Deep well roadway three-level thick layer anchoring strengthening support device

Abstract

The utility model discloses a deep well roadway three-level thick layer anchoring strengthening support device which comprises a loosening ring, a plastic zone and an elastic zone rock mass which are sequentially located on the outer ring of a roadway, the plastic zone is located on the outer ring of the loosening ring, and the elastic zone rock mass is located on the outer ring of the plastic zone. The inner wall of the roadway is anchored into the loose circle through an anchor rod in a surrounding manner; the inner wall of the roadway is anchored into the plastic area through a flexible anchor rod in a surrounding manner; the inner wall of the roadway is anchored into the rock mass of the elastic area through a long anchor cable in a surrounding mode. An existing deep thick-layer rock roadway surrounding rock supporting technology is innovated, the overall strength of an anchoring layer can be remarkably improved by adopting a three-stage thick-layer anchoring reinforced supporting mode, deformation of the deep thick-layer rock roadway surrounding rock is effectively controlled, the long-time stability of a roadway is improved, and the supporting effect is good. The bearing capacity and stability of a roadway surrounding rock structure are ensured, and the roadway stability control requirement is met; the method is simple in implementation process and low in supporting cost.

Description

Technical Field

[0001] The utility model relates to the technical field of roadway support, in particular to a three - level thick - layer anchoring and strengthening support device for deep roadway. Background Technique

[0002] In the process of underground mine production, with the increase of mining depth, the in - situ stress is high and the mining influence is strong, resulting in the fragmentation, large deformation and serious damage of roadway surrounding rock, which brings great challenges to the safe production and efficient mining of the mine. Compared with ordinary roadways, the loose and broken range of deep rock roadways is larger, the deformation and failure phenomenon is more serious, the roadway support difficulty is higher, and the existing support methods are difficult to effectively control the deformation of surrounding rock of deep thick - layer rock roadways. Traditional support methods, such as shotcrete - bolt support and steel arch support, although they can improve the stability of the roadway to a certain extent, under the condition of thick - layer rock, the support effect of these methods is often not ideal. Especially in thick - layer rock roadways, the deformation and damage of roadway surrounding rock are more serious, and traditional support means are difficult to meet the stability requirements.

[0003] At present, for deep thick - layer rock roadways, bolt and long cable - anchor support forms and roadway re - excavation after large deformation are often adopted, but this support method still has the following defects: ① Conventional support methods cannot meet the requirements of roadway stability control. The support of deep thick - layer rock roadways still consists of the combined support of conventional bolts and long cable - anchors. The length of the bolt is about 2 - 2.5m, the bolt anchoring layer is thin, and the anti - deformation ability is weak. The length of the cable - anchor is more than 6m. The cable - anchor has poor effect on strengthening a large - range rock mass under limited prestress, and the coupling support effect of bolts and cable - anchors is not good. ② The loose and broken range of the roadway is large. Due to the loose and broken surrounding rock and low rock strength, the surface cracks of the surrounding rock develop rapidly under the action of in - situ stress, mining stress and other stresses, the degree of fragmentation is high, which is extremely easy to cause large deformation of roadway surrounding rock, and even caving may occur in serious cases, and the ranges of the broken circle and plastic circle are greatly increased. ③ The re - excavation and repair work are frequent. Conventional support methods are difficult to effectively control the long - term stability of deep - broken roadways. After roadway support, large deformation and other phenomena will still occur, and it is necessary to re - excavate and repair deep thick - layer rock roadways, which greatly affects the safe production of the mine. When re - excavating after large deformation of the roadway, it is often necessary to re - arrange the support system, increasing the construction complexity and risk. At the same time, the space of the roadway after re - excavation increases, and the design and implementation difficulty of the support structure are further increased.

[0004] Bolts mainly control the shallow - part deformation of the roadway, while long cable - anchors are used to control the stability of deep - part rock masses. In some cases, these two may not form a coordinated support system, resulting in poor support effect in local areas. In addition, the bolts and cable - anchors that can be grouted in the existing schemes are both structures with grouting steel pipes in the middle, and their strength is significantly lower than that of traditional solid bolts and cable - anchors. At the same time, the cost of special steel pipes is high and the cost is high.

[0005] Therefore, in order to effectively control the surrounding rock deformation of deep thick-layer rock roadways to meet the control requirements of roadway stability, there is an urgent need to provide a device capable of strengthening the support of the surrounding rock of deep thick-layer rock roadways. Summary of the Invention

[0006] The technical problem to be solved by the present utility model is: how to provide a device capable of strengthening the support of the surrounding rock of deep thick-layer rock roadways.

[0007] To solve the above technical problem, the present utility model provides the following technical solutions:

[0008] A three-level thick-layer anchoring and strengthening support device for deep well roadways, including loose circle, plastic zone and elastic zone rock masses located in the outer circle of the roadway in sequence. The plastic zone is located in the outer circle of the loose circle, and the elastic zone rock mass is located in the outer circle of the plastic zone;

[0009] The inner wall of the roadway is surrounded and anchored into the loose circle through bolts;

[0010] The inner wall of the roadway is surrounded and anchored into the plastic zone through flexible bolts. An integrated anchor grouting device is connected to the flexible bolts, and grout is injected into the plastic zone through the integrated anchor grouting device;

[0011] The inner wall of the roadway is surrounded and anchored into the elastic zone rock mass through long cable bolts. An integrated anchor grouting device is connected to the long cable bolts, and grout is injected into the elastic zone rock mass through the integrated anchor grouting device.

[0012] This application innovates the existing support technology for the surrounding rock of deep thick-layer rock roadways. The method of three-level thick-layer anchoring and strengthening support can significantly improve the overall strength of the anchoring layer, effectively control the deformation of the surrounding rock of deep thick-layer rock roadways, improve the long-term stability of the roadways, ensure the bearing capacity and stability of the surrounding rock structure of the roadways, and meet the requirements of roadway stability control; the implementation process of this method is simple and the support cost is low. It can effectively cope with the situation of large loose and broken range, serious deformation and failure phenomena, and difficult roadway support in deep rock roadways, significantly improving the overall support effect of the surrounding rock of the roadways. Especially under the condition of thick-layer rock, it can also achieve good support effect; and by using the integrated anchor grouting device to cooperate with flexible bolts for shallow surrounding rock grouting, the loose surrounding rock can be fully cemented by the injected grout, improving the defect of insufficient bearing capacity caused by relying solely on the self-strength of broken rock.

[0013] As a further solution of the present utility model: the flexible bolt includes a flexible bolt body, a locking sleeve and an arch-shaped tray. One end of the flexible bolt body is inserted into the loose circle and the plastic zone, and a locking sleeve is arranged on the outer side of the other end. An arch-shaped tray is arranged on the outer side of the locking sleeve and fixed to the inner wall of the roadway.

[0014] As a further solution of the utility model: A yielding ring is also fixed by a ball head nut on the outer side of the locking sleeve and on one side of the arch-shaped tray.

[0015] As a further solution of the utility model: The integrated bolt-grouting device includes an anti-twist tray, a bolt-grouting sleeve and a grouting elbow pipe. An anti-twist tray is also arranged on the inner side of the arch-shaped tray and on the outer side of the flexible bolt body. A bolt-grouting sleeve is arranged on one side of the anti-twist tray. One end of the bolt-grouting sleeve is inserted into the loose circle, and the other end of the bolt-grouting sleeve is connected to the grouting elbow pipe.

[0016] As a further solution of the utility model: A sealing sleeve is fixed between the outer side of the bolt-grouting sleeve and the borehole of the loose circle.

[0017] As a further solution of the utility model: The diameter of the long anchor cable is greater than the diameter of the flexible bolt which is greater than the diameter of the bolt.

[0018] As a further solution of the utility model: A plurality of flexible bolts are provided, and the spacing range between adjacent two flexible bolts is 600-1000mm.

[0019] As a further solution of the utility model: The radius of the plastic zone is greater than the radius of the loose circle.

[0020] Compared with the prior art, the beneficial effects of the utility model are as follows:

[0021] 1. This application innovates the existing support technology for the surrounding rock of deep thick-layer rock roadways. The method of adopting three-level thick-layer anchoring and strengthening support can significantly improve the overall strength of the anchoring layer, effectively control the deformation of the surrounding rock of deep thick-layer rock roadways, improve the long-term stability of the roadways, ensure the bearing capacity and stability of the surrounding rock structure of the roadways, and meet the requirements of roadway stability control; The implementation process of this method is simple and the support cost is low. It can effectively cope with the situation of large loose and broken range, serious deformation and damage phenomenon, and difficult roadway support in deep rock roadways, and significantly improve the overall support effect of the roadway surrounding rock. Especially under the condition of thick-layer rock, it can also have an effective and good support effect;

[0022] 2. This application uses a number of bolts anchored deep into the loose circle to construct a primary support structure, which can tightly combine the loose surrounding rock within the loose circle into an integral structure. It not only avoids the further fragmentation of the loose surrounding rock, but also enables the loose surrounding rock within the loose circle to have self-bearing capacity, which is conducive to uniform load transfer for the secondary support structure and the tertiary support structure;

[0023] 3. The present application constructs a secondary support structure by using several flexible bolts anchored in the shallow stable surrounding rock on the periphery of the loosening zone. It can closely combine the loosening zone anchored as an integral structure with the shallow stable surrounding rock, further forming a larger integral structure. In this way, the surrounding pressure of the roadway surrounding rock is significantly increased by the combined support of bolts and flexible bolts, and the self-bearing capacity of the integral structure is effectively improved, which is conducive to the transfer of greater loads;

[0024] 4. The present application constructs a tertiary support structure by using several long cable bolts anchored in the deep stable surrounding rock on the periphery of the shallow stable surrounding rock. It can closely combine the loosening zone anchored as an integral structure, the shallow stable surrounding rock, and the deep stable surrounding rock, further forming the largest integral structure. Thus, the roadway surrounding rock is reinforced three times by the coupling support of bolts, flexible bolts, and long cable bolts, significantly increasing the overall strength of the anchorage layer and constructing a thick anchorage layer with good stability and strong bearing capacity, effectively improving the stability of the thick-layer rock roadway and ensuring the safety of roadway construction;

[0025] 5. On the basis of the thick anchorage layer, the present application uses an integrated bolt-grouting device to cooperate with flexible bolts for grouting the shallow surrounding rock. The grouting liquid can be used to fully cement the loose surrounding rock, improving the defect of insufficient bearing capacity caused by solely relying on the strength of the broken rock itself. Furthermore, the mechanical properties of the loosening zone surrounding rock are changed, avoiding the short-board effect of the support and enhancing the overall bearing capacity of the surrounding rock; Based on the shallow surrounding rock grouting, deep pressure-increasing grouting is carried out, which can effectively improve the modification effect of the deep surrounding rock grouting, and then significantly enhance the strength and stability of the deep surrounding rock. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic structural diagram of the three-level thick-layer anchoring and strengthening support for the deep well roadway in the embodiment of the present utility model;

[0027] Figure 2 It is a schematic diagram of the cooperation between the integrated bolt-grouting device and the flexible bolt in the embodiment of the present utility model;

[0028] DESCRIPTION OF THE REFERENCE NUMERALS

[0029] 1, roadway; 2, loosening zone; 3, bolt;

[0030] 4, flexible bolt; 41, flexible bolt body; 42, locking sleeve; 43, ball head nut; 44, yielding ring; 45, arched tray;

[0031] 5, long cable bolt; 6, plastic zone; 7, anti-twist tray; 8, grouting elbow; 9, bolt-grouting sleeve; 10, sealing sleeve. DETAILED DESCRIPTION OF THE INVENTION

[0032] To make the objectives, technical solutions and advantages of the embodiments of the present utility model clearer, the technical solutions in the embodiments of the present utility model will be clearly and completely described below in conjunction with the embodiments of the present utility model. Obviously, the described embodiments are some but not all of the embodiments of the present utility model. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present utility model without creative efforts shall fall within the protection scope of the present utility model.

[0033] Referring to Figure 1 , successively around the outer circle of the roadway 1 are the loosening zone 2, the plastic zone 6 rock mass and the elastic zone rock mass, where the plastic zone 6 rock mass is located outside the loosening zone 2, and the elastic zone rock mass is located outside the plastic zone 6 rock mass;

[0034] Referring to Figure 1 , a three - level thick - layer anchoring and strengthening support device for deep - well roadways includes bolts 3, flexible bolts 4, long cable bolts 5, anti - torsion trays 7, grouting elbow pipes 8, grouting sleeves 9 and sealing sleeves 10. Among them, several bolts 3 are anchored into the loosening zone 2 from the inner wall of the roadway 1 around the roadway to achieve the primary support of the deep well; then, flexible bolts 4 are anchored into the plastic zone 6 from the inner wall of the roadway 1 around the roadway. An integrated grouting and anchoring device is connected to the flexible bolt 4, and grout is injected into the plastic zone 6 through the integrated grouting and anchoring device to achieve the secondary support of the deep well; long cable bolts 5 are anchored into the elastic zone rock mass from the inner wall of the roadway 1 around the roadway. An integrated grouting and anchoring device is connected to the long cable bolt 5, and grout is injected into the elastic zone rock mass through the integrated grouting and anchoring device to achieve the tertiary support of the deep well.

[0035] It should be noted that the diameter of the long cable bolt 5 is greater than the diameter of the flexible bolt 4 which is greater than the diameter of the bolt 3, and the radius of the plastic zone 6 is greater than the radius of the loosening zone 2.

[0036] It should be noted that in order to enable the loosening zone to form a structurally tight and performance - stable overall structure with the deep - seated stable surrounding rock, in step S3, the spacing and row spacing range of the flexible bolts 4 are both 600 - 1000 mm; the range of the flexible bolts 4 here is for reference only and should not be construed as a limitation of this application.

[0037] As a preference, the bolt 3 is a deformed steel bolt.

[0038] Among them, the flexible bolt 4 includes a flexible bolt body 41, a locking sleeve 42, a ball - head nut 43, a yielding ring 44 and an arch - shaped tray 45. One end of the flexible bolt body 41 is inserted into the loosening zone and the plastic zone, and the other end is provided with a locking sleeve 42 on the outer side. An arch - shaped tray 45 is arranged on the outer side of the locking sleeve 42 and fixed to the inner wall of the roadway. A yielding ring 44 is also fixed by a ball - head nut 43 on the outer side of the locking sleeve 42 and on one side of the arch - shaped tray 45;

[0039] The integrated bolting and grouting device includes an anti-twist tray 7, a grouting casing 9, a sealing sleeve 10, and a grouting elbow 8. An anti-twist tray 7 is further provided on the outer side of the flexible bolt body 41 and inside the arch-shaped tray 45. A grouting casing 9 is provided on one side of the anti-twist tray 7. One end of the grouting casing 9 is inserted into the loosened zone and fixed with a sealing sleeve between it and the loosened zone. The other end of the grouting casing 9 is connected to the grouting elbow 8;

[0040] The construction method of the flexible bolt 4 in cooperation with the integrated bolting and grouting device is as follows: First, put the anti-twist tray 7 on the grouting casing 9, then put the sealing sleeve 10 on the flexible bolt rod body 41, then tighten the grouting elbow 8 and adjust its direction to be opposite to the flexible bolt rod body 41. Finally, install the sealing ring on the side of the bolt near the rock surface to construct the flexible bolt and the integrated bolting and grouting device.

[0041] The construction method of the long cable bolt 5 in cooperation with the integrated bolting and grouting device: Increase the length of the grouting casing 9, install the integrated bolting and grouting device outside the long cable bolt 5 in the same way, and then carry out the construction in the same way.

[0042] The specific operation method of this application is as follows:

[0043] Step S1: After the roadway 1 is excavated, determine the range of the loosened zone 2 in the surrounding rock of the roadway;

[0044] It should be noted that in step S1, the range of the loosened zone 2 in the surrounding rock of the roadway is determined by methods such as theoretical calculation, numerical simulation, or on-site measurement. The radius of the loosened zone 2 is R;

[0045] In order to accurately determine the range of the loosened zone 2, in step S1, the radius R of the loosened zone 2 in the surrounding rock 6 of the roadway is determined according to formula (1);

[0046]

[0047] In the formula, c is the cohesion of the rock mass; γ is the unit weight of the rock mass; φ is the internal friction angle of the rock mass; σ0 is the initial in-situ stress; σc is the uniaxial compressive strength of the rock mass.

[0048] Step S2: According to the different ranges of the loosened zone 2, determine the thickness of the anchorage layer to be constructed and select a flexible bolt 4 with a suitable length;

[0049] It should be noted that in order to ensure the effect of subsequent support and fully improve the bearing capacity and stability of the surrounding rock structure of the roadway, in step S2, the thickness of the anchorage layer to be constructed (i.e., the thickness of the plastic zone 6) is greater than the radius R of the loosened zone 2.

[0050] Step S3: Construct a thick anchorage layer through three - level support, that is, a primary support structure with bolt 3 as the support material. A number of bolts 3 are anchored deep into the loosening zone 2 around the roadway 1 to form a shallow - layer extrusion arch bearing structure (i.e., the arch - shaped radius range formed after the bolts are introduced into the loosening zone 2). A secondary support structure with flexible bolt 4 as the support material. A number of flexible bolts 4 are anchored into the shallow - layer stable surrounding rock on the periphery of the loosening zone 2 of the roadway 1, that is, the plastic zone 6, to construct a thick anchorage layer structure; and a tertiary support structure with long cable bolt 5 as the support material. A number of long cable bolts 5 are anchored into the deep - layer stable surrounding rock on the periphery of the shallow - layer stable surrounding rock around the roadway 1 to maintain the stability of the surrounding rock 6 of the deep - well roadway.

[0051] In step S3, the radius range of the extrusion arch formed by the bolts is set as b, and the calculation formula (2) for the radius b is:

[0052]

[0053] Where l is the length of the bolt, α is the control angle of the bolt for the broken rock mass, and a is the bolt spacing.

[0054] In order to ensure the effect of subsequent grouting modification and effectively utilize the injected grout to cooperate with the bolts and cable bolts to improve the anchoring effect synergistically, in step S3, after the support of the roadway 1, shotcreting operation is carried out on the surface of the anchored roadway 1 to seal the surface of the surrounding rock, and the thickness range of the shotcrete layer is ensured to be 5 - 30 mm to provide a grout - stopping layer for subsequent grouting. The thickness range here is for reference only and should not be construed as a limitation to this application.

[0055] As a preference, in step S3, the length of bolt 3 is not greater than 3 m, the length range of flexible bolt 4 is 3 - 6 m, and the length of long cable bolt 5 is greater than 6 m. The length ranges of bolt 3, flexible bolt 4, and long cable bolt 5 here are one of the implementation manners provided by this application and should not be construed as a limitation to this application.

[0056] In order to be conducive to the collaborative control of the surrounding rock through the three - layer anchoring structure, so that the thick - layer rock roadway can form an integral whole to fully improve the anchoring effect. At the same time, in order to reduce the situation of the bolts, flexible bolts 4, and long cable bolts 5 breaking, in step S3, the difference between the length of long cable bolt 5 and the length of flexible bolt is not greater than 3 m, and the difference between the length of flexible bolt 4 and the length of bolt 3 is not greater than 3 m.

[0057] Step S4: According to the fragmentation degree of the surrounding rock 6 of the roadway and the range of the loosening zone 2, use an integrated bolt - grouting device to cooperate with flexible bolt 4 for shallow - layer surrounding - rock grouting;

[0058] Alternatively, according to the actual fragmentation condition of the surrounding rock in the roadway and in combination with the obtained range of the loosening zone 2, optionally, the original long cable bolts 5 in the support are replaced with hollow grouting cable bolts, and deep-hole pressure-increasing grouting is carried out on the basis of the shallow grouting layer. By increasing the grouting pressure, the grouting modification effect of the deep surrounding rock is improved.

[0059] It should be noted that, in order to fully ensure the effect of grouting and anchoring, in step S4, when shallow surrounding rock grouting is adopted, cement slurry or other grouting materials with relatively low fluidity are selected; when deep pressure-increasing grouting is adopted, chemical slurries with characteristics such as strong fluidity and slow setting time are selected.

[0060] Furthermore, in order to fully improve the bearing capacity and stability of the surrounding rock structure in the roadway, in step S4, when the grouting modification of the shallow surrounding rock in the roadway is carried out by cooperating with the flexible bolt 4 through the integrated bolt-grouting device, the slurry is diffused from the integrated bolt-grouting device into the cracks of the fragmented surrounding rock, and the surrounding rock within the anchoring range of the flexible bolt 4 is fully reinforced, and the injected slurry and the primary support are used together to maintain the stability of the surface surrounding rock.

[0061] The method of deep pressure-increasing grouting is as follows: First, shallow surrounding rock grouting is carried out through the grouting elbow 8 exposed by the flexible bolt 4 and the integrated bolt-grouting device after installation and construction, with the aim of forming a grout-stop layer within the range of the shallow surrounding rock in the roadway. Subsequently, deep grouting of the surrounding rock is carried out through the long cable bolt 5 after installation and construction and the integrated bolt-grouting device with a longer anchor-grouting sleeve 8 length. Due to the effect of the shallow grout-stop layer, a relatively large grouting pressure and diffusion range are allowed.

[0062] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A three-level thick layer anchoring and strengthening support device for deep well tunnels, characterized in that: It comprises a loose zone (2), a plastic zone (6) and an elastic zone rock mass which are sequentially located on the outer ring of a roadway (1), wherein the plastic zone (6) is located on the outer ring of the loose zone (2), and the elastic zone rock mass is located on the outer ring of the plastic zone (6); The inner wall of the tunnel (1) is anchored into the loose circle (2) by anchor rods (3) in a surrounding manner; The inner wall of the tunnel (1) is anchored into the plastic zone (6) by a flexible anchor rod (4) in a surrounding manner, wherein the flexible anchor rod (4) is connected to an anchor-grouting integrated device, and grouting is injected into the plastic zone (6) through the anchor-grouting integrated device; The inner wall of the tunnel (1) is anchored into the elastic zone rock mass in a surrounding manner through a long anchor cable (5), wherein the long anchor cable (5) is connected to an anchor-grouting integrated device, and grouting is injected into the elastic zone rock mass through the anchor-grouting integrated device.

2. A three-level thick layer anchoring and strengthening support device for deep well tunnels according to claim 1, characterized in that: The flexible anchor rod (4) comprises a flexible anchor rod body (41), a locking sleeve (42) and an arched tray (45), wherein one end of the flexible anchor rod body (41) is inserted into the loosening circle (2) and the plastic zone (6), and the locking sleeve (42) is provided on the outside of the other end, and the arched tray (45) is arranged on the outside of the locking sleeve (42) and fixed to the inner wall of the tunnel.

3. A three-level thick layer anchoring and strengthening support device for deep well tunnels according to claim 2, characterized in that: A pressure ring (44) is fixed on the outer side of the locking sleeve (42) and on one side of the arched tray (45) via a ball nut (43).

4. A three-level thick layer anchoring and strengthening support device for deep well tunnels according to claim 2, characterized in that: The anchor-grouting integrated device comprises an anti-twist tray (7), an anchor-grouting sleeve (9) and a grouting elbow (8), wherein an anti-twist tray (7) is further provided on the outside of the flexible anchor rod body (41) and inside the arch tray (45), and an anchor-grouting sleeve (9) is further provided on one side of the anti-twist tray (7), one end of the anchor-grouting sleeve (9) is inserted into the loosening ring, and the other end of the anchor-grouting sleeve (9) is connected to the grouting elbow (8).

5. A three-level thick layer anchoring and strengthening support device for deep well tunnels according to claim 4, characterized in that: A sealing sleeve (10) is arranged outside the anchoring sleeve (9) and fixed between the borehole of the loosening ring (2).

6. The three-level thick layer anchoring and strengthening support device for deep well tunnel according to claim 1 is characterized in that: The diameter of the long anchor cable (5) is larger than the diameter of the flexible anchor rod (4) and larger than the diameter of the anchor rod (3).

7. The deep well tunnel three-level thick layer anchoring reinforcement support device according to claim 1 is characterized in that: A plurality of flexible anchor rods (4) are provided, and the distance between two adjacent flexible anchor rods (4) is in the range of 600 to 1000 mm.

8. The deep well tunnel three-level thick layer anchoring reinforcement support device according to claim 1 is characterized in that: The radius of the plastic zone (6) is greater than the radius of the loose zone (2).

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