Predicting the behavior of nonwoven geotextile materials made of polyester and polypropylene fibers

Abstract

Predicting the behavior of geotextiles made of polyesters and polypropylene fibers is described by differential equations derived from mechanical models. Thereby, we describe the behavior of geotextiles up to the elastic limit. The elastic limit represents the permissible load which the geotextile material may be subjected to during exploitation, and without distorting its structure. The elastic limit is defined by analyzing the stress–strain curve of analyzed geotextiles. Nonwoven geotextile materials of polyester and polypropylene fibers with surface mass of 150, 200, 250, 300 and 500 g/m² were used as experimental material.

Keywords

deformation geotextiles elastic limit model force elongation

Geotextile materials have been used on many world building sites for years. Through their application, roads, railroads, drainage systems, coastal engineering and protective walls can be cheaper to build. According to purpose, the structural and mechanical properties of geotextile materials are predicted.^1–5

During production process using needles, fibers in felt are interlocked using special serrated needles that transfer fibers into the felt depth. In this way a product of special structure is produced which is resistant to mechanical action and therefore finds broad and various applications. The kind of fiber that is used for its formation,⁶ geotextile surface mass⁴ and technological parameters of geotextiles production process⁷ all have a significant impact on the performance of nonwoven geotextiles. The action of tensile force produces deformation of the geotextile with sliding between fibers and their orientation along the force action.⁸ Deformation of geotextiles during stretching depends on technological parameters in the production process of geotextiles.⁹

Nonwoven textile materials produced using needles are complex three-dimensional fiber structures and have the application in many industrial fields. Anisotropic structure of needled nonwoven materials¹⁰ contributes to various, sometimes hardly explicable, behaviors of nonwoven textiles during stretching.¹¹ The properties of geotextile materials could be predicted using empiric models,¹ finite model theory and composite material theory,¹² using computer prediction models of nonwoven textile stretching¹³ and also using mechanical models,^14–16 whereby the geotextile behavior is described by differential equations. In this way, every type of real material deformation is simulated with a simple model or this simulation is presented by complex models formed by a combination of simple models. Simple models used to describe elastic, viscoelastic and plastic deformations are models defining the properties of ideal materials not existing in nature but their properties, under specific stress conditions and other external influence, approximately reflect the behavior of real materials. A significant contribution to the review of mechanical models describing the behavior of textile materials is given in the work of Krucińska et al.¹⁴ The authors of this work¹⁴ suggest a model which describes the behavior of nonwoven geotextiles under compression. Needled nonwoven geotextile of polypropylene fibers was used as an experimental material. The correlation coefficients of theoretical and experimental curves confirm the validity of suggested models. In the work of Gao et al.,¹⁵ the authors considered the possibilities of using Kelvin's model, Burger's model, two-term generalized Kelvin's model and Zurek's model for describing the crawling of nonwoven materials. In this work,¹⁶ an attempt is made to use the Lethersich model to describe the behavior of geotextile material made of regular and recycled polyester fibers with surface mass of 300 g/m². The behavior of geotextile material was observed up to its breaking. It was concluded that the shape of the force–elongation curve obtained on a tensometer and Lethersich curve shape do not fit after the elasticity limit. However, up to the elasticity limit, the Lethersich model describes the geotextile behavior correctly. Therefore, the aim of this study is to develop a model that could describe the behavior of needled textiles in the elastic deformation zone, i.e. to the elasticity limit because it defines the load allowed during exploitation.

The needled nonwoven textile is a fibrous product where even the smallest stress can cause the sliding between fibers and resulting in plastic deformation. The term “elastic limit”, used in this work, does not describe Hook's law elasticity but defines the upper limit of domination of elastic deformations of needled geotextile. This is the limit where material starts a faster deformation under stress. Therefore, it should be regarded as the limit of permissible loads under stress. The Lethersich model, having a generally viscoelastic character, was selected for the describing of geotextile behavior up to the “elastic limit”. Experimental results¹⁶ confirm the viscoelastic behavior of needled geotextiles from the beginning of stretching up to “the elastic limit”, that is why this model was selected.

In this study, first, limits of elastic deformations were defined, then, using the Lethersich model the behavior of geotextile material made of polyester and polypropylene fibers was described in the region up to the elastic limits. The method presented can be used for predicting behavior of needled nonwoven geotextile materials of PES and PP fibers in the region of elastic limits.

Theoretical considerations

The rheological model for elastic material is an elastic spring (Hook's spring). Under monoaxial load, this material behaves in accordance with Hook's law. The rheological model for a viscous material is a piston moving in oil (Newton's body). As the real materials almost always contain, more or less, elements of both models, it is obvious that there is one more type of material named viscoelastic material. Under a load, this material shows, at the same time, properties of both elastic bodies and viscous fluids, meaning that strain in them depends on both the rate and magnitude of deformation.

Combining the basic rheological models, a rheological model for the Lethersich body was established (Figure 1).

Figure 1.

Model of Lethersich body.

The Lethersich body (L) represents a serial link between Newton (N) and Kelvin models (K):¹⁶

L = N - K

(1)

The deformation rate of the Lethersich body is equal to the sum of those of the Newton and Kelvin bodies:

{\overset{\cdot}{ɛ}}_{L} = {\overset{\cdot}{ɛ}}_{N} + {\overset{\cdot}{ɛ}}_{K}

(2)

where

{\overset{\cdot}{ɛ}}_{N}

is the deformation rate of the Newton body and

{\overset{\cdot}{ɛ}}_{K}

is the deformation rate of the Kelvin body.

The deformation rate of the Newton body is equal to

{\overset{\cdot}{ɛ}}_{N} = \frac{σ}{η_{N}}

(3)

where

η_{N}

is the viscosity coefficient of the Newton body.

The deformation rate of the Kelvin model is equal to

{\overset{\cdot}{ɛ}}_{K} = \frac{σ}{η_{K}} - \frac{E_{K}}{η_{K}} \cdot ɛ_{K}

(4)

where E_K is the elasticity modulus of the Kelvin model and

η_{K}

is the viscosity coefficient of the Kelvin model.

After some mathematical operations the following expression is obtained for the rate of deformation of the Lethersich body:

\overset{\cdot}{ɛ} = \frac{σ}{η_{N}} + \frac{σ}{η_{k}} - \frac{E_{K}}{η_{K}} \cdot \exp (- \frac{E_{K}}{η_{K}} \cdot t) \cdot [ɛ_{0} + \frac{1}{η_{K}} \cdot \int σ \cdot \exp (\frac{E_{K}}{η_{K}} \cdot t) d t]

(5)

where ε₀ is the initial relative elongation.

Differentiation by time and rearrangement of the previous expression gives a differential equation of the rheological model in the following form:

\overset{··}{ɛ} \cdot η_{K} + \overset{\cdot}{ɛ} \cdot E_{K} \cdot η_{K} = \overset{\cdot}{σ} (η_{N} + η_{K}) + σ \cdot E_{K}

(6)

where

\overset{\cdot}{ɛ}, \overset{··}{ɛ}

are the first and the second derivative by time and

σ, \overset{\cdot}{σ}

arethe stress and the first derivative by time.

As $\overset{\cdot}{ɛ} = const$ and $\overset{··}{ɛ} = 0$ , equation (6) is reduced to the following equation:

\overset{\cdot}{ɛ} \cdot E_{K} \cdot η_{K} = \overset{\cdot}{σ} (η_{N} + η_{K}) + σ \cdot E_{K}

(7)

The solution of the differential equation (7) can be expressed in the form

σ = - C \cdot \exp (- \frac{E_{K}}{η_{K} + η_{N}} \cdot t) + η_{N} \cdot \overset{\cdot}{σ}

(8)

The integration constant, C, is determined from the initial conditions t = 0, σ = 0. The relationship stress–time after determining the integration constant, has the form

σ = η_{N} \cdot \overset{\cdot}{σ} \cdot [1 - \exp (\frac{t}{τ_{r}})]

(9)

where τ_r = (η_N + η_K)/E_K is the relaxation time. The stress–strain relationship has the form

σ = η_{N} \cdot \overset{\cdot}{σ} \cdot [1 - \exp (\frac{l_{o}}{100 \cdot v \cdot τ_{r}} \cdot ɛ)]

(10)

where l₀ is initial sample length and v is the testing speed.

Material and methods

For the production of nonwoven geotextile material polyester (PES) and polypropylene (PP) fibers were used. Table 1 shows the main characteristics of these fibers. Polyester fibers are produced from polyethylene terephthalate (PET). Using Ramp method in the range of 50–300℃ on a differential scanning calorimeter (DSC; Q20 V24.11 Build 124), melting points of PES and PP fibers were determined. The melting point of PES fibers is 245.34℃ and for PP fibers is 152.85℃. On Video Analyser 2000 it was determined that PES have a circular cross-section and PP fibers have a polygonal cross-section.

Table 1.

Characteristics of fibers used for geotextile.

Type of fiber	Average fiber length [mm]	Fiber fineness [dtex]	Tenacity [cN/tex]	CV [%]	Breaking elongation [%]	CV [%]
PES	62.0	6	44.3	8.9	32.7	22.0
PP	86.4	6	48.2	23.3	68.7	25.2

CV, coefficient of variation.

Geotextile materials were produced under industrial conditions from 100% PES fibers and 100% PP fibers (Table 1). Geotextile materials with surface masses of around 150, 200, 250, 300 and 500 g/m² were produced.

All geotextile samples analyzed were formed using the needlefelting method. The felt is formed by laying web into the felt using equipment for web crosslaying. The crossed fiber position is accomplished in the way that the web from a carding machine is placed on a transporter moving square to the felt direction. In such a laying, the position of fibers could not be exactly square because the web is laid in layers which are, due to the movement of the transporter with the felt, placed under a certain angle. The web laying angle in the felt can be obtained from the relation

α = arc tg \frac{ν_{p}}{ν_{k}} [^{\circ}]

(11)

where α is the web laying angle in the felt [⁰] (Table 2) v_p is the felt moving speed (the speed of the transporter with felt) [m/min] and v_k is the web moving speed (the speed of the transporter with the web) [m/min].

Table 2.

Dynamic viscosity coefficient. Elasticity modulus up to the elastic limit and web laying angle in the left.

Geotextile	Length		Width		Web laying angle in the left
Geotextile	η (kNs²/m)	E (kN/m²)	η (kNs²/m)	E (kN/m²)	α (^o)
150 PES	15.376	0.305	15.054	0.455	4.6
200 PES	24.474	0.475	37.653	0.942	3.8
250 PES	143.043	2.668	74.310	1.730	3.6
300 PES	117.044	1.915	115.167	2.326	3.3
500 PES	397.337	7.074	556.281	6.905	1.9
150 PP	17.985	0.274	35.451	0.993	4.6
200 PP	89.064	1.066	147.813	4.341	3.8
250 PP	77.637	1.235	216.483	5.852	3.6
300 PP	219.627	2.799	307.230	6.749	3.3
500 PP	587.607	7.572	2614.626	21.248	1.9

Web laying angles in the felt are equal for geotextile materials made of PES and PP fibers with the same surface mass (Table 2).

The same technical and technological parameters were used for specific surface weights of geotextiles during production. It was easier to understand the impact of fiber type on the quality of obtained geotextiles using the same technological parameters in the production of geotextiles with the same surface weights but from different fibers. Table 3 shows the needling parameters, i.e. needle type, depth and the density of needling. Needling is done on a machine company “DILO”.

Table 3.

The needling parameters.

Geotextile	Needling parameters
	Needle type		Depth of needling (mm)	Density of needling (cm⁻²)
	Input board	Output board	Depth of needling (mm)	Density of needling (cm⁻²)
150 PES	15 × 18 × 36 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	15.5	91.4
150 PP	15 × 18 × 36 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	15.5	91.4
200 PES	15 × 18 × 36 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	16.0	109.7
200 PP	15 × 18 × 36 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	16.0	109.7
250 PES	15 × 18 × 36 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	16.5	115.5
250 PP	15 × 18 × 36 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	16.5	115.5
300 PES	15 × 18 × 32 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	17.0	120.4
300 PP	15 × 18 × 32 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	17.0	120.4
500 PES	15 × 18 × 32 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	17.5	169.7
500 PP	15 × 18 × 32 × 3R333 G1002	15 × 18 × 36 × 3R333 G1002	17.5	169.7

For the testing of geotextile materials the following test methods were used:

– SRPS EN ISO 9864 - Geotextile - Determination of mass per surface unit;

– SRPS EN ISO 10319 - Geotextile - Tensile test of broad laboratory sample.

Determination of breaking force and deformation at the highest load was measured with a preload of 0.02 kN, at grips distance of 100 mm and the speed of 20 mm/min (Tensolab strength tester 2510). The sampling was done in accordance with ISO 9862:2005 standard. From each roll of geotextile, five samples were taken in the direction of the longitudinal axis of geotextiles and five samples in the direction of the transverse axis. The samples size was 200 mm × 200 mm ± 1 mm.

From the F–ε graph the values of forces and relative elongations at elastic limits were determined, which can be numerically determined at the maximum of the first derivative of F(ε) function where F″(ε) = 0.¹⁶

Figure 2 presents a force–elongation function (Figure 2a) and the function first derivative (Figure 2b) and its second derivative (Figure 2c). The first derivative maximum (Figure 2b) indicates the limit of permissible loads. Up to this point, geotextile material exhibits higher resistance to stretching forces (F′(ε) function grows). When the first derivative function reaches the maximum, the second derivative is 0 (Figure 2c). Then, a faster geotextile deformation is set in, up to material destruction (F′(ε) function declines).

Figure 2.

The graph of force–elongation function F(ε), first F′(ε) and second F″(ε) derivatives of the function.

Results and discussion

In Table 4 we show the processed test results for geotextile materials made of PES and PP fibers. The table shows the average values and variation coefficients of the results obtained. The average values are determined analyzing five rolls of geotextile of each surface mass.

Table 4.

Testing results of PES and PP geotextile materials.

Geotextile	Direction	Maximum breaking force		Deformation at maximum load		Force at elastic limit		Elongation at elastic limit		Breaking work		Work up to elasticity limit
Geotextile	Direction	(kN)	CV (%)	(%)	CV (%)	(kN)	CV (%)	(%)	CV (%)	(J)	CV (%)	(J)	CV (%)
150 PES	Length	0.53	8.7	96.6	16.6	0.31	20.0	66.7	25.6	19.7	22.3	7.4	28.1
150 PES	Width	0.89	5.5	76.1	19.7	0.58	7.0	59.6	18.9	23.0	24.1	10.9	15.6
200 PES	Length	0.84	13.5	96.1	22.7	0.51	9.8	66.0	19.8	32.9	28.2	12.2	16.4
200 PES	Width	1.51	8.9	77.9	13.4	1.00	10.0	59.3	13.2	43.3	10.8	20.1	11.9
250 PES	Length	1.71	14.1	65.8	11.5	1.05	13.1	43.5	8.5	49.9	16.5	17.9	9.5
250 PES	Width	2.06	12.3	73.4	3.7	1.33	10.9	52.8	3.7	62.1	13.8	26.0	10.9
300 PES	Length	1.83	26.4	81.1	9.9	1.11	24.8	54.5	15.4	63.5	20.3	23.2	14.2
300 PES	Width	2.61	3.9	78.0	9.6	1.72	5.6	57.1	12.5	82.0	5.1	35.7	12.0
500 PES	Length	3.79	17.3	64.9	7.0	2.01	4.6	38.1	9.2	110.2	9.6	33.5	14.0
500 PES	Width	4.12	12.1	70.4	8.6	2.46	14.7	43.5	5.1	136.9	13.9	45.9	17.6
150 PP	Length	0.76	25.5	140.1	25.1	0.42	22.0	90.8	34.9	43.3	20.3	13.1	27.5
150 PP	Width	2.20	7.8	103.1	14.6	1.05	7.4	52.6	14.4	110.0	18.6	18.5	9.7
200 PP	Length	1.30	10.8	140.3	8.1	0.54	8.2	59.9	9.8	92.4	10.5	13.2	3.8
200 PP	Width	3.44	7.6	104.0	10.1	1.27	8.3	28.3	7.5	227.0	14.4	14.8	4.5
250 PP	Length	1.70	5.4	108.8	18.2	0.92	3.7	65.0	22.9	83.3	10.2	23.5	14.9
250 PP	Width	4.11	13.8	73.1	23.7	1.85	19.0	39.0	31.1	137.7	11.9	27.4	12.0
300 PP	Length	2.65	11.7	112.2	22.9	1.24	22.7	50.1	7.0	151.0	24.2	26.1	16.1
300 PP	Width	4.67	3.4	91.9	27.8	1.93	13.7	31.8	6.2	250.7	36.9	26.0	14.6
500 PP	Length	5.07	7.6	93.9	3.6	2.41	5.4	41.7	10.6	255.8	11.4	44.7	10.5
500 PP	Width	7.97	6.7	69.5	4.3	3.45	4.9	27.3	7.0	303.3	9.7	44.1	7.5

CV, coefficient of variation.

In Figure 3 we show the relationship between the forces at the elastic limit and maximum breaking forces of the analyzed geotextile materials made of PES fibers.

Figure 3.

The relationship between force at the elastic limit and maximum breaking force of geotextile made of PES fibers: (a) in length direction; (b) in width direction.

In Figure 4 we present the relationship between forces at the elastic limit and maximum breaking forces of the analyzed geotextile materials made of PP fibers.

Figure 4.

The relationship between force at the elastic limit and maximum breaking force of geotextile made of PP fibers: (a) in length direction; (b) in width direction.

The relationship of the force at elastic limit and maximum breaking force of needled nonwoven geotextile materials made of PES and PP fibers can be presented by regression equations (Table 5).

Table 5.

The relationship between elastic limit force and maximum breaking force of geotextile.

Geotextile	F_e = a + bF_b [kN]
Geotextile	Direction	a	Standard error	b	Standard error
PES	Length	0.01938	0.03478	0.59424	0.01798
PES	Width	−0.01295	0.04697	0.63327	0.01888
PP	Length	0.05984	0.05147	0.46429	0.01886
PP	Width	0.10582	0.13666	0.40744	0.02776

F_e, the force at geotextile elastic limit [kN]; F_b, maximum breaking force of geotextile [kN].

Based on the results obtained it can be concluded that all types of nonwoven geotextiles have higher strength in width direction than in length direction, as a result of fiber orientation in the felt. The angle of laying felt sheets ranges from 1.9° (geotextile 500 g/m²) to 4.6° (geotextile 150 g/m²), resulting in anisotropy of nonwoven geotextile materials. When breaking force intensities are compared with the intensities of forces at elastic limit of the analyzed geotextile materials it can be concluded that results recommend PP fibers to be used for making needled nonwoven geotextile materials.

Analyzing the results in Table 4 it could be concluded that the limit of elastic deformation in length direction for PES geotextile ranges from 52.98% to 61.67% of the maximum tensile force, but in width direction the force at elastic limit amounts to 59.83% to 66.29% of the maximum tensile force of geotextile.

Force value at the elastic limit of geotextile made of PP fibers ranges from 41.31% to 55.75% of the maximum breaking force in length direction and from 36.96% to 45.84% of the maximum tensile force in width direction.

Elastic limits of nonwoven geotextile materials, defined in this way, served as limit values in developing mathematical models. This means that, the behavior of geotextile in the region of elastic deformations was described, and the model describes the material behavior from the beginning of stretching to the elastic limit.

During stretching on a tensometer, speed of deformation has the constant value.

Initial sample length is 0.1 m; the speed of tensometer grips is 0.000333333 m/s.

Inserting the above data into equation (10) and assuming the equal viscosity coefficients ( $η_{N} = η_{k}$ ), the following equation is obtained:

σ = a \cdot [1 - \exp (- b \cdot ɛ)]

(12)

Fitting of experimental data in equation (12) and using appropriate software package, values of the coefficients “a” and “b” were determined.

In Table 6 we show the values of model coefficients “a” and “b” obtained from rheological model that was produced on the basis of experimental data for geotextile material made of PES and PP fibers.

Table 6.

Model coefficients up to the elastic limit.

Geotextile	Length		Width
Geotextile	a	b	a	b
150 PES	−0.05125	−0.02979	−0.05018	−0.04534
200 PES	−0.08158	−0.02909	−0.12551	−0.03754
250 PES	−0.47681	−0.02798	−0.24770	−0.03493
300 PES	−0.39015	−0.02454	−0.38389	−0.03029
500 PES	−1.32462	−0.02670	−1.85427	−0.01862
150 PP	−0.05995	−0.02289	−0.11817	−0.04202
200 PP	−0.29688	−0.01795	−0.49271	−0.04405
250 PP	−0.25879	−0.02386	−0.72161	−0.04055
300 PP	−0.73209	−0.01912	−1.02410	−0.03295
500 PP	−1.95869	−0.01933	−8.71542	−0.01219

Figures 5 –9 show relationship force–elongation (real and by mathematical model) of PES geotextile in the region of elastic deformation.

Figure 5.

The relationship force–elongation (real and by model) of 150 PES geotextile: (a) in length direction; (b) in width direction.

Figure 6.

The relationship force–elongation (real and by model) of 200 PES geotextile: (a) in length direction; (b) in width direction.

Figure 7.

The relationship force–elongation (real and by model) of 250 PES geotextile: (a) in length direction; (b) in width direction.

Figure 8.

The relationship force–elongation (real and by model) of 300 PES geotextile: (a) in length direction; (b) in width direction.

Figure 9.

The relationship force–elongation (real and by model) of 500 PES geotextile: (a) in length direction; (b) in width direction.

The real curve (black) depicts experimental results. The red curve (model curve) was obtained by approximation of experimental results and mathematical model describing the behavior of the Lethersich body, and the green curve depicts the model relative error. The model relative error is determined from the equation

r_{e} = \frac{F_{e} - F_{m}}{F_{e}} \cdot 100 . [%]

(13)

where r_e is the model relative error (%), F_e is the real value of the geotextile stretching force (measured on the tensometer) and F_m is stretching force based on the mathematical model.

Figures 10 –14 show the relationships force–elongation (real and by mathematical model) of PP geotextile in the region of elastic deformation.

Figure 10.

The relationship force–elongation (real and by model) of 150 PP geotextile: (a) in length direction; (b) in width direction.

Figure 11.

The relationship force–elongation (real and by model) of 200 PP geotextile: (a) in length direction; (b) in width direction.

Figure 12.

The relationship force–elongation (real and by model) of 250 PP geotextile: (a) in length direction; (b) in width direction.

Figure 13.

The relationship force–elongation (real and by model) of 300 PP geotextile: (a) in length direction; (b) in width direction.

Figure 14.

The relationship force–elongation (real and by model) of 500 PP geotextile: (a) in length direction; (b) in width direction.

The plots based on experimental results (black) are not linear, indicating that fibrous textile materials do not behave ideally elastically even under lower strains. On the basis of experimental results and the shape of force-elongation curves (Figures 4 –14) it can be concluded that on all needled geotextile materials, viscoelastic behavior was observed in the analyzed region. The elastic limit is actually the limit of elastic deformations in material. Beyond the elastic limit faster deformation of material occurs and the structure of needled geotextile is disturbed. Therefore, the elastic limit of geotextile represents the maximum permissible load. Some deformations under stress occur also in this region but they would not affect the structure stability and durability of needled geotextile.

Analysis of the graphs reveals that the model correctly describes PES and PP geotextile behavior in the region of elastic deformation (the relative model error, according to equation (13), is in the interval below 10%).

Using “a” and “b” coefficients, determined from experimental results, the values of elastic modulus and coefficients of dynamic viscosity of PES and PP geotextile were calculated from the following equations:

a = η \cdot \overset{\cdot}{ɛ} = η \cdot \frac{v}{l_{o}} \Rightarrow | η | = \frac{a \cdot l_{o}}{v}

(14)

b = \frac{l_{o}}{100 \cdot v \cdot τ_{r}} \Rightarrow τ_{r} = \frac{l_{o}}{100 \cdot b \cdot v} = \frac{2 \cdot η}{E}

(15)

E = 200 \cdot a \cdot b

(16)

where: E is Young's modulus of elasticity [kN/m²] and η is the coefficient of dynamic viscosity [kNs²/m].

In Table 2 we give the values of coefficients of dynamic viscosity and elasticity modulus for geotextile material made of PES and PP fibers in the region of elastic deformation.

Figure 15 shows the relationship between elasticity modulus and surface mass of PES and PP geotextiles.

Figure 15.

The elasticity modulus of PES and PP geotextiles depending on the surface mass: (a) in length direction; (b) in width direction.

Figure 16 shows the relation between elastic modulus and the web laying angle in the felt during forming of geotextile of PES and PP fibers.

Figure 16.

The elasticity modulus of PES and PP geotextile depending on the web laying angle in the felt: (a) in length direction; (b) in width direction.

The elastic modulus results of the analyzed materials recommend the application of PP fibers for the production of needled geotextiles. It can also be ascertained that along the length, PES and PP geotextiles have similar values of elastic modulus (Figures 15a and 16a). This is the result of web laying method in the felt, where fibers are oriented across the felt longitudinal axis resulting in lower geotextile strength along the length. Along the width (Figures 15b and 16b), PP geotextiles have higher elastic modulus values compared with PES geotextile and this difference is more evident with higher geotextile surface mass and with lower web laying angles in the felt.

Conclusions

Mechanical characteristics of needled nonwoven geotextile materials depend on their structural design, and also on technological conditions during production. Thereby, the most significant roles are played by the structural–mechanical characteristics of fibers, fiber orientation, geotextile surface mass and parameters of the needling process.

Analysis of the relationship between mechanical characteristics of nonwoven geotextile materials allows correct purpose-oriented design of geotextiles. Defining elasticity limits of nonwoven geotextile provides data on the maximum force intensities that can be applied to geotextiles without disturbing their quality. The results obtained indicate that permanent deformation of geotextile made of PES fibers in the length direction occurs under loads which are 52.98–61.67% of the maximum tensile force, while in width direction the limits of elastic deformation range from 59.83% to 66.29% of the maximum tensile force. Moreover, the results indicate that the permanent deformation of PP geotextile in length direction occurs under loads which are 41.31–55.75% of the maximum tensile force, while in width direction, the limit of elastic deformation ranges from 36.96% to 45.84% of the maximum tensile force.

Based on physical models and experimental results a rheological model is developed which can be used for simulation of the behavior of PES and PP nonwoven geotextile materials. The model describes the behavior of geotextile under loads up to the limits of elastic deformations. The developed models can also be used for predicting limit loads of nonwoven PES and PP geotextiles, after which occurs the irreversible deformation of these materials.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is part of the research project “The Development of New and the Improvement of the Existing Technological Processes for the Production of Technical Textiles” (grant number TR 34020), funded by the Ministry of Education and Science of the Republic of Serbia.

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