge drainage based on the real-time water level of the filter sedimentation tank 1.

[0084] During the pressurized recharge and drainage process, the recharge flow rate and pressure provided by the recharge pump are monitored in real time, and the corresponding recharge volume per unit pressure is calculated. The recharge volume per unit pressure is equal to the ratio of the recharge flow rate to the recharge pressure. The recharge pressure is dynamically adjusted based on the recharge volume per unit pressure, specifically including:

[0085] If the real-time value of the unit pressure reinjection volume continues to decrease within a preset time period and is lower than the preset permeability reduction threshold, the reinjection pressure will be increased in stages by 0.05~0.1MPa, and the increased reinjection pressure will not exceed the preset maximum safe pressure.

[0086] If the real-time value of the unit pressure reinjection volume continues to rise within a preset time period and exceeds the preset permeability increase threshold, or if abnormal seepage or slurry leakage is detected around reinjection well 2, the reinjection pressure will be reduced by 0.1~0.2MPa, and the reduced reinjection pressure will not be lower than the preset minimum safe pressure.

[0087] The pressurized recharge drainage method in this embodiment uses the recharge volume per unit pressure as the core monitoring indicator to provide real-time feedback on changes in the instantaneous permeability of the formation. This indicator directly reflects the actual flow capacity of the formation under unit recharge pressure. In engineering practice, formation permeability can dynamically change due to factors such as particle migration and blockage, chemical precipitation, or changes in surrounding rock stress. If the recharge pressure remains constant, a decrease in formation permeability will lead to a significant reduction in recharge efficiency; conversely, an abnormally high permeability may cause safety risks such as hydraulic fracturing. Therefore, the dynamic adjustment mechanism of recharge pressure based on real-time permeability feedback adopted in the pressurized recharge drainage method of this embodiment is precisely to fundamentally solve the adaptability problem of fixed-pressure recharge methods in changing formations, ensuring that it can continuously and reliably balance drainage efficiency and engineering safety under complex geological conditions.

[0088] The permeability reduction threshold and permeability increase threshold are taken as 90%~95% and 115%~130% of the benchmark value of unit pressure reinjection in the initial stable stage, respectively; the maximum safe pressure is determined based on the formation's fracturing resistance and field tests, and is usually not higher than 80% of the critical fracturing pressure; the minimum safe pressure is required to maintain the necessary flow in the pipeline, and is generally set at 0.3~0.5MPa.

[0089] For example, in a tunnel section traversing moderately weathered sandy mudstone strata, the baseline value was measured to be 10.0 m³ / h / MPa. Based on this, the reduction threshold was set at 9.2 m³ / h / MPa, and the increase threshold at 12.5 m³ / h / MPa. If the unit pressure reinjection rate continuously decreases from 10.0 to 8.8 m³ / h / MPa within 5 minutes, the reinjection pressure is gradually increased in increments of 0.07 MPa. If it continuously increases from 10.0 to 13.0 m³ / h / MPa within 5 minutes, or if slurry seepage occurs around the well, the reinjection pressure is immediately reduced by 0.15 MPa.

[0090] The pressurized recharge drainage method in this embodiment adjusts the recharge pressure based on the formation permeability, achieving an adaptive response to the formation state. When permeability shows a decreasing trend, the recharge efficiency is maintained by increasing the pressure in stages; when permeability is abnormally high or there are signs of danger, the pressure is rapidly reduced to prevent damage to the formation structure, thereby reliably ensuring the efficiency and safety of the drainage process under dynamic geological conditions.

[0091] In the configuration of two anchor pipe recharge well units, the aforementioned dynamic pressure adjustment logic based on recharge volume per unit pressure operates in conjunction with the flow control logic based on the pressure balance of the two recharge branch pipes. The control unit simultaneously monitors the pressure values ​​and recharge volume per unit pressure of the two recharge branch pipes. First, it adjusts the opening of the flow control valves of each recharge branch pipe according to the pressure balance logic to balance the recharge resistance of the two recharge wells. Then, based on the real-time recharge volume per unit pressure of each recharge well, it judges changes in formation permeability and subsequently fine-tunes the output pressure of the corresponding recharge pump by controlling it, or coordinates the increase and decrease of the total pressure. This collaborative control mechanism, while ensuring balanced recharge reinforcement on both sides of the tunnel, achieves dynamic adaptation to changes in formation permeability and efficient and safe recharge.

[0092] Dynamically adjusting the reinjection pressure based on the unit pressure reinjection volume also includes:

[0093] During the phased increase of reinjection pressure, if the real-time value of the reinjection volume per unit pressure rises and exceeds the permeability reduction threshold after the increase, the increase is paused and the current reinjection pressure is maintained to continue reinjection.

[0094] After reducing the reinjection pressure by 0.1~0.2MPa, if the real-time value of the unit pressure reinjection volume is lower than the permeability increase threshold and the abnormal seepage or slurry leakage disappears, then maintain the reduced reinjection pressure and continue reinjection; otherwise, continue to reduce the reinjection pressure by 0.05~0.1MPa until the minimum safe pressure is reached.

[0095] During pressurization, once the reinjection efficiency is detected to have recovered, the current reinjection pressure is automatically maintained, avoiding unnecessary further pressurization and thus saving energy. During depressurization, a low-pressure state is maintained only after it is confirmed that the safety risk has been eliminated; otherwise, the pressure continues to decrease slightly until the safety threshold is reached, ensuring the reliability of risk control. These steps prevent under- or over-adjustment and optimize the pressure configuration during long-term operation, reducing operating costs while ensuring drainage efficiency and formation safety.

[0096] The hollow inner cavity of the anchor pipe 4 is periodically flushed to remove any attached materials or blockages.

[0097] During the pressurized recharge and drainage process, periodic pulse disturbance operations are performed, as follows:

[0098] The current reinjection pressure value is used as the reference pressure P0;

[0099] Repeat the pulse disturbance cycle 2 to 4 times. The pulse disturbance cycle includes: within 30 to 60 seconds, increasing the reinjection pressure to 1.2 to 1.8 times P0, and the reinjection pressure after the increase must not exceed the preset maximum safe pressure, and maintaining the increased reinjection pressure for 60 to 120 seconds; within 20 to 40 seconds, decreasing the reinjection pressure to 0.3 to 0.6 times P0.

[0100] The pressurized recharge drainage method in this embodiment employs two proactive maintenance measures to prevent and remove blockages. The first is a periodic flushing operation. When cleaning is required, the pressurized recharge drainage process is paused, and the hollow interior of the anchor pipe 4 and the permeable holes 5 are flushed using the flushing pipe and rotating nozzle within the anchor pipe 4 to directly remove attached materials and blockages. The second is a periodic pulse disturbance operation. This operation is implemented periodically during normal pressurized recharge drainage, using rapid and significant pressure fluctuations to generate physical impact and suction on the formation and filtration structure.

[0101] These two anti-clogging methods are separate in timing but complementary in function. Periodic flushing powerfully removes existing internal blockages, completely restoring the flow capacity of anchor pipe 4; while pulse disturbance is an online preventative measure, proactively disturbing the interface between the formation and the filter layer during reinjection to delay external siltation. The combination of these two methods significantly slows the decline in system permeability, ensuring efficient drainage while optimizing maintenance cycles and improving overall long-term operational reliability and economy.

[0102] The pressurized recharge drainage device and method of this embodiment simplify the structure and facilitate construction, making it adaptable to various complex geological conditions. Furthermore, relying on multi-parameter sensors and intelligent control units for water level, pressure, flow rate, etc., it achieves automated operation of the entire recharge, drainage, recharge, and cleaning process, significantly reducing manual intervention, improving drainage efficiency, and enhancing long-term operational stability.

[0103] The embodiments of this application have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A pressurized recharge drainage device for tunnel reverse slope, characterized in that: Includes a filtration and sedimentation tank for collecting and pre-treating tunnel water, and at least one anchor pipe recharge well unit; The anchor pipe recharge well unit includes a recharge well, a recharge water pump, and an anchor pipe installed in the recharge well. The anchor pipe is hollow and has water-permeable holes on its pipe wall. The anchor pipe is fixed in the recharge well by an anchoring component. Filter gravel is filled between the anchor pipe and the recharge well. The inlet of the recharge pump is connected to the filter sedimentation tank, and the outlet is connected to the top of the anchor pipe, so as to send the accumulated water in the filter sedimentation tank to the anchor pipe.

2. The pressurized recharge and drainage device for tunnel reverse slope as described in claim 1, characterized in that: The filtration and sedimentation tank includes a sedimentation tank and a clear water tank arranged sequentially along the water flow direction, and the sedimentation tank and the clear water tank are connected by an overflow outlet; the sedimentation tank is equipped with a filter screen and a sand collection hopper, the filter screen is horizontally arranged, the sand collection hopper is located at the bottom of the sedimentation tank and directly below the filter screen, and the bottom of the sand collection hopper is provided with a first sand discharge outlet; the clear water tank is provided with an outlet connected to the inlet of the reinjection pump, and the bottom of the clear water tank is a slope structure sloping to one side, and the low point of the slope is provided with a second sand discharge outlet.

3. The pressurized recharge and drainage device for tunnel reverse slope as described in claim 1, characterized in that: The anchor pipe recharge well unit also includes a flushing pipe and a cleaning pump. The flushing pipe is coaxially arranged inside the anchor pipe, and multiple rotating nozzles are distributed along its axial direction. The top end of the flushing pipe extends to the outside of the anchor pipe and is connected to the outlet end of the cleaning pump. The inlet end of the cleaning pump is connected to the filter sedimentation tank.

4. The pressurized recharge and drainage device for tunnel reverse slope as described in claim 1, characterized in that: The number of anchor pipe recharge well units is two, and the recharge wells of the two anchor pipe recharge well units are respectively located at the arch foot on both sides of the tunnel; It also includes a control component, which comprises a main recharge pipe, two branch recharge pipes, and a control unit; One end of each of the two reinjection branch pipes is connected to the top of the anchor pipe of the two anchor pipe reinjection well units, and the other end is connected to one end of the reinjection main pipe through a tee fitting. The other end of the reinjection main pipe is connected to the outlet of the filter sedimentation tank. Each reinjection branch pipe is equipped with a flow regulating valve and a pressure sensor. The control unit is electrically connected to the flow regulating valve and the pressure sensor, and is configured to: compare the pressure values ​​detected by the pressure sensors on the two reinjection branch pipes in real time, and dynamically adjust the opening of the flow regulating valve on the corresponding reinjection branch pipe according to the pressure value, so that the pressure difference between the two reinjection branch pipes is maintained within a preset range.

5. A pressurized recharge and drainage device for tunnel reverse slope as described in claim 1, characterized in that: The filter gravel material includes an inner ring reverse filter layer, a middle ring water guiding layer and an outer ring buffer layer, which are filled from the inside to the outside between the anchor pipe and the recharge well. A permeable isolation net is provided between the inner ring reverse filter layer and the outer wall of the anchor pipe, and a geotextile separation layer is provided between the inner ring reverse filter layer and the middle ring water guiding layer.

6. A pressurized recharge and drainage device for tunnel reverse slope as described in claim 5, characterized in that: The inner ring filter layer is made of quartz sand and gravel with a particle size of 1~3mm and a filling thickness of 6~8cm; The middle ring water-conducting layer is made of basalt gravel with a particle size of 8~12mm and a filling thickness of 10~12cm; The outer ring buffer layer is made of graded sand and gravel mixture with a particle size of 5~20mm and a filling thickness of 12~15cm. The permeable mesh is made of stainless steel with a pore size of 0.5mm; The geotextile separator layer is a short-fiber needle-punched nonwoven geotextile with a basis weight ≥200g / m². 2 The fracture strength is ≥15kN / m.

7. A pressurized recharge drainage method for tunnel reverse slope, characterized in that, The device applied to the booster recharge drainage system as described in any one of claims 1 to 6 includes: Collect the accumulated water in the tunnel face area and introduce it into a filter sedimentation tank for solid-liquid separation and sedimentation treatment; The water level of the filter sedimentation tank is monitored in real time. When the water level reaches the preset high water level, the recharge pump is started to pressurize and transport the water treated by the filter sedimentation tank to the hollow inner cavity of the anchor pipe. The water seeps out through the permeable holes on the wall of the anchor pipe and is injected into the surrounding soil and rock to achieve pressurized recharge drainage. When the water level drops to the preset low water level, the recharge pump is stopped.

8. A pressurized recharge drainage method for tunnel reverse slope as described in claim 7, characterized in that, During the pressurized reinjection and drainage process, the reinjection flow rate and reinjection pressure provided by the reinjection pump are monitored in real time, and the corresponding unit pressure reinjection volume is calculated. The unit pressure reinjection volume is equal to the ratio of the reinjection flow rate to the reinjection pressure. The reinjection pressure is dynamically adjusted according to the unit pressure reinjection volume, specifically including: If the real-time value of the unit pressure reinjection volume continues to decrease within a preset time period and is lower than the preset permeability reduction threshold, the reinjection pressure will be increased in stages by 0.05~0.1MPa, and the increased reinjection pressure will not exceed the preset maximum safe pressure. If the real-time value of the unit pressure reinjection volume continues to rise within a preset time period and exceeds the preset permeability increase threshold, or if abnormal seepage or slurry leakage is detected around the reinjection well, the reinjection pressure will be reduced by 0.1~0.2MPa, and the reduced reinjection pressure will not be lower than the preset minimum safe pressure.

9. A pressurized recharge drainage method for tunnel reverse slope as described in claim 8, characterized in that: The method of dynamically adjusting the reinjection pressure based on the unit pressure reinjection volume also includes: During the phased increase of reinjection pressure, if the real-time value of the reinjection volume per unit pressure rises and exceeds the permeability reduction threshold after the increase, the increase is paused and the current reinjection pressure is maintained to continue reinjection. After reducing the reinjection pressure by 0.1~0.2MPa, if the real-time value of the unit pressure reinjection volume is lower than the permeability increase threshold and the abnormal seepage or slurry leakage disappears, then the reduced reinjection pressure is maintained and reinjection continues; otherwise, the reinjection pressure is further reduced by 0.05~0.1MPa until the minimum safe pressure is reached.

10. A pressurized recharge drainage method for tunnel reverse slope as described in claim 8, characterized in that, The hollow inner cavity of the anchor pipe is periodically flushed to remove any attached materials or blockages. During the pressurized recharge and drainage process, periodic pulse disturbance operations are performed, as follows: The current reinjection pressure value is used as the reference pressure P0; Repeat the pulse disturbance cycle 2 to 4 times. The pulse disturbance cycle includes: within 30 to 60 seconds, increasing the reinjection pressure to 1.2 to 1.8 times P0, and the reinjection pressure after the increase shall not exceed the preset maximum safe pressure, and maintaining the increased reinjection pressure for 60 to 120 seconds; within 20 to 40 seconds, decreasing the reinjection pressure to 0.3 to 0.6 times P0.

Images