阅读说明：本技术 一种扩径套管混凝土桩及其施工方法 (Expanded casing concrete pile and construction method thereof ) 是由 章丽莎 应宏伟 李冰河 张金红 刘冠 于 2021-09-17 设计创作，主要内容包括：本发明公开了一种扩径套管混凝土桩及其施工方法,属于软土地基处理及桩基础技术领域,包括自下而上连接的预制锥尖、桩身套筒和预制桩头,桩身套筒由塑料套管和扩径套管交替连接组成,扩径套管的内侧套设有加劲筒,加劲筒由两个刚性环和若干个加劲肋组成,刚性环位于扩径套管的上下两端,加劲肋分布在刚性环的周向上,刚性环与加劲肋固定连接；通过刚性环支撑扩径套管的两端,通过加劲肋支撑扩径套管的主体。在注浆压力下,扩径套管发生膨胀,扩径套管能与桩侧土体紧密接触,从而能快速生成桩侧摩阻力；塑料排水板能及时排出打设混凝土桩所产生的超静孔隙水压力,有效提高软土地基强度,进一步提高扩径套管混凝土桩的承载力。(The invention discloses an expanding sleeve concrete pile and a construction method thereof, belonging to the technical field of soft soil foundation treatment and pile foundation, comprising a prefabricated cone tip, a pile body sleeve and a prefabricated pile head which are connected from bottom to top, wherein the pile body sleeve is formed by alternately connecting plastic sleeves and expanding sleeves; the two ends of the expanding sleeve are supported by the rigid rings, and the main body of the expanding sleeve is supported by the stiffening ribs. Under the grouting pressure, the expanding sleeve expands and can be in close contact with the soil body on the pile side, so that the pile side frictional resistance can be quickly generated; the plastic drainage plate can timely discharge the ultra-static pore water pressure generated by driving the concrete pile, effectively improve the strength of the soft soil foundation and further improve the bearing capacity of the expanded casing concrete pile.)

1. An expanded casing concrete pile comprises a prefabricated cone tip, a pile body sleeve and a prefabricated pile head which are connected from bottom to top, and is characterized in that the pile body sleeve is formed by alternately connecting plastic sleeves and expanded sleeves, a stiffening cylinder is sleeved on the inner side of the expanded sleeve and consists of two rigid rings and a plurality of stiffening ribs, the rigid rings are positioned at the upper end and the lower end of the expanded sleeve, the stiffening ribs are distributed on the circumferential direction of the rigid rings, and the rigid rings are fixedly connected with the stiffening ribs; the two ends of the expanding sleeve are supported by the rigid rings, and the main body of the expanding sleeve is supported by the stiffening ribs.

2. The expanded casing concrete pile according to claim 1, wherein a casing connector is fixedly connected to the prefabricated cone tip, and the pile body sleeve is fixedly connected to the prefabricated cone tip through the casing connector.

3. The expanded casing concrete pile according to claim 1, wherein the top end and the bottom end of the pile body sleeve are plastic casings, and the plastic casings are arranged outside the expanded casing.

4. The concrete pile with an enlarged sleeve according to claim 1, wherein the material of the enlarged sleeve is rubber, and the enlarged sleeve deforms and expands radially under grouting pressure after concrete is poured into the enlarged sleeve.

5. The expanded casing concrete pile according to claim 1, wherein the stiffening cylinder is made of stainless steel, the number of the stiffening ribs is four, and the stiffening ribs are uniformly distributed along the circumferential direction of the rigid ring.

6. The method for constructing an expanded casing concrete pile according to any one of claims 1 to 5, comprising the steps of:

s1, measuring and paying off, and determining pile positions and inserting and beating positions of plastic drainage plates among piles; inserting and punching a plastic drainage plate, and connecting a drainage system with the plastic drainage plate through a drainage pipe; drilling holes at the characteristic positions, mounting a plurality of pore water pressure sensors, backfilling, and connecting the pore water pressure sensors with a collecting system through leads;

s2, inserting the pile body sleeve into the sleeve connecting piece of the prefabricated conical tip for fixed connection;

s3, inserting the pile body sleeve connected with the prefabricated conical tip into a steel cylinder of the pile driver by using a lifting rope, wherein the lower end of the steel cylinder props against the prefabricated conical tip; then, starting a pile driver, vertically and downwards driving a pile body sleeve with a prefabricated conical tip into a foundation, and starting a drainage system connected with a plastic drainage plate to continuously drain outwards;

s4, after the prefabricated cone point reaches the designed pile depth, injecting water into the pile body sleeve, pulling up the steel cylinder after 1/2 pile long water is injected, injecting water while pulling up, and keeping the pile body sleeve and the prefabricated cone point in the foundation;

s5, repeating the steps S3 and S4 until all pile body sleeves are completely drilled, completely pumping water in the pile body sleeves by using a water pump, uniformly pouring concrete into the pile body sleeves, and vibrating to be compact;

s6, installing a prefabricated pile head, and inserting a reserved steel bar of the prefabricated pile head into the concrete poured in the pile body sleeve;

and S7, paving a sand-stone cushion layer after paving large-area high-strength geotextile on the top of the precast pile head, wherein a drain pipe connected with the drain plate is arranged in the sand-stone cushion layer.

7. The method for constructing an enlarged casing concrete pile according to claim 6, wherein said step S5 further comprises grouting a gap between a pile body sleeve of the enlarged casing concrete pile and a soil body.

8. The method for constructing an expanded casing concrete pile according to claim 6, wherein in step S1, the drainage system includes a vacuum pump and a mud-water separation device.

Technical Field

The invention belongs to the technical field of soft soil foundation treatment and pile foundations, and particularly relates to an expanded casing concrete pile and a construction method thereof.

Background

As a soft foundation treatment technology, the plastic sleeve concrete pile is mainly applied to projects such as expressways, trunk roads, municipal roads and the like in soft soil areas, and achieves a good project reinforcing effect.

In the traditional plastic sleeve concrete pile construction process, a plastic sleeve is inserted into a steel cylinder of a pile driver, and after the front end of the steel cylinder props against a prefabricated pile tip, the prefabricated cone tip and a pile body sleeve are driven into a foundation in a static pressure or impact vibration mode. Therefore, the diameter of the pile body of the plastic sleeve concrete pile is certainly smaller than the radial size of the prefabricated cone tip, so that the pile soil in the main body range of the pile body is emptied in a large area, and the bearing capacity of the plastic sleeve concrete pile is almost provided only by the resistance of the pile end. Along with the time extension, the ultra-static pore water pressure in the driving area of the plastic sleeve concrete pile is slowly dissipated, the side frictional resistance of the pile is gradually formed and continuously increased after the pile soil is slowly contacted, and the bearing capacity of the pile is increased. Therefore, the early bearing capacity strength of the traditional plastic sleeve concrete pile is seriously insufficient and is easily influenced by soil layer permeability and pile driving construction site factors, the time for the bearing capacity to meet the design requirement is difficult to determine, and certain engineering risks exist. Chinese patent CN 101532290B discloses a plastic sleeve grouting pile for reinforcing soft soil foundation and a pile-forming reinforcing construction method thereof, the pile is composed of a pile cap, a threaded sleeve, geotextile, a joint, a pile body and a pile tip, the top of the sleeve is connected with the pile cap, the bottom is connected with the pile tip, the side wall of the sleeve is provided with an opening, the geotextile is coated outside, each section of sleeve is connected with the joint, granules are put in the sleeve and grouted, and the periphery of the pile body and the pile are slurry diffusion zones: the pile-forming reinforcing method is that the sleeve is connected to the pile length depth by means of joint, then the pile tip is connected and placed in the immersed tube together, the sleeve is driven into the foundation by means of driving machine, the sleeve and pile tip are remained in the foundation, the granular material is placed into the sleeve and grouted so as to form the slurry solid bulk material column body, under the condition of grouting pressure the slurry is diffused around the pile to form diffusion zone or the geotechnical cloth is expanded outwards so as to form calabash pile body, the pile cap is poured on the pile top, after the pile body and pile cap are dried and solidified, the reinforced material and broken stone cushion layer are laid so as to form the composite foundation. However, the pile-type slurry is easy to diffuse and pollute the environment, and particularly when the pile-type slurry meets a gravel soil or gravel layer with good permeability, the cement consumption is too large, and the requirements of low carbon and environmental protection are not met; meanwhile, as with the traditional plastic sleeve concrete pile, the pile tip with the inner diameter larger than the diameter of the pile body is adopted, and the pile tip and the sleeve are driven into the foundation in a static pressure or impact vibration mode, so that the early bearing capacity strength of the pile body is insufficient.

In addition, after the pile is sunk, due to the soil squeezing effect of the pile body, hyperstatic pore water pressure can be generated in the surrounding soil body, the pore water pressure around the pile body is slowly dissipated in the normal construction process, and the pile side can be subjected to downward negative friction resistance after the soil body is solidified, so that the bearing capacity of the pile is reduced. Therefore, in order to reduce the above negative effects caused by pile sinking and soil squeezing in construction, the hyperstatic pore water pressure generated by the soil squeezing effect in the construction process must be reduced and the dissipation thereof is accelerated; the drainage effect of the foundation in the construction process is directly related to the quality of the pile sinking.

Therefore, in order to solve the problem that the early bearing capacity of the existing plastic sleeve concrete pile is insufficient and ensure the construction efficiency and the reinforcement effect of the plastic sleeve concrete pile for reinforcing the soft soil foundation, the development of the sleeve concrete pile which can increase the pile side frictional resistance and can drain water and the construction method thereof are particularly urgent.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides the expanding sleeve concrete pile, which can quickly generate and utilize the side frictional resistance of the pile and effectively improve the early bearing capacity of the expanding sleeve concrete pile.

In order to achieve the purpose of the invention, the method is specifically realized by the following technologies:

an expanded casing concrete pile comprises a prefabricated cone tip, a pile body sleeve and a prefabricated pile head which are connected from bottom to top, wherein the pile body sleeve is formed by alternately connecting plastic sleeves and expanded sleeves, a stiffening cylinder is sleeved on the inner side of each expanded sleeve and consists of two rigid rings and a plurality of stiffening ribs, the rigid rings are positioned at the upper end and the lower end of each expanded sleeve, the stiffening ribs are distributed on the circumferential direction of the rigid rings, and the rigid rings are fixedly connected with the stiffening ribs; the two ends of the expanding sleeve are supported by the rigid rings, and the main body of the expanding sleeve is supported by the stiffening ribs.

In the process of pouring concrete, the diameter-expanding sleeve of the diameter-expanding sleeve concrete pile expands under the grouting pressure, and the diameter of the diameter-expanding sleeve can be close to or larger than that of the prefabricated cone tip; the expanding sleeve can be in close contact with the soil body on the pile side, so that the pile side frictional resistance can be generated quickly, the early bearing capacity of the concrete pile of the expanding sleeve can be effectively improved, and the reinforcement speed of a soft soil foundation can be improved. In addition, a stiffening cylinder is arranged in the expanding sleeve, so that the expanding effect can be achieved, and the pile body length of the concrete pile of the expanding sleeve can be ensured.

Furthermore, a sleeve connecting piece is fixedly connected to the prefabricated cone tip, and the pile body sleeve is fixedly connected with the prefabricated cone tip through the sleeve connecting piece.

Furthermore, the top end and the bottom end of the pile body sleeve are both plastic sleeves, and the plastic sleeves are sleeved outside the expanding sleeve. The bottom end of the pile body sleeve is provided with a plastic sleeve, and the plastic sleeve has small deformation degree after concrete is poured and is convenient to be fixedly connected with the prefabricated conical tip; the top end of the pile body sleeve is a plastic sleeve which is convenient to be fixedly connected with the prefabricated pile head.

Furthermore, the diameter-expanding sleeve is made of rubber, and after concrete is poured into the diameter-expanding sleeve, the diameter-expanding sleeve deforms and expands in the radial direction under grouting pressure. The elastic modulus and the thickness of the rubber are determined according to the designed diameter expansion value of the diameter expansion sleeve concrete pile; the arrangement of the expanding sleeve should avoid the stratum containing sharp gravel to prevent the expanding sleeve from being damaged to cause water leakage and slurry leakage.

Furthermore, the material of a stiffening section of thick bamboo is the stainless steel, the quantity of stiffening rib is four, the stiffening rib is followed the circumference evenly distributed of rigid ring. The expanded diameter sleeve is convenient to support.

The invention also provides a construction method of the expanded casing concrete pile, which comprises the following steps:

s1, measuring and paying off, and determining pile positions and inserting and beating positions of plastic drainage plates among piles; inserting and punching a plastic drainage plate, and connecting a drainage system with the plastic drainage plate through a drainage pipe; drilling holes at the characteristic positions, mounting a plurality of pore water pressure sensors, backfilling, and connecting the pore water pressure sensors with a collecting system through leads;

s2, inserting the pile body sleeve into the sleeve connecting piece of the prefabricated conical tip for fixed connection;

s3, inserting the pile body sleeve connected with the prefabricated conical tip into a steel cylinder of the pile driver by using a lifting rope, wherein the lower end of the steel cylinder props against the prefabricated conical tip; then, starting a pile driver, vertically and downwards driving a pile body sleeve with a prefabricated conical tip into a foundation, and starting a drainage system connected with a plastic drainage plate to continuously drain outwards;

s4, after the prefabricated cone point reaches the designed pile depth, injecting water into the pile body sleeve, pulling up the steel cylinder after 1/2 pile long water is injected, injecting water while pulling up, and keeping the pile body sleeve and the prefabricated cone point in the foundation;

s5, repeating the steps S3 and S4 until all pile body sleeves are completely drilled, completely pumping water in the pile body sleeves by using a water pump, uniformly pouring concrete into the pile body sleeves, and vibrating to be compact;

s6, installing a prefabricated pile head, and inserting a reserved steel bar of the prefabricated pile head into the concrete poured in the pile body sleeve;

and S7, paving a sand-stone cushion layer after paving large-area high-strength geotextile on the top of the precast pile head, wherein a drain pipe connected with the drain plate is arranged in the sand-stone cushion layer.

Further, in step S5, grouting is performed between the pile body sleeve of the expanded casing concrete pile and the soil body.

Further, in step S1, the drainage system includes a vacuum pump and a mud-water separation device.

Further, in step S7, the high-strength geotextile at the top of the precast pile head is connected into a whole. The integrity of the expanded casing concrete pile in the soft soil foundation is improved, and the reinforcing effect of the soft soil foundation is improved.

Starting from the root cause of insufficient early bearing capacity of the traditional sleeve concrete pile, on one hand, the invention adopts the expanding sleeve to solve the problem of pile soil void caused by using a prefabricated cone tip (the inner diameter of which is larger than the diameter of the pile body) and a pile body sleeve, so that the pile body is in close contact with the soil body on the pile side, and the friction force on the pile side can be quickly generated; on the other hand, the plastic drainage plate can quickly dissipate the ultra-static pore water pressure generated by the static pressure or impact vibration pile forming mode, improve the effective stress of the soil body and the bearing capacity of the foundation, increase the friction force of the pile soil, enable the expanded casing concrete pile to exert the bearing capacity as soon as possible, and effectively improve the early bearing capacity of the expanded casing concrete pile; the early bearing capacity of the concrete pile is improved through the joint action of the expanding sleeve and the plastic drainage plate.

Compared with the prior art, the invention has the advantages that:

(1) in the concrete pouring and vibrating process, the expanding sleeve expands radially and is in close contact with the soil body on the pile side, so that the pile side frictional resistance can be generated quickly, and the early bearing capacity of the expanding sleeve concrete pile is improved effectively; in addition, the bearing capacity of the pile body can be increased and the deformation of the pile body can be reduced in the long-term service process of the expanded casing concrete pile.

(2) The plastic drainage plate can timely discharge the ultra-static pore water pressure generated by driving the expanded casing concrete pile through a drainage system, thereby effectively improving the strength of a soft soil foundation; the pile side friction resistance and the bearing capacity of the expanded casing concrete pile are further improved, the foundation reinforcement speed is increased, and the foundation reinforcement effect is improved.

(3) The high-strength geotextile which is connected into a whole in a large area is laid and fixed at the top of the precast pile head, the integrity of the large-area expanded casing concrete pile in the soft soil foundation can be improved, and the reinforcing effect of the soft soil foundation is improved.

(4) In the construction method, the gap between the pile body sleeve and the soil body is grouted, so that the soil around the pile can be improved, the side frictional resistance of the pile is further improved, and the reinforcing speed and the reinforcing effect of the soft soil foundation are improved.

(5) The plastic drainage plate is reserved in the reinforced soil body, and can drain accumulated water in the soil layer in time in the long-term service process of the reinforced foundation of the expanded casing concrete pile, so that the strength and the stability of the foundation are ensured.

Drawings

Fig. 1 is a schematic structural view of an expanded casing concrete pile according to an embodiment of the present invention;

FIG. 2 is a schematic sectional view taken along line A-A of FIG. 1;

FIG. 3 is a schematic cross-sectional view taken along line B-B of FIG. 1;

FIG. 4 is a schematic cross-sectional view of an expanded casing concrete pile according to an embodiment of the present invention after completion of construction;

wherein: 1. a plastic sleeve; 2. a stiffening cylinder; 2-1, a rigid ring; 2-2, a stiffening rib; 3. expanding the sleeve; 4. a casing connector; 5. prefabricating a cone tip; 6. concrete; 7. and (5) prefabricating the pile head.

Detailed Description

The technical solutions of the present invention will be described clearly and completely below, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In the description of the present invention, it should be noted that the terms "middle", "upper", "lower", "left", "right", "inner", "outer", etc. indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplification of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," "third," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

The technical solution of the present invention will be described in detail with reference to the accompanying drawings in conjunction with embodiments.

As shown in fig. 1 to 4, the embodiment provides an expanded casing concrete pile, which includes a prefabricated cone 5, a pile body sleeve and a prefabricated pile head 7 connected from bottom to top, wherein a casing connector 4 is fixedly connected to the prefabricated cone 5, and the pile body sleeve and the prefabricated cone 5 are tightly connected through the casing connector 4; concrete 6 is poured in the pile body sleeve, the pile body sleeve is formed by alternately connecting plastic sleeves 1 and expanding sleeves 3 from bottom to top, and the upper end and the lower end of the pile body sleeve are both the plastic sleeves 1; the plastic sleeve 1 is sleeved outside the expanding sleeve 3, and the end head between the plastic sleeve 1 and the expanding sleeve 3 is firmly connected by PVC adhesive; the expanding sleeve 3 is made of rubber, and the elastic modulus and the thickness of the expanding sleeve are determined according to the expanding design value of the concrete pile of the expanding sleeve; the inner side of the expanding sleeve 3 is sleeved with a stiffening cylinder 2, the stiffening cylinder 2 consists of an upper rigid ring 2-1, a lower rigid ring 2-1 and four stiffening ribs 2-2, the two rigid rings 2-1 are respectively sleeved on the inner sides of the upper end and the lower end of the expanding sleeve 3, the four stiffening ribs 2-2 are uniformly distributed on the circumferential direction of the rigid ring 2-1, the rigid ring 2-1 and the stiffening ribs 2-2 are made of stainless steel, and the stiffening cylinder 2 is formed by rigid connection in a welding mode; both ends of the expanding sleeve 3 are supported by the rigid rings 2-1, and the main body of the expanding sleeve 3 is supported by the stiffening ribs 2-2. The end head between the rigid ring 2-1 and the expanding sleeve 3 is connected by PVC adhesive. The plastic sleeve 1 at the top of the pile body sleeve is coaxially and fixedly connected with a prefabricated pile head 7, and a reserved steel bar of the prefabricated pile head 7 is inserted into concrete poured in the plastic sleeve 1 6.

As shown in fig. 4, the expanding sleeve 3 of the expanding sleeve concrete pile of the invention expands under the grouting pressure during the concrete pouring process, and the diameter of the expanding sleeve 3 can be close to or larger than that of the prefabricated cone tip 5; therefore, the expanding sleeve 3 can be in close contact with the soil body on the pile side, so that the frictional resistance on the pile side can be generated quickly, the early bearing capacity of the concrete pile of the expanding sleeve can be effectively improved, and the reinforcement speed of a soft soil foundation can be improved. In addition, the stiffening cylinder 2 is arranged in the expanding sleeve 3, so that the expanding effect can be achieved, and the pile body length of the expanding sleeve concrete pile can be ensured.

The number of the stiffening ribs 2-2 can be adjusted according to the design requirement of the expanded casing concrete pile in the engineering; the arrangement position of the expanding sleeve 3 should avoid the stratum containing sharp gravel to prevent the expanding sleeve 3 from being damaged to cause water leakage and slurry leakage; the concrete strength grade of the prefabricated conical tip 5 and the prefabricated pile head 7 is greater than C30.

The embodiment also provides a construction method of the expanded casing concrete pile, which comprises the following steps:

s1, measuring and paying off, and determining pile positions and inserting and beating positions of plastic drainage plates among piles; inserting and beating a plastic drainage plate, and connecting the plastic drainage plate with a vacuum pump containing a mud-water separation device through a drainage pipe; drilling holes at the characteristic positions, mounting a plurality of pore water pressure sensors, backfilling, and connecting the pore water pressure sensors with a collecting system through leads;

s2, inserting the plastic sleeve 1 into a sleeve connecting piece 4 of a prefabricated conical tip 5 for fixed connection, and sequentially and alternately connecting an expanded sleeve 3 with a stiffening cylinder 2 and the plastic sleeve 1 until the designed pile length is reached;

s3, inserting the pile body sleeve connected with the prefabricated conical tip 5 into a steel cylinder of the pile driver by using a lifting rope, wherein the lower end of the steel cylinder props against the prefabricated conical tip 5; then, starting a pile driver, vertically and downwards driving a pile body sleeve with a prefabricated conical tip 5 into the foundation in a static pressure or impact vibration mode, and starting a vacuum pump connected with a plastic drainage plate to continuously drain water outwards;

s4, when the prefabricated cone tip 5 reaches the designed pile depth, injecting water into the pile body sleeve, pulling up the steel cylinder after 1/2 pile length water is injected, injecting water while pulling up, and keeping the pile body sleeve and the prefabricated cone tip 5 in the foundation;

s5, repeating the steps S3 and S4 until all pile body sleeves are completely drilled, completely pumping water in the pile body sleeves by using a water pump, uniformly pouring concrete into the pile body sleeves, and vibrating to be compact;

s6, installing a prefabricated pile head 7, and inserting a reserved steel bar of the prefabricated pile head 7 into the concrete 6 poured in the pile body sleeve;

s7, laying large-area high-strength geotextile on the top of the prefabricated pile head 7, then laying a gravel cushion layer, and arranging a drain pipe in the gravel cushion layer; after the vacuum pump stops working, the connection between the drain pipe of the plastic drain board and the vacuum pump is disconnected, and the drain pipe is connected with the drain ditch; and finishing the reinforcement of the soft soil foundation.

In the step S1, the inserting and driving positions of the plastic drainage plates are determined according to the driving depth and the distance of the expanded casing concrete piles; the characteristic positions and the installation quantity of the pore water pressure sensors are determined according to the shape, the area and the depth of a reinforced area and the driving position of the expanded casing concrete pile;

in step S2, all parts of the expanded casing concrete pile are ensured to be connected in a sealing mode so as to ensure that water injection does not leak in step S4, and concrete is poured in step S5 so as not to leak slurry.

In the steps S3-S5, the drainage speed of the vacuum pump is determined by the change situation of the hyperstatic pore water pressure value measured by the pore water pressure sensor and is related to the pile head size and the driving speed of the expanded casing concrete pile; in the steps S3-S7, the vacuum pump continues the drainage operation until the hyperstatic pore water pressure in the soil-squeezing area is completely dissipated, namely the hyperstatic pore water pressure value measured by the pore water pressure sensor is equal to zero, and the drainage operation can be stopped.

In step S5, if the early pile side frictional resistance is to be further improved, grouting may be performed between the pile body sleeve of the expanded casing concrete pile and the soil body.

In step S7, the geotextiles at the tops of the precast pile heads 7 are connected into a whole to improve the integrity of the expanded casing concrete pile in the soft soil foundation and improve the reinforcing effect of the soft soil foundation.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.