阅读说明：本技术 一种新型高聚物纳米生态固沙材料及其加固方法 (Novel high polymer nano ecological sand fixation material and reinforcement method thereof ) 是由 袁进科 裴钻 杨森林 于 2021-09-14 设计创作，主要内容包括：本发明公开了一种新型高聚物纳米生态固沙材料及其加固方法,属于地质保护材料技术领域,包括水溶液以及固体物料,所述固体物料为沙质材料以及高聚物纳米材料,所述水溶液为自来水,所述水溶液以及固体物料的液固比为1:2,所述水溶液以及固体物料通过基质胶结作用形成网膜,所述网膜铺设于沙质斜坡的坡表,所述网膜厚2cm,将沙质斜坡的表面进行包裹并且自然风干形成固化体。该新型高聚物纳米生态固沙材料及其加固方法,通过按照沙质斜坡的理论冲刷量以及试验冲刷量进行水溶液质量与固体物料质量的比值调配,并根据理论冲刷量以及试验冲刷量两者进行对比,合理选择液固比,使得固沙材料的防护效果达到最大限度的体现。(The invention discloses a novel high polymer nano ecological sand fixation material and a reinforcing method thereof, belonging to the technical field of geological protection materials, and comprising an aqueous solution and a solid material, wherein the solid material is a sand material and a high polymer nano material, the aqueous solution is tap water, the liquid-solid ratio of the aqueous solution to the solid material is 1:2, the aqueous solution and the solid material form a net film through matrix cementation, the net film is laid on the slope surface of a sand slope, the thickness of the net film is 2cm, and the surface of the sand slope is wrapped and naturally air-dried to form a solidified body. According to the novel high polymer nano ecological sand fixation material and the reinforcement method thereof, the ratio of the quality of the aqueous solution to the quality of the solid material is prepared according to the theoretical scouring amount and the experimental scouring amount of a sand slope, the comparison is carried out according to the theoretical scouring amount and the experimental scouring amount, and the liquid-solid ratio is selected reasonably, so that the protection effect of the sand fixation material is reflected to the maximum extent.)

1. A novel high polymer nanometer ecological sand fixation material comprises an aqueous solution and a solid material, and is characterized in that the solid material is a sandy material and a high polymer nanometer material, the aqueous solution is tap water, the sandy material, the high polymer nanometer material and the tap water are subjected to ratio blending of the quality of the aqueous solution and the quality of the solid material according to the theoretical scouring amount and the experimental scouring amount of a sandy slope, the liquid-solid ratio of the aqueous solution to the solid material is 1:2, the aqueous solution and the solid material form a net film through matrix cementation, the net film is laid on the slope surface of the sandy slope, the thickness of the net film is 2cm, the surface of the sandy slope is wrapped and naturally air-dried to form a solidified body.

2. The novel high polymer nano ecological sand fixing material as claimed in claim 1, wherein the theoretical scouring amount of the sandy slope is calculated as follows:

the single-width-diameter flow of the slope surface water and sand flow unit body (the cross-sectional area is 1cm multiplied by 1cm) with the length delta x is changed intoAnd under the influence of rainfall and infiltration factors, the single-width-diameter flow of the slope water and sand flow unit body with the length delta x is (Q-I) cos theta delta x, and the single-width-diameter flow at the slope length S is as follows:

in the formula: q is the single width flow (m) of the unit body of the water and sand flow²S); q is single wide rainfall intensity (m/s); i is single-width infiltration coefficient (m/s); s is the slope length (m); θ is slope (°);

the flow velocity v of the water and sand flow at the slope length S can be obtained by the Manning formula as follows:

in the formula: v is the flow velocity (m/s) of the water sand flow; h is the average depth (m) of water infiltration; θ is slope (°); n is the equivalent roughness coefficient of the slope;

combining formula (1) and formula (2) to give formula (3):

according to the law of conservation of energy, the scouring action of the water and sand flow can be analyzed through energy conversion, and by analyzing the material change and the energy conversion of the water and sand flow in the process of flowing on the slope, a water and sand body scouring energy balance equation is established as follows:

in the formula: e_hIs the initial potential energy (J) of the water-sand flow unit at the top of the slope; e₁ ^vThe kinetic energy (J) of the water-sand flow unit at the top of the slope; e_fFriction energy consumption (J) when the water and sand flow unit flows through the slope; e₂ ^vThe kinetic energy (J) of the water-sand flow unit at the toe of the slope;

because the slope surface catchment condition does not exist on the natural sand slope, namely the initial speed of the water-sand flow unit body at the top of the slope is 0, according to the formula (4), namely E₁ ^vIs zero; initial potential energy E at the top of the slope_hSee formula (5):

E_h＝mgH＝mgS sinθ (5)

in the formula: m is the initial mass (kg) of the water-sand flow unit; h is the initial slope height (m) of the water-sand flow unit;

the friction energy consumption of the water and sand flow unit when flowing through the slope is related to the mass change of the unit body; from the formula (1), the slope flow change is linearly related to the slope length, and the sand content is much smaller than the water flow, so that the water-sand flow change is approximately considered to be linearly related to the slope length, and the water-sand flow quality at any distance x of the slope isThe frictional energy consumption being related to the frictional force, i.e. frictionThe friction energy is calculated as:

in the formula: Δ m is the water sand flow change (kg);

the united vertical type (4), (5) and the formula (6) obtain a water sand body scouring energy balance equation:

mgS sinθ＝ngS(m+0.5Δm)cosθ+0.5(m+Δm)v² (7)

in the formula: v is the velocity (m/s) of the water sand flow at the toe of the slope;

obtaining a water and sand rheological variable calculation formula through the formula (7):

since the water-sand flow change amount Δ m is the sum of the water change amount Δ Q and the sand change amount Δ m', the water-sand flow change amount Δ m is smaller than the sand flow change amount Δ Q

Δmˊ＝Δm-ΔQ (9)

In the formula: Δ Q is the amount of change in water (kg); Δ m' is the amount of change in sand (kg);

the variation Δ Q of the water in equation (9) is related to the water flow Q and the time t, where t is:

in the formula: t is the slope catchment time(s);

combining formulae (1), (3), (9), and (10) to give the following formula:

Δ m' in formula (11) is the amount of change in sand, the total amount of sand washed is to be considered in conjunction with the total flow of water; catchment on the slope approximately equals the total flow at the toe, i.e.

M＝ρVB (12)

In the formula: ρ is the density of water (kg/m)³) (ii) a V is the volume of water (m)³) (ii) a The flow and time conversion can be carried out; b is the slope width (m);

according to equations (11) and (12), the total sand-wash quantity can be obtained, namely:

in the formula: m' is the total flush (g); and m is the initial unit mass of the water sand flow and is 0.1 kg.

3. The novel high polymer nano ecological sand fixing material as claimed in claim 2, wherein the parameters of rainfall intensity, rainfall duration, gradient, equivalent roughness coefficient and permeability coefficient are reasonably selected by influencing the slope scouring, and are brought into formula (13) to obtain the theoretical calculation results of scouring amount under different conditions.

4. The novel high polymer nano ecological sand fixing material as claimed in claim 1, wherein the test scouring amount of the sandy slope is calculated as follows:

selecting four factors of rain intensity, gradient, duration and different liquid-solid ratios to carry out indoor scouring simulation tests, wherein the test rainfall intensity is 150mm/h, 200mm/h and 250mm/h, and the rainfall converted by a rain intensity formula is respectively 3.5L/min, 4.6L/min and 5.8L/min; the rainfall lasts for 10min, 20min and 30 min; the gradient is 30 degrees, 40 degrees and 50 degrees; the liquid-solid ratio is 0:0, 1:2 and 1: 3; nine groups of tests are respectively designed through an orthogonal method, and the influence of different influence factors on the simulated slope surface scouring is known through the scouring magnitude value and the infiltration rate change of the nine groups of tests.

5. A method for reinforcing a novel high polymer nano ecological sand fixing material, which is characterized in that the novel high polymer nano ecological sand fixing material is reinforced based on the claims 1 to 4, and comprises the following specific reinforcing steps:

s1, mixing the aqueous solution and the solid material according to the liquid-solid ratio of 1:2 to prepare the membrane, wherein the aqueous solution and the solid material form a membrane through matrix cementation;

s2, paving the surface of the sandy slope by adopting a C25 concrete rib framework;

s3, installing an anchor rod and hanging a net, and paving the net film in the S1;

and S4, performing regular maintenance at the later stage.

6. The method for reinforcing novel high polymer nano ecological sand-fixing material as claimed in claim 5, wherein in S3, the net film is laid to a thickness of 2cm, the surface of the sandy slope is wrapped and air-dried naturally to form a solidified body.

Technical Field

The invention belongs to the technical field of geological protection materials, and particularly relates to a novel high polymer nano ecological sand fixation material and a reinforcement method thereof.

Background

Scouring of desert slopes is an extremely complex physical, chemical and biological process. The method is influenced by a plurality of external natural factors, such as sand, terrain, climate, vegetation and the like, and is also interfered by human behaviors, and the factors have complicated interaction. The influence result comprises runoff quantity, splash erosion capacity of rainfall on a sand table and the like, and the parameters depend on rainfall characteristics, geological characteristics, landform, vegetation development and the like.

In the prior art, the sand fixing material is not selected in a mode of being suitable according to local conditions, and early calculation and test cannot be performed according to the local slope environment, so that the sand fixing material cannot achieve the expected ideal effect easily. In order to solve the problems, a novel high polymer nano ecological sand fixing material and a reinforcing method thereof are provided.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a novel high polymer nano ecological sand fixation material and a reinforcing method thereof, aiming at solving the problems in the background technology.

In order to achieve the purpose, the invention provides the following technical scheme: a novel high polymer nanometer ecological sand fixation material comprises an aqueous solution and a solid material, wherein the solid material is a sandy material and a high polymer nanometer material, the aqueous solution is tap water, the sandy material, the high polymer nanometer material and the tap water are subjected to ratio blending of the mass of the aqueous solution and the mass of the solid material according to the theoretical scouring amount and the experimental scouring amount of a sandy slope, the liquid-solid ratio of the aqueous solution and the solid material is 1:2, the aqueous solution and the solid material form a net film through matrix cementation, the net film is laid on the slope surface of the sandy slope, the thickness of the net film is 2cm, and the surface of the sandy slope is wrapped and naturally air-dried to form a solidified body.

Further optimizing the technical scheme, the theoretical scouring amount of the sandy slope is calculated according to the following mode:

the single-width-diameter flow of the slope surface water and sand flow unit body (the cross-sectional area is 1cm multiplied by 1cm) with the length delta x is changed intoAnd under the influence of rainfall and infiltration factors, the single-width-diameter flow of the slope water and sand flow unit body with the length delta x is (Q-I) cos theta delta x, and the single-width-diameter flow at the slope length S is as follows:

in the formula: q is the single width flow (m) of the unit body of the water and sand flow²S); q is single wide rainfall intensity (m/s); i is single-width infiltration coefficient (m/s); s is the slope length (m); θ is slope (°);

the flow velocity v of the water and sand flow at the slope length S can be obtained by the Manning formula as follows:

in the formula: v is the flow velocity (m/s) of the water sand flow; h is the average depth (m) of water infiltration; θ is slope (°); n is the equivalent roughness coefficient of the slope;

combining formula (1) and formula (2) to give formula (3):

according to the law of conservation of energy, the scouring action of the water and sand flow can be analyzed through energy conversion, and by analyzing the material change and the energy conversion of the water and sand flow in the process of flowing on the slope, a water and sand body scouring energy balance equation is established as follows:

in the formula: e_hIs the initial potential energy (J) of the water-sand flow unit at the top of the slope; e₁ ^vThe kinetic energy (J) of the water-sand flow unit at the top of the slope; e_fFriction energy consumption (J) when the water and sand flow unit flows through the slope; e₂ ^vFor water-sand flow units at the toe of a slopeKinetic energy (J);

because the slope surface catchment condition does not exist on the natural desert slope, namely the initial speed of the water-sand flow unit body at the top of the slope is 0, according to the formula (4), namely E₁ ^vIs zero; initial potential energy E at the top of the slope_hSee formula (5):

E_h＝mgH＝mgS sinθ (5)

in the formula: m is the initial mass (kg) of the water-sand flow unit; h is the initial slope height (m) of the water-sand flow unit;

the friction energy consumption of the water and sand flow unit when flowing through the slope is related to the mass change of the unit body; from the formula (1), the slope flow change is linearly related to the slope length, and the sand content is much smaller than the water flow, so that the water-sand flow change is approximately considered to be linearly related to the slope length, and the water-sand flow quality at any distance x of the slope isThe frictional energy consumption being related to the frictional force, i.e. frictionThe friction energy is calculated as:

in the formula: Δ m is the water sand flow change (kg);

the united vertical type (4), (5) and the formula (6) obtain a water sand body scouring energy balance equation:

mgSsinθ＝ngS(m+0.5Δm)cosθ+0.5(m+Δm)v² (7)

in the formula: v is the velocity (m/s) of the water sand flow at the toe of the slope;

obtaining a water and sand rheological variable calculation formula through the formula (7):

since the water-sand flow change amount Δ m is the sum of the water change amount Δ Q and the sand change amount Δ m', the water-sand flow change amount Δ m is smaller than the sand flow change amount Δ Q

Δmˊ＝Δm-ΔQ (9)

In the formula: Δ Q is the amount of change in water (kg); Δ m' is the amount of change in sand (kg);

the variation Δ Q of the water in equation (9) is related to the water flow Q and the time t, where t is:

in the formula: t is the slope catchment time(s);

combining formulae (1), (3), (9), and (10) to give the following formula:

Δ m' in formula (11) is the amount of change in sand, the total amount of sand washed is to be considered in conjunction with the total flow of water; catchment on the slope approximately equals the total flow at the toe, i.e.

M＝ρVB (12)

In the formula: ρ is the density of water (kg/m)³) (ii) a V is the volume of water (m)³) (ii) a The flow and time conversion can be carried out; b is the slope width (m);

according to equations (11) and (12), the total sand-wash quantity can be obtained, namely:

in the formula: m' is the total flush (g); and m is the initial unit mass of the water sand flow and is 0.1 kg.

The technical scheme is further optimized, and by influencing the slope scouring, parameters of rainfall intensity, rainfall duration, gradient, equivalent rough coefficient and permeability coefficient are reasonably selected and are carried into the formula (13), so that theoretical calculation results of scouring amounts under different conditions are obtained.

Further optimizing the technical scheme, the test scouring amount of the sandy slope is calculated according to the following mode:

selecting four factors of rain intensity, gradient, duration and different liquid-solid ratios to carry out indoor scouring simulation tests, wherein the test rainfall intensity is 150mm/h, 200mm/h and 250mm/h, and the rainfall converted by a rain intensity formula is respectively 3.5L/min, 4.6L/min and 5.8L/min; the rainfall lasts for 10min, 20min and 30 min; the gradient is 30 degrees, 40 degrees and 50 degrees; the liquid-solid ratio is 0:0, 1:2 and 1: 3; nine groups of tests are respectively designed through an orthogonal method, and the influence of different influence factors on the simulated slope surface scouring is known through the scouring magnitude value and the infiltration rate change of the nine groups of tests.

A strengthening method of a novel high polymer nanometer ecological sand fixation material is based on the strengthening of the novel high polymer nanometer ecological sand fixation material, and comprises the following concrete strengthening steps:

s1, mixing the aqueous solution and the solid material according to the liquid-solid ratio of 1:2 to prepare the membrane, wherein the aqueous solution and the solid material form a membrane through matrix cementation;

s2, paving the surface of the sandy slope by adopting a C25 concrete rib framework;

s3, installing an anchor rod and hanging a net, and paving the net film in the S1;

and S4, performing regular maintenance at the later stage.

Further optimizing the technical scheme, in the step S3, the thickness of the net film is laid to be 2cm, the surface of the sandy slope is wrapped, and the sandy slope is naturally air-dried to form a solidified body.

Compared with the prior art, the invention provides a novel high polymer nano ecological sand fixation material and a reinforcing method thereof, and the novel high polymer nano ecological sand fixation material has the following beneficial effects:

according to the novel high polymer nano ecological sand fixation material and the reinforcement method thereof, the ratio of the quality of the aqueous solution to the quality of the solid material is prepared according to the theoretical scouring amount and the experimental scouring amount of a sand slope, the comparison is carried out according to the theoretical scouring amount and the experimental scouring amount, and the liquid-solid ratio is selected reasonably, so that the protection effect of the sand fixation material is reflected to the maximum extent.

Drawings

FIG. 1 is a schematic flow chart of a novel reinforcement method of a high polymer nano ecological sand-fixing material provided by the invention;

FIG. 2 is a schematic diagram of a test model of a novel high polymer nano ecological sand-fixing material provided by the invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious 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.

The first embodiment is as follows:

a novel high polymer nanometer ecological sand fixation material comprises an aqueous solution and a solid material, wherein the solid material is a sandy material and a high polymer nanometer material, the aqueous solution is tap water, the sandy material, the high polymer nanometer material and the tap water are subjected to ratio blending of the mass of the aqueous solution and the mass of the solid material according to the theoretical scouring amount and the experimental scouring amount of a sandy slope, the liquid-solid ratio of the aqueous solution and the solid material is 1:2, the aqueous solution and the solid material form a net film through matrix cementation, the net film is laid on the slope surface of the sandy slope, the thickness of the net film is 2cm, and the surface of the sandy slope is wrapped and naturally air-dried to form a solidified body.

Specifically, the theoretical scouring amount of the sandy slope is calculated according to the following mode:

the single-width-diameter flow of the slope surface water and sand flow unit body (the cross-sectional area is 1cm multiplied by 1cm) with the length delta x is changed intoAnd under the influence of rainfall and infiltration factors, the single-width-diameter flow of the slope water and sand flow unit body with the length delta x is (Q-I) cos theta delta x, and the single-width-diameter flow at the slope length S is as follows:

in the formula: q is the single width flow (m) of the unit body of the water and sand flow²S); q is single wide rainfall intensity (m/s); i is single-width infiltration coefficient (m/s); s is the slope length (m); θ is slope (°);

the flow velocity v of the water and sand flow at the slope length S can be obtained by the Manning formula as follows:

in the formula: v is the flow velocity (m/s) of the water sand flow; h is the average depth (m) of water infiltration; θ is slope (°); n is the equivalent roughness coefficient of the slope;

combining formula (1) and formula (2) to give formula (3):

according to the law of conservation of energy, the scouring action of the water and sand flow can be analyzed through energy conversion, and by analyzing the material change and the energy conversion of the water and sand flow in the process of flowing on the slope, a water and sand body scouring energy balance equation is established as follows:

in the formula: e_hIs the initial potential energy (J) of the water-sand flow unit at the top of the slope; e₁ ^vThe kinetic energy (J) of the water-sand flow unit at the top of the slope; e_fFriction energy consumption (J) when the water and sand flow unit flows through the slope; e₂ ^vThe kinetic energy (J) of the water-sand flow unit at the toe of the slope;

because the slope surface catchment condition does not exist on the natural desert slope, namely the initial speed of the water-sand flow unit body at the top of the slope is 0, according to the formula (4), namely E₁ ^vIs zero; initial potential energy E at the top of the slope_hSee formula (5):

E_h＝mgH＝mgS sinθ (5)

in the formula: m is the initial mass (kg) of the water-sand flow unit; h is the initial slope height (m) of the water-sand flow unit;

the friction energy consumption of the water and sand flow unit when flowing through the slope is related to the mass change of the unit body; from the formula (1), the slope flow change is linearly related to the slope length, and the sand content is much smaller than the water flow, so that the water-sand flow change is approximately considered to be linearly related to the slope length, and the water-sand flow quality at any distance x of the slope isThe frictional energy consumption being related to the frictional force, i.e. frictionThe friction energy is calculated as:

in the formula: Δ m is the water sand flow change (kg);

the united vertical type (4), (5) and the formula (6) obtain a water sand body scouring energy balance equation:

mgSsinθ＝ngS(m+0.5Δm)cosθ+0.5(m+Δm)v² (7)

in the formula: v is the velocity (m/s) of the water sand flow at the toe of the slope;

obtaining a water and sand rheological variable calculation formula through the formula (7):

since the water-sand flow change amount Δ m is the sum of the water change amount Δ Q and the sand change amount Δ m', the water-sand flow change amount Δ m is smaller than the sand flow change amount Δ Q

Δmˊ＝Δm-ΔQ (9)

In the formula: Δ Q is the amount of change in water (kg); Δ m' is the amount of change in sand (kg);

the variation Δ Q of the water in equation (9) is related to the water flow Q and the time t, where t is:

in the formula: t is the slope catchment time(s);

combining formulae (1), (3), (9), and (10) to give the following formula:

Δ m' in formula (11) is the amount of change in sand, the total amount of sand washed is to be considered in conjunction with the total flow of water; catchment on the slope approximately equals the total flow at the toe, i.e.

M＝ρVB (12)

In the formula: ρ is the density of water (kg/m)³) (ii) a V is the volume of water (m)³) (ii) a The flow and time conversion can be carried out; b is the slope width (m);

according to equations (11) and (12), the total sand-wash quantity can be obtained, namely:

in the formula: m' is the total flush (g); and m is the initial unit mass of the water sand flow and is 0.1 kg.

Specifically, parameters of rainfall intensity, rainfall duration, gradient, equivalent roughness coefficient and permeability coefficient are reasonably selected by influencing the slope scouring, and are brought into the formula (13), so that theoretical calculation results of scouring amounts under different conditions are obtained.

Specifically, the test scouring amount of the sandy slope is calculated according to the following mode:

as shown in fig. 2, in the test model, four factors of rain intensity, gradient, duration and different liquid-solid ratios are selected to carry out an indoor scouring simulation test, the test rainfall intensity is 150mm/h, 200mm/h and 250mm/h, and the rainfall is converted by a rain intensity formula to be 3.5L/min, 4.6L/min and 5.8L/min respectively; the rainfall lasts for 10min, 20min and 30 min; the gradient is 30 degrees, 40 degrees and 50 degrees; the liquid-solid ratio is 0:0, 1:2 and 1: 3; nine groups of tests are respectively designed through an orthogonal method, and the influence of different influence factors on the simulated slope surface scouring is known through the scouring magnitude value and the infiltration rate change of the nine groups of tests. The results of the nine sets of simulations are shown in table 1.

TABLE 1 rainfall erosion simulation test theoretical calculation and test comparison

It can be seen from table 1 that the analysis test value is closer to the calculated value, but the equivalent roughness coefficient changes with the change of the rainfall erosion test parameter, and through comparison, the slope of the 1:2 liquid-solid ratio reinforcing material generates more runoff, the sand-covered particles are larger, and the corresponding erosion amount is also larger.

Example two:

referring to fig. 1, a method for reinforcing a novel high polymer nano ecological sand-fixing material, based on the embodiment, includes the following specific reinforcing steps:

s1, mixing the aqueous solution and the solid material according to the liquid-solid ratio of 1:2 to prepare the membrane, wherein the aqueous solution and the solid material form a membrane through matrix cementation;

s2, paving the surface of the sandy slope by adopting a C25 concrete rib framework;

s3, installing an anchor rod and hanging a net, and paving the net film in the S1;

and S4, performing regular maintenance at the later stage.

Specifically, in S3, the net film is laid to a thickness of 2cm, and the surface of the sandy slope is wrapped and naturally air-dried to form a solidified body.

The invention has the beneficial effects that: according to the novel high polymer nano ecological sand fixation material and the reinforcement method thereof, the ratio of the quality of the aqueous solution to the quality of the solid material is prepared according to the theoretical scouring amount and the experimental scouring amount of a sand slope, the comparison is carried out according to the theoretical scouring amount and the experimental scouring amount, and the liquid-solid ratio is selected reasonably, so that the protection effect of the sand fixation material is reflected to the maximum extent.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

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.