The model of abrasive wear of concrete in hydraulic structures

Wear 256 (2004) 787–796

The model of abrasive wear of concrete in hydraulic structures E. Horszczaruk∗ Faculty of Civil Engineering and Architecture, Technical University of Szczecin, Al. Plastow 50, Szczecin 70 311, Poland Received 11 March 2002; received in revised form 13 May 2003; accepted 7 July 2003

Abstract Abrasion wear of concrete in hydraulic construction is caused by movement of rubble carried by water. Difficulties in methodology of modelling this process in a laboratory scale constitute an obstacle to the rational assessment of influence of material and environmental conditions on durability of objects exposed to these actions. This paper presents a new concept of testing the abrasion of concrete by rubble carried by water, modelling the natural mechanisms present in the environment. It was shown that loss of mass in abraded concrete can be expressed as function of work by the abrasive mix and a material parameter depending on composition and independent of the intensity of environmental action. The results of tests allowed the criteria to be given for the selection of the composition of concrete exposed to abrasion-wear. © 2003 Elsevier B.V. All rights reserved. Keywords: Wear; Abrasion erosion; Abrasion resistance; Technology of concrete

1. Introduction Abrasion wear of concrete in hydraulic structures is mainly caused by rubble dragged by flowing water. Damage of concrete structures caused by the abrasion process is very severe and indicate the necessity of taking into account the influence of this process while designing concrete mixtures and building constructions. It should be emphasised that the unified and general criterion of acceptable range of destruction of such type structures is difficult to formulate. The second, very important issue is the methodology of testing concrete resistance to abrasion wear. Examinations carried out so far have mainly dealt with the determination of concrete resistance properties. The process of abrasion was simulated artificially (e.g. shot blasting, sand blasting, abrasive disks) and did not reflect natural conditions of the environment. Obtained results, due to the application of various testing methods, cannot be assessed on the basis of comparative analysis. Problems of modelling abrasion wear of concrete in laboratory conditions were the subject of papers by Małasiewicz [1], Bania [2,3], Horszczaruk [4,5] and Haroske [6]. Authors of the above mentioned papers agree that the results are appreciably affected by the way of modelling environment influence. The importance of technological factors determining the composition and way of compacting and curing ∗ Tel.: +48-91-449-40-59; fax: +49-91-449-43-69. E-mail address: [email protected] (E. Horszczaruk).

0043-1648/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0043-1648(03)00525-8

of concrete exposed to abrasion–erosion is stressed in publications by McDonald [7], Omoregie et al. [8], Scrivener et al. [9,10] and Naik et al. [11,12]. Up till now, however, no comparative analysis was carried out of the importance of individual material and environmental factors on abrasion of concrete by sediment transport dragged by flowing water. The majority of devices described in professional literature designed to test abrasive resistance of concrete is used for simulating mechanisms of sand blasting [13–15] and grooving [12,16–18] with dry friction. Very few publications [2,4,6,9] and ASTM standard test method [19] describe research done in conditions similar to the natural influence of environment with the applications of devices enabling to model the process of concrete abrasion with the mixture of aggregate and water. Generally, the construction of these devices does not allow to model the movement of the whole grain composition of the rubble. Most often the mixture of small sand fractions and water is used as an abrasive; the mixture is ejected on the concrete surface under pressure and with high speed. While discussion results of various tests, one can compare only those that were based on the same tribological mechanisms of samples abrasion. These mechanisms are description by four basic external parameters: composition (hardness), size of abrasive grains, their speed and glancing angle on the sample. The alteration of one of these parameters causes change of the abrasive mechanism and thus the comparative analysis of test results is not possible. Laboratory simulation of abrasion process in conditions similar to natural influence of the environment enables

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E. Horszczaruk / Wear 256 (2004) 787–796

to assess properly the resistance of concrete to abrasive erosion. The objective of the current research work was not only to build a device for simulating natural conditions of concrete abrasion, but also to work out a numerical model enabling to forecast disintegration progress of concrete structure according to hydraulic conditions of rubble movement. 2. Experimental 2.1. Erosion tests The scheme of the test stand for testing concrete resistance to abrasion erosion is shown in Fig. 1. The device consists of steel drum of 155 cm in diameter and length of 228 cm; in its horizontal axle there is a fixed drive shaft with 36 beds for fixing tested concrete samples. The shaft with fixed samples is powered by an electric motor. The belt transmission allows to regulate the number of drive shaft rotations, simulating the speed of rubble flow dragged by water. The drum is filled with the mixture of aggregate and water, which is changed after each series of tests. Tested samples of concrete are fixed to the drive shaft in three or six rows, six pieces in each row. Geometrical relationships presented in Fig. 1 allow at the same time to abrade samples fixed only in one row. Between the drum and the belt transmission there are the following parts: flexible coupling, torque meter with a collector and reducer. Forces of abrasive mixture reacting on the tested concrete samples cause torsion of the drive shaft whose deformations are measured with a set of extensometers. A signal from the collector of the torque meter is transmitted to the amplifier and then converted to numerical signal and recorded on a PC disk. Installed meter circuit allows to estimate the value of the torque moment of the drum’s drive shaft:
t2 t U dt Mp = k 1 (1) t2 − t1

where k is the experimentally determined coefficient of shift and U the voltage obtained from the measurement in time t = t2 − t1 . Defined values of moment Mp enable to determine forces P of the abrasive mixture reaction on the tested concrete samples: P=

Mp − M0 ri

(2)

where M0 is the moment of resistance caused by the dead movement of the system without the abrasive mixture, r the arm of the acting force P and i the number of samples fixed in one row of the drive shaft of the device. Voltage measurement U during tests was made each time and in determined time periods, immediately before the inspection of abrasive concrete mass decrement change. 2.2. Material preparation Five series of basic tests were carried out on concrete of various components subjected to abrasion by mixture of aggregate and water, at constant velocity of 2.5 m/s and a series of investigations in which the abrasion–erosion process was modelled using various velocities of rubble transport: v = 2.5, 3.5 and 4.0 m/s (Series IV). The samples for individual series of tests were prepared according to following assumptions: • Series I. Portland cement without additives (CEM I 32.5 R), natural aggregate with continuous but differing grain size distribution: 0–4, 0–8, 0–16 mm, unchanged value of water/cement ratio, w/c = 0.5, constant consistence of mix (plastic). • Series II. Portland cement without additives (CEM I 32.5 R), natural aggregate up to 16 mm with continuous grain size distribution, variable value of water/cement ratio, w/c = 0.4, 0.5 and 0.6, constant consistence of mix (plastic).

Fig. 1. Scheme of the device for testing abrasive erosion of concrete.

E. Horszczaruk / Wear 256 (2004) 787–796

• Series III. Various kinds of class 32.5 cements: Portland cement with addition of blast furnace slag (CEM II/A-S), Portland with addition of fly-ash (CEM II/A-V), blast-furnace cement (CEM III A), natural aggregate with continuous grain size distribution up to 16 mm, steady value of water/cement ratio, w/c = 0.5, constant consistence of the mix (plastic). • Series IV. Portland cement without additives, CEM I 32.5 R, natural aggregate up to 16 mm with continuous grain size distribution, unchanged value of water/cement ratio, w/c = 0.5, constant consistence of mix K-3, various velocities of abrasive mix movement. • Series V. Portland cement without additives, CEM I 32.5 R, natural aggregate up to 16 mm with continuous grain size distribution, continuous value of water/cement ratio, w/c = 0.5, variable consistence of the mix K-1–K-5 (from damp to liquid consistence) defined by variable dis-

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persion factor Dm of aggregate particles in the hardened concrete matrix. • Series VI. In Series I mixes, natural gravel was replaced by crushed basaltic aggregate without altering the quantitative composition of individual fractions. 2.3. Experimental procedure Basic tests were carried out on cylindrical samples h = φ = 80 mm. Sets of 18 samples were made from particular concrete mixtures. After 28 days of hardening, they were soaked up to constant weight and then subjected to abrasion by aggregate–water mix. The abrasive mixture consisted of natural aggregate of 8–32 mm grain size to which water was added in volumetric proportion 1:3. The choice of grain size of aggregate follows from the analysis of rubble transport conditions at the water velocities assumed in the model. The

Fig. 2. Changes of relative mass decrements, work and power of abrasive mixture (Series II).

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E. Horszczaruk / Wear 256 (2004) 787–796

process of the tested samples abrasion was carried out in 96-h period. The mass of the concrete samples was checked performed after 1, 2, 6, 12, 18, 24, 36, 48 and 96 h of the device functioning. Before the periodical check of the mass of the concrete samples the measurements of voltage alteration U of the meter circuit were made; the meter circuit enabled to define forces P of the abrasive mixture influence. Except for the basic tests the concrete samples of each series were exposed to the resistance tests after 28 days of setting as well as to absorbability tests.

3. Experimental results Example results of abrasive wear of concrete tests are presented in Figs. 2 and 3 showing relative changes of the abrasive material mass in time function: m/m0 = f(t). Particular mass decrements m/m0 are the mean value obtained from 18 pieces of samples abraded at the same time. Mean values of standard deviation of relative samples mass decrement, determined in appointed check time, changed from s = 0.0026 after 1 h of the abrasive mixture reaction to s = 0.0163 after 96 h of abrasion.

∆ m/m0

0,10

SERIES IV

0,09

m03 =884.97 g

0,08

m02 =903.69 g

0,07 0,06

m01 =889.26 g

0,05 0,04 0,03

v=2.5 m/s v=3.5 m/s v=4 m/s

0,02 0,01 0,00 0

12

24

36

48

60

72

84

96

t [h]

40000

W s [kJ] 35000 30000 25000 20000

v=2,5 m/s v=3,5 m/s v=4,0 m/s

15000 10000 5000

0

12

24

36

48

60

72

84

96

0

50 100 150 200 250 300 350 400 450 500

t [h] M=163,1 kJ/kg M=291,9 kJ/kg

M=438,82 kJ/kg

v=2,5 m/s v=3,5 m/s v=4,0 m/s

M [kJ/kgh]

Fig. 3. Changes of relative mass decrements, work and power of abrasive mixture (Series IV).

E. Horszczaruk / Wear 256 (2004) 787–796

Applied testing device enabled check of abrasive conditions of the tested concretes. Determination of force values P of the mixture reaction on the tested samples allowed to define work W and abrasive power M of concretes from the particular series. These values, dependant first of all on the speed of rubble movement may be subject to slight alterations, even at its assumed constant speed. Presented results of tests show that changes in mass of the tested concretes caused by abrasive erosion are conditioned by both their composition and intensity of the abrasive mixture influence.

4. Theoretical model From the classic kinetic-molecular theory point of view we can examine the concrete as a solid substance built of the particular molecules. These molecules are in several energetic states and their permanent position in the material volume is maintained by the power of their interactions. Change of the molecule position that initiates disintegration process of the structure requires increasing its energy to an activation energy E—higher than the energy of the existing bonds. In accordance with Maxwell and Boltzmann distribution law the probability pi of the particular molecule being in an energetic state qi is described by the following formula:   qi pi = const exp − (3) qm where qm is the mean energy of the molecules in the substance. We can assume the probability of the molecule with an energy q ≥ E that makes change of its location possible:   E pi = const exp − (4) qm Because of the complexity of the concrete we can interpret the values of E and qm as the energy values that characterise volume unit of the substance. Mean energy qm that characterises concrete structure state is specified by the concrete mix proportions, type of ingredients, the hydration level and hardening conditions. The work that is done during reaction of aggregate–water mix with concrete is partially dissipated and partially used for the increase of the internal energy of the concrete. Marking this part of work as (aW) the disintegration process of the concrete begins when it reaches the state: q + aW ≥ E

(5)

The volume of the substance with an energy higher than the activation energy E is dv = C1 v exp(−aW) dW

(6)

791

Eq. (6) and the earlier assumptions leads to a differential formula that determines the mass decrement of the abraded concrete related to the work of the abrasive mix: d( m) = C1 exp(−aW) dW (7) m0 where m0 is the initial mass of the concrete and m the mass decrement caused by the abrasion. Integrating Eq. (7) we get the formula describing mass decrement of the abraded concrete:  m  W d( m) = C1 exp(−aW) dW, m0 0 0 m C1 = A[1 − exp(−aW)], where A = (8) m0 a Value of the parameter a describes the abrasive “resistance” of the concrete. For a → 0 the whole work of the abrasive mix is dissipated and the sample is wear resistant: m lim = lim [C1 a exp(−aW)] = 0 (9) a→0 m0 a→0 For a sufficient period of the abrasive interaction the work W → 0 and the mass decrement m → m0 . We can conclude that the value of the parameter A (Eq. (8)) should be 1. Finding the logarithm of the expression (7) we get the equation:   d( m) 1 ln = ln C1 − aW (10) dW m0 that helps us to determine unknown parameters C1 and a of the kinetic equation (8). Eq. (10) in a coordinate system with axis y = ln[(d( m)/dW)(1/m0 )] and x = W represents a straight line with a slope to an axis of abscissa dy/dx = −a and an ordinate point W = 0, y = ln C1 . 5. Precise description of the properties of the abraded concrete Section 4 of this paper characterises the properties of the abraded concrete with a discrete value of the parameter a— that describes the “resistance” of the material to an abrasive action of the aggregate–water mix. This assumption leads to the formulas that determine kinetics of the concrete wear during the initial period of the abrasive action. The results of the analysis show that we must search the precise description of the kinetics of the abrasive concrete wear through establishing the spectrum of the parameter a: a1 , a2 , . . . , an that specify the local properties of the abraded material. As it was mentioned before—this way we can characterise the properties of the concrete much better because it contains a lot of ingredients with different physio-mechanical qualities. Establishing the discrete spectrum of the parameter a (that characterises local “resistance” of the ingredients against the abrasive wear) Eq. (7) is transformed to:

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E. Horszczaruk / Wear 256 (2004) 787–796

d( m) = a1 p1 exp[−a1 W] + a2 p2 exp[−a2 W] m0 dW n  + · · · + an pn exp[−an w] = ai pi exp[−ai W] i=1

(11) where pi is the probability of occurrence of the parameter ai . For the continuous spectrum, Eq. (7) is transformed to:  ∞ d( m) = f(a)a exp(−aW) da (12) m0 dW 0 where f(a) is the probability density function of the random variable a. Determining the parameter Q = Ma, where M is the power of abrasion (W = Mt) we define the wear rate as:  ∞ d( m) v= = f(Q)Q exp(−Qt) dQ (13) dt m0 0 To determine the variable Q(a) we use gamma distribution. It is asymmetrical, applies to positive values—so it has a theoretical basis in this case: 1 α α−1 λ Q f(Q) = exp(−λQ) for Q ≥ 0 (14) Γ(α) Combining Eqs. (13) and (14) we find the following form of the solution for Eq. (13):  ∞ d( m) 1 1 α α v= = λ Q exp[−Q(λ + t)] dQ dt m0 0 Γ(α)  α+1 α λ 1 α Γ(α + 1) λ = = , Γ(α) (λ + t)α+1 λ λ+t  α+1 d( m) 1 α λ v(t) = = (15) dt m0 λ λ+t Integrating the above equation from t = 0 to t we obtain the formula that describes the mass decrement of the abraded concrete:  α+1 α   m λ α t λ (t) = dt = 1 − (16) m0 λ 0 λ+t λ+t The quotient α/λ determines the expected value of the parameter Q because  ∞  ∞ λα E(Q) = f(Q)Q dQ = Qα e−λQ dQ Γ(α) 0 0 λα Γ(α + 1) α = (17) = Γ(α) λα+1 λ Eqs. (15) and (16) allow us to easily express the rate and relative change in mass decrement of the abraded material in function of work W of the abrasive mix:  α+1 α λM v(W) = (18) λM λM + W α  λM m (W) = 1 − (19) m0 λM + W

The expected value of the variable a is expressed by the formula: 1 α 1 = E(Q) (20) E(a) = λM M For W → 0 we can transform Eq. (19) into the formula:  α m 1 =1− m0 1 + (W/λM)  (λM/W)(Wa) 1 =1− , 1 + (1/(λM/W))  −(λM/W)(Wa) m 1 = 1 − lim 1 + lim W→0 m0 W→0 (λM/W) = 1 − e−Wa

(21)

that is equivalent to Eq. (8).

6. About the solution The result from Eqs. (15) and (16) (that determine rate and relative changes in mass decrement of the abraded concrete in function of time t) and from Eqs. (18) and (19) (that express these quantities in function of work W of the abrasive mix) is that the expected value of the random variable a(Q) is the parameter that express the disintegration rate of the material for W = 0 (t = 0): α α v(W = 0) = = E(a), v(t = 0) = = E(Q) (22) λM λ In general, to satisfy a condition: E(a1 ) ≥ E(a2 ) ∪ E(Q1 ) ≥ E(Q2 )

(23)

does not unambiguously determine inequality: m m (α1 , λ1 , t) ≥ F2 = (α2 , λ2 , t) for t ≥ 0 m0 m0 m F1 = (α1 , λ1 , W) ≥ F2 m0 m = (α2 , λ2 , W) for W ≥ 0 (24) m0

F1 = or

The necessary and sufficient condition that for every t ≥ 0 ∪ W ≥ 0 exists a relation F1 ≥ F2 is F1 (α1 , λ1 , t ∪ W) = v1 (α1 , λ1 , t ∪ W) ≥ F2 (α, λ, t ∪ W) = v2 (α2 , λ2 , t ∪ W) The analysis of Eqs. (15) and (18) show that for E(a1 ) ≥ E(a2 ) ∪ E(Q1 ) ≥ E(Q2 ) these inequalities are true (Fig. 4): v1 (α1 , λ1 , t) ≥ v2 (α2 , λ2 , t) ∪ v1 (α1 , λ1 , W) ≥ v2 (α2 , λ2 , W) for α1 ≥ α2

(25)

E. Horszczaruk / Wear 256 (2004) 787–796

793

Fig. 4. Geometrical interpretation of relation (25).

7. Description of the abrasive wear of the concrete The results of the experiments on the relative mass decrement of the abraded concrete allow us to determine unknown parameters α and λ form Eqs. (15) and (19) that define the wear process. To minimise the following formula: Ω(α, λ) =

N  

 F(α, λ, t ∪ W) −

i=1

m m0

 2 i

,

i = 1, . . . , N

I used the algorithm of searching the parameters α and λ that determine function F(α, λ, t ∪ W). The parameter E(Q) determines the resistance of the concrete for the abrasive wear. The lower the value of E(Q) the higher the resistance of the concrete. Fig. 5 show the results from the measurement of the relative mass decrement of the samples in relation to work of the abrasive mix. Results of calculations for individual test series are presented in Table 1. In case of different velocities of the abrasive mix for the samples from Series IV (concrete made of the same mix) I obtained the same expected value of the parameter E(a) = α/λ for all three velocities: E(a) = 1.6 × 10−5 kg/kJ. The results of Series II prove the thesis of this paper—that the resistance of the concrete for the abrasive actions in conventional standard conditions can be characterised with—as the other physio-mechanical properties—a material factor dependent only of the concrete’s ingredients.

The expected values of the parameter a obtained for Series II (that was characterised by a different water–cement ratio w/c = 0.4–0.6) are: • E(a) = 0.79 × 10−5 kg/kJ for concrete on w/c = 0.4, • E(a) = 1.02 × 10−5 kg/kJ for concrete on w/c = 0.5, • E(a) = 1.48 × 10−5 kg/kJ for concrete on w/c = 0.6. It means that a concrete with lower water–cement ratio has a higher abrasive resistance (Fig. 7a). 8. Results and discussion Comparative analysis of concrete composition influence on its wear due to abrasion by aggregate/water mix was carried out by determining unknown values of E(a) parameter for each group of abraded samples in individual test series. Many properties of hardened concrete are traditionally assessed on the basis of its compressive strength fc and absorbability η. Relationships between strength fc, absorbability η and the values of parameter E(a) determined for concrete of all series analysed are shown in Fig. 6. Presented relationships indicate that there is no connection between concrete resistance to abrasion–erosion and its strength or absorbability. Resistance of concrete to abrasion–erosion depends both on the quantitative proportion of hardened slurry in unit of volume of the material as well as on its quality depending on the value of ratio w/c and the kind of cement and additives. It

794

E. Horszczaruk / Wear 256 (2004) 787–796 0,08

F=∆m/m0

0,07

SERIES II

0,06 0,05 0,04 0,03 0,02 0,01 0,00

0

2000

4000

0.024

w/c=0.4

F=1-[3045.89/(3045.89+W)]

w/c=0.5

F=1-[2828.25/(2828.25+W)]

w/c=0.6

F=1-[2615.23/(2615.23+W)]

6000

0.029 0.039

8000

10000

12000

14000

16000

W [kJ/kg]

F=∆m/m0

0,10

SERIES IV

0,08

0,06 F=1-[1977.98/(1977.98+W)]

0.032

0,04

v=2.5 m/s v=3.5 m/s v=4 m/s

0,02

0,00

0

11250

22500

33750

45000

W [kJ/kg] Fig. 5. Changes in relative loss of mass of Series IV concrete samples depending on the work of abrasive mix.

-5

-5

E(a)x10 [kg/kJ]

E(a)x10 [kg/kJ]

5

5

4

4

3

3

2

2

1

1 fc [MPa]

0 35 (a)

35.5

36 36.5

37

37.5

38

38.5

η

[%]

0

39

1

1.4

1.8

2.2

2.6

3

3.4

(b) Fig. 6. Values of E(a) parameter of investigated concrete depending on: (a) compressive strength and (b) absorbability.

3.8

E. Horszczaruk / Wear 256 (2004) 787–796

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Table 1 Values of α and λ parameters as well as expected values E(Q) and E(a) Details of series

α

λ

E(Q) (1/h)

M (kJ/kg h)

λM

E(a) × 10−5 (kg/kJ)

Series I Gravel of 2–4 mm Gravel of 2–8 mm Gravel of 2–16 mm

0.064 0.043 0.032

9.57 9.98 12.74

0.0067 0.0043 0.0026

144.9 156.1 163.1

1386.00 1557.10 2078.18

4.6 2.7 1.5

Series II w/c = 0.4 w/c = 0.5 w/c = 0.6

0.024 0.029 0.039

18.88 17.32 16.66

0.0013 0.0017 0.0023

161.3 163.3 157.0

3045.89 2828.25 2615.23

0.7 1.0 1.4

Series III CEM I CEM II(A-S) CEM II(A-V) CEM IIIA

0.032 0.032 0.029 0.030

12.74 10.83 17.11 9.92

0.0026 0.0030 0.0017 0.0030

163.1 162.4 166.3 158.8

2078.18 1758.32 2844.68 1575.94

1.5 1.8 1.0 1.9

Series IV v = 2.5 m/s v = 3.5 m/s v = 4 m/s

0.032 0.031 0.032

12.74 6.70 4.51

0.0026 0.0046 0.0071

163.1 291.9 438.8

2078.18 1955.73 1977.98

1.6 1.6 1.6

Series V K-1 K-2 K-3 K-4 K-5

0.030 0.031 0.032 0.030 0.032

8.02 10.03 12.74 17.32 12.40

0.0037 0.0030 0.0026 0.0017 0.0026

148.2 152.9 163.1 167.4 156.0

1188.48 1533.08 2078.18 2897.81 1934.07

2.5 2.0 1.5 1.0 1.7

Series VI Basalt of 2–4 mm Basalt of 2–8 mm Basalt of 2–16 mm

0.032 0.028 0.025

11.86 13.08 16.84

0.0027 0.0022 0.0015

146.4 148.2 159.0

1735.74 1937.51 2676.83

1.8 1.4 0.9

follows from Fig. 7 that greater resistance to these reactions is displayed by concrete of lower water/cement ratios. Concrete prepared using cements: CEM I 32.5 R, CEM II/A-S R and CEM III A/NW NA 32.5 showed similar loss of mass during the period of their abrasion and, suitably, similar values of E(a) parameter. In contrast, only the samples prepared using CEM II A-V 32.5 R cement with ad-

E(a)x10-5[kg/kJ]

dition of fly-ash is characteristic by its greater resistance to abrasion–erosion. In view of similar strength properties of cements used, attention should be paid to types of additives used in their production. Addition of fly-ash to cement causes changes on the structure of porosity in the slurry and causes the decrease of portlandite, favouring increase of aggregate grain adhesion to the matrix.

E(a)x10-5[kg/kJ]

3

1,8

2,5

1,6

1,58

1,71 1,6

1,4 2

1,2 1,02

1

1,5

0,8 1

0,6 0,4

0,5

0,2

0 0.2

(a)

0.4

0.6

0.8

1

w/c

0

(b)

CEM I

CEM II/A-S

CEM II/A-V

CEM III/A

Fig. 7. Values of E(a) parameter of investigated concrete depending on: (a) water/cement ratio and (b) kind of cement used.

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E. Horszczaruk / Wear 256 (2004) 787–796

9. Conclusion Presented theoretical model of the abrasive wear of the concrete was experimentally verified for the initial period of wear of the hydrotechnical constructions (the fastest change of the concrete wear rate). The analysis of the results shows that the concrete wear caused by interaction with the aggregate–water mix can be expressed in relation to a parameter that describes its composition (structure) and the work of the abrasive mix. To extend all the derived kinetic formulas for the longer periods of abrasive mix interaction we need more precise description of the material properties of the abraded concrete and more experiments. References [1] A. Małasiewicz, Abrasion of concrete used in hydraulic structures at various angles of incidence on sample of rubble carried by water, Rozprawy Hydrotechniczne, PAN 32 (1973) 239–246. [2] A. Bania, Bestimmung des Abriebs und der Erosion von Betonen mittels eines Gesteinsstoff-Wassergemisches, Dissertation B, TH Wismar, 1989. [3] A. Bania, New device for testing abrasion and erosion of concrete, Ochrona przed Korozj˛a 1 (1991) 15–17. [4] E. Horszczaruk, New Test Method for Abrasion Erosion of Concrete, WPK, Krakow, July 19–22, 1996. [5] E. Horszczaruk, Wear of concrete due to action of aggregate and water, Ph.D. Thesis, Technical University of Szczecin, 1999, pp. 31–35. [6] G. Haroske, Erosionsverschleiss an Betonoberflächen durch Geschiebetransport, Dissertation, TH Wismar, 1998, pp. 53–63.

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