Fast-Track Construction with Slag Cement Concrete: Adiabatic Strength Development and Strength...

(ProQuest-CSA LLC: ... denotes formulae omitted.)

INTRODUCTION

In recent years, fast-track construction has created a need for early-age estimates of concrete strength. Fast-track construction can have considerable economic benefits. Accelerated construction schedules that put a new, repaired, or overlaid pavement into service require adequate concrete strength to withstand traffic loads. Typical applications include localized repairs, replacement of busy intersections, and major slipform paving. In structural components, the early removal of forms or the application of post-tensioning and the termination of curing in cold weather have safety implications as well as potential cost savings.1 Because fasttrack construction requires high early-age strengths, the factors affecting these properties must be considered. Factors include the composition of the concrete mixture, such as cement type and use of supplementary cementitious materials, and the use of retarding or accelerating admixtures. The strength development of a concrete is also influenced by temperature, with strength gain more rapid at higher temperatures and slower at lower temperatures. If the temperature is too low, strength gain will cease. The temperature inside the concrete depends on the heat of hydration produced by the reaction of cement, the size and shape of the structural element, the ambient temperature, and the use of insulation.

Slag cement is commonly used in concrete in combination with portland cement. It can improve the performance of both fresh and hardened concrete, producing improved workability, reduced heat of hydration, higher ultimate strength, and enhanced durability.2-4 The strength development of slag cement concrete under standard curing conditions, however, is slower than that of portland-cement concrete. Slag cement, along with other supplementary cementitious materials such as fly ash, is not therefore commonly used in applications where high early-age strength is required, for example fast-track construction. There is evidence, however, that these materials are heavily penalized by standard 20 °C (68 °F) curing temperatures and can achieve significantly improved early-age strength development under elevated curing temperatures. The higher early-age temperatures occurring inside structural elements, due to heat of hydration of the binder, appear to be sufficient to produce a considerable improvement in the early-age strength of slag cement concrete.3,5,6

To provide guidance on the use of slag cement in fast-track construction, it is necessary to model the strength development of the concrete under elevated, variable temperature conditions. Several maturity functions exist in the literature,7-14 which predict the strength development of concrete from its temperature history. These models use the experimentally determined strength-age relationship at a reference temperature to predict the strength at any other temperature. These models, however, were developed for portland-cement concrete and, because the temperature sensitivity of slag cement is much greater than that of portland cement, it is unlikely that these functions can be directly applied to slag cement concrete without modification.

The work described herein forms part of a 3-year project funded by the Engineering and Physical Sciences Research Council (EPSRC), UK. The aims of the project included:

* Quantifying the enhancement in strength that may be expected due to high early-age temperatures in structural elements. The initial part of the investigation looked at the strength development of concretes, with low, medium, and high strengths, and with up to 70% of the total binder being slag cement, under adiabatic conditions. The enhancement of strength was compared with that of cubes cured at 20 °C (68 °F).

* The applicability of maturity functions, determined empirically from work on portland-cement concretes, for slag cement concretes. Relationships between strength and maturity were determined using data from cubes cured at 20 °C (68 °F). These relationships were then used together with the adiabatic temperature history to predict the strength development under adiabatic curing conditions.

RESEARCH SIGNIFICANCE

Higher in-place temperatures in structural elements, occurring as a result of cement hydration, enhance the early-age strength of slag cement concrete. The enhancement to strength has been quantified for adiabatic conditions for contractors to be in a position to take advantage of these enhanced strengths for fast-track construction. It is also necessary to predict the strength development under elevated, variable early-age temperature conditions. The suitability of existing maturity functions for predicting slag cement concrete's strength development was assessed.

REVIEW OF MATURITY FUNCTIONS

The strength development of concrete is affected by its mixture proportions, its age, and its temperature history. Strength development of concrete is commonly determined at standard curing temperatures, but it will change if the concrete is cured at a different temperature. At elevated temperatures, the strength is often higher at early ages but lower at later ages, with the reverse effect observed at low temperatures. The concept of concrete maturity was introduced to describe the combined effect of temperature and age on concrete strength development. A given concrete at a particular maturity should have the same strength regardless of its actual age and temperature history. Maturity functions predicting the strength development of concrete, based on its temperature history, have been developed by several researchers.7-14 If the strength development of a particular concrete is known at a reference temperature T^sub ref^, these maturity functions enable the prediction of strength for any other temperature history of the concrete. The functions were generally developed using data for portland-cement concrete under isothermal curing conditions.

The oldest and simplest of these maturity functions was developed by Nurse7 and Saul8 (NS) to describe the effects of steam curing on concrete. Maturity was defined as

... (1)

where M equals maturity, °C-days (°F-days); t equals time, days; T equals average temperature during time interval ?t, °C (°F); and T^sub 0^ equals datum temperature, °C (°F)-the temperature at which strength gain is assumed to cease, taken as -11 °C (12 °F) in this work.

The introduction of a reference temperature T^sub ref^, at which the strength-maturity relationship is determined, leads to the concept of equivalent age, that is, the time at the reference temperature t^sub e^ at which the concrete has the same strength as at a time t. For the Nurse-Saul method,6,7 this is expressed mathematically as

... (2)

The method developed by Weaver and Sadgrove9 (WS) uses an equivalent age model that also depends on temperature and time only

... (3)

The model was developed based on portland-cement concretes but has also been applied by Wimpenny and Ellis10 and Clear11 to concretes containing slag cement at various levels up to 70%.

Later developments by Freiesleben Hansen and Pedersen12 (FHP) use the Arrhenius function to describe the temperature sensitivity of the binder reaction

... (4)

where k equals rate constant, days^sup -1^; A equals constant, days^sup -1^; E^sub a^ equals apparent activation energy, J/gmol (in.-lbf/lbm-mol); and R equals universal gas constant: 8.314 J/gmol*K (18,544 in.-lbf/lbm-mol-Rankine).

This results in the following expression for equivalent age

... (5)

...

Whereas these three models are adequate for many early-age applications, they are unable to accurately predict later-age strengths as they assume that the ultimate strength of the concrete is the same regardless of its temperature history. As mentioned previously, higher temperatures lead to increased early-age strength, but reduced later-age strength.6,13,14 The model developed by Freiesleben Hansen and Pedersen, however, is accurate in predicting relative strength development,15 that is, the ratio of actual strength to actual ultimate strength. Recent developments are therefore based on modifications of their approach to account for reduced/enhanced later-age strength.

Chanvillard and D'Aloia13 (CD) developed a model in which the 28-day strength of the concrete is assumed to decrease linearly with increasing curing temperature. The model defines a hydration degree α

... (6)

where S equals the compressive strength, MPa (psi); S^sub 28,Tref^ equals the 28-day strength at the reference temperature, MPa (psi); and p is a constant (= 0.01).

The relationship between the hydration degree α and equivalent age is determined at the reference temperature, and the strength can then be determined from

... (7)

where

... (8)

Kjellsen and Detwiler's model14 (KD) accounts for changes in later-age strength by defining the apparent activation energy as a function of relative strength rather than as a constant. The relative strength f^sub cr^ in this case is the strength relative to the 28-day strength at the reference temperature. The apparent activation energy is described in Eq. (9) to (12)

... (9)

where the initial apparent activation energy is defined by

... (10)

...

where τ^sub e^ equals the age to reach f^sub cr^ equals 0.2 at reference temperature T^sub ref^; and t^sub T^ equals age to reach f^sub cr^ equals 0.2 at temperature T.

For f^sub cr^ < 0.2

... (11)

For f^sub cr^ = 0.2 and T < 20 °C (68 °F)

... (12)

(SI units)

...

(in.-lb units, °F)

For f^sub cr^ = 0.2 and T > 20 °C (68 °F)

... (13)

(SI units)

...

(in.-lb units, °F)

The apparent activation energy described by these equations decreases with increasing relative strength, that is, the reaction of the binder is more sensitive to curing temperature at early ages than at later ages. The equivalent age is defined as

... (14)

(SI units)

...

(in-lb units, °F)

The suitability of the aforementioned maturity functions for slag cement concretes under adiabatic conditions has been investigated in this paper.

MATERIALS AND EXPERIMENTAL PROCEDURES

A total of 15 concrete mixtures were tested. The target 28-day mean strengths were approximately 40, 70, and 100 MPa (5075, 10,150, and 14,500 psi). The actual achieved strengths were in the ranges of 31 to 36 MPa (4500 to 5220 psi), 57 to 79 MPa (8270 to 11,460 psi), and 94 to 105 MPa (13,630 to 15,230 psi). The percentage slag cement of the total binder was 0, 20, 35, 50, and 70%. Mixture proportions are given in Table 1.

Materials

Single batches of portland cement and slag cement were used throughout. The fine aggregate was fine sand, where 81% of the particles passed through the 600 µm (0.022 in.) sieve and had a fineness modulus of 1.68. The coarse aggregate was crushed granite with a maximum aggregate size of 20 mm (0.79 in.). All aggregates were oven-dried before use and allowance was made for absorption when calculating batch weights for mixing. The high-range water-reducing admixture used was a polycarboxylate polymer.

Mixing, casting, curing, and testing of concrete specimens

The materials were weighed and mixed for 5 minutes in a 0.1 m^sup 3^ (0.13 yd^sup 3^) capacity horizontal pan mixer. The concrete was cast into the molds and compacted on a vibrating table. The following specimens were cast from each batch of concrete

* 100 mm (4 in.) cube specimens for curing under standard 20 °C (68 °F) conditions. After casting, these specimens were covered with damp sacking and polythene sheeting. After 24 hours, they were demolded and transferred to a water curing tank set at 20 °C (68 °F).

* A 200 x 200 x 200 mm (7.9 x 7.9 x 7.9 in.) concrete specimen was cast in a 240 x 240 x 240 mm (9.4 x 9.4 x 9.4 in.) plywood mold lined with 20 mm (0.79 in.) expanded polystyrene for insulation and heavy-duty polythene to prevent moisture loss. The specimen was transferred immediately to a temperature/humiditycontrolled environmental cabinet, and two copper/ constantan thermocouples were inserted in it through a hole in the top of the mold. Two more copper/ constantan thermocouples were used to monitor the temperature of the cabinet. The thermocouples were all connected to a computer that recorded the temperatures and controlled the cabinet temperature to be approximately the same as that of the specimen, that is, to within 1 °C (1.8 °F). The test was continued for 5 days. It can be assumed, based on the fact that there was no temperature drop after the maximum had been reached, that there was only very little heat loss and no adjustment was needed for the results. The adiabatic test setup is illustrated in Fig. 1.

* 100 mm (4 in.) cube specimens for curing under adiabatic conditions. These specimens were placed in the environmental cabinet alongside the adiabatic test specimen described previously immediately after casting. They were therefore cured under adiabatic temperature conditions. The relative humidity of the air in the cabinet was maintained at 90%. Early-age specimens were demolded before testing. Later-age specimens were demolded after 5 days and wrapped in damp sacking and polythene sheeting. They were then transferred to a constant temperature oven set at the maximum temperature reached in the adiabatic test.

It should be noted that curing cubes at 90% relative humidity rather than under water is not believed to have had a significant effect on the strength development of the adiabatically cured cubes and, therefore, the standard and adiabatic cube strengths can be directly compared. This was confirmed experimentally for one of the concrete mixtures (medium-strength portland-cement concrete) where three sets of cubes cured: 1) under water; 2) at 90% relative humidity; and 3) sealed, all had the same strength development for adiabatic temperature conditions.

The standard and adiabatically-cured cubes were tested in compression at 1, 2, 3, 5, 7, 14, 28, and 91 days. Three cubes from each curing regime were tested at each testing age.

RESULTS AND DISCUSSION

Adiabatic temperature rise

The adiabatic temperature rises of all the concretes are shown in Fig. 2. An initial period of near-constant temperature, corresponding to the so-called dormant period of cement hydration, is followed by an acceleration of temperature rise, which subsequently tends asymptotically to a nearmaximum value. This is not a true maximum, as some heat will continue to be generated for some time. The resulting temperature increase, however, was not measurable with the test system, and was considered negligible in the analysis of the results. The maximum temperature rise of portlandcement (PC) concretes increased from 36 °C (65 °F) for the low-strength concrete to 47 °C (85 °F) for the medium-strength concrete, but slightly reduced to 45 °C (81 °F) for the high-strength concrete. This is despite cement contents increasing from 300 kg/m^sup 3^ (506 lb/yd^sup 3^) to 375 kg/m^sup 3^ (632 lb/yd^sup 3^) and to 465 kg/m^sup 3^ (784 lb/yd^sup 3^). It appears that the heat output per unit mass of cement is reduced significantly at very low w/c; a w/c of ~0.4 would be needed for complete hydration of the cement.16 It is also noted that high levels of slag cement, that is, 50 and 70%, are required for any significant reduction in the peak temperature, especially at high strengths. Lower levels of 20 and 35% appeared to give a bigger reduction in the peak temperature at low-strength grades while this reduction was negligible at higher-strength grades.

Because of the asymptotic nature of the temperature rise curves at the end of the dormant period and when approaching the maximum temperature, the following parameters were used:

1. The dormant period, defined as the time to reach a 10 °C (18 °F) temperature rise; and

2. The time to reach 95% of the maximum temperature rise.

The dormant periods (refer to Fig. 3) appear to increase with increasing percentage of slag cement in the binder. The increases were substantial for the low-strength concretes containing 50 and 70% slag cement. For example, the dormant period for low-strength portland-cement concrete was approximately 7 hours, whereas for 70% slag cement concrete, the dormant period was 25 hours. For high-strength concrete, while the dormant period for portland-cement concrete remained the same as for low-strength concrete (~7 hours), the dormant period of 70% slag cement concrete was reduced to 11 hours. The incorporation of slag cement resulted in retardation in the time to reach 95% of the maximum temperature (Fig. 3); this is due to the slower secondary reaction of slag cement. As with the dormant period, however, increasing concrete strength seemed to reduce this retardation effect of slag cement.

Strength development under adiabatic and standard curing conditions

The strength development of all the portland-cement concretes and concretes with 35 and 70% slag cement are shown in Fig. 4 to 6. Trends for the 20 and 50% slag cement concretes are similar. The solid line shows the strength development of concretes cured at 20 °C (68 °F), that is, standard curing regime, while the dashed line is for the concretes cured under adiabatic conditions. For clarity, error bars are not shown but the errors in the strength values, based on three replicate specimens, are approximately ±2 MPa (±290 psi). All concretes showed improved early-age strength development when cured under adiabatic conditions. The high early-age temperatures, however, were detrimental to the long-term strengths of concretes. Strengths can be reduced by as much as 20% at 28 days. A similar reduction has been quoted by Bamforth.17 The impaired long-term strength development, resulting from heating concrete at a very early age, is believed to be due to a fundamental change in the hydration products formed. Mechanical breakdown between the cement paste and aggregate as a result of thermal stressing has also been suggested. There is an indication that the detrimental effect at 28 days was lower for increasing percentage levels of slag cement. This is again in agreement with Bamforth's results,17 which showed that the ratio between the heat-cycled strength and the standard cured strength at 28 days remained above unity. A word of caution is necessary, however, as later-age strengths, usually recommended to benefit from the later-age strength development of slag cement concretes, may show 20% strength reduction at 56 days in the case of slag cement concretes, as has been shown by Bamforth's experimental work.17

Figure 7(a) shows the ratio of strengths of slag cement concretes to the strengths of portland-cement concretes for cubes cured at 20 °C (68 °F). Concretes with slag cement, even the ones with 70% slag cement, had very similar 28-day strengths to the portland-cement concretes. The early-age strengths, however, were adversely affected by increasing levels of cement substitution with slag cement; for example, at 1 day, the strength of 70% slag cement can be as low as 16% of the strength of the portland-cement concrete at the same age.

Figure 7(b) shows the ratio of adiabatic strength of slag cement concretes to the adiabatic strength of the portlandcement concrete. The slag cement concretes certainly benefited much more from the adiabatic temperature rise than the portland-cement concrete; for example, the 20 and 35% slag cement concretes had similar or even higher strengths than the portland-cement concrete even at 1 day. The peak temperature of concretes with higher levels of cement replacements, that is, 50 and 70% slag cement, was reached after the first day, and they therefore showed a more marked improvement in strength at 3 days for low-strength concrete and at 2 days for medium- and high-strength concretes. This is consistent with the time required for the concretes to reach 95% of maximum temperature rise under adiabatic conditions (Fig. 3). Figure 7(b) also shows that all high-strength slag cement concretes, including 70% slag cement, had comparable strengths to the portland-cement concrete from 2 days onward. The most impressive strength enhancement was that of 70% slag cement high-strength concrete at 2 days-the adiabatic strength was 78.5 MPa (11,390 psi) compared with a standard cured strength of only 29.8 MPa (4320 psi). High-strength concretes with slag cement, irrespective of the percentage level, had at least 90% of the portland-cement concrete strength from 2 days onward for high- and medium-strength concretes, and from 3 days onward for low-strength concretes.

Determination of model parameters for maturity functions

Strength predictions for nine of the mixtures (0, 35, and 70% slag cement at three strength grades) described previously were calculated. The strength development under standard 20 °C (68 °F) curing conditions of each concrete is shown in Fig. 4 to 6. The compressive strength S was related to equivalent age by the following equation14

... (15)

where S∞ equals estimated compressive strength at infinite time, MPa (psi); k equals rate constant, days-1; and t^sub 0^ equals time at which strength gain is assumed to begin, days.

The values S∞, k, and t^sub 0^, producing the best fit to the experimental data at 20 °C (68 °F) were determined for each concrete by regression analysis and are listed in Table 2.

The apparent activation energy of each concrete was determined according to the ASTM C 1074 method,18 and the values obtained19 are given in Table 2. These values were also used as the initial apparent activation energies in applying the Kjellsen-Detwiler14 function. This removes the need for knowledge of the early-age strength development, which is required in their definition of the initial value of the apparent activation energy (Eq. (9)) and is difficult to determine under variable temperature conditions.

Determination of the constant p in the Chanvillard-D'Aloia13 function, based on the equivalent mortars mentioned previously, produced values close to 0.01, in agreement with their work. It was noted that using the individual value obtained for each mortar gave better agreement in predicting the adiabatic concrete strength development than using the value of 0.01 for all concretes. The values of p used in each case are quoted in Table 2.

Predicted strength development based on maturity functions

The equivalent age and, hence, the predicted adiabatic strength for each concrete were both calculated from the recorded adiabatic temperature history using the five maturity functions described previously with the appropriate parameters. Predicted strengths were then compared with the actual strengths of cubes cured adiabatically to investigate the accuracy of the functions.

Figures 8 to 10 compare the experimentally determined adiabatic strength developments with those predicted by maturity functions. In the low-strength (Fig. 8) and mediumstrength (Fig. 9) grades, the two models that incorporate the effects of temperature on later-age strength13,14 produced the best fit to the experimental data for all slag cement levels.

The situation is more complex for the high-strength grade concretes (Fig. 10). The strength development of the 70% slag cement concrete was again reasonably well predicted by the Chanvillard-D'Aloia13 and Kjellsen-Detwiler14 functions, as was for the lower-strength grades. In the portland-cement high-strength concrete, the later-age strengths under adiabatic curing conditions were similar to those under standard conditions, and the Nurse-Saul7,8 and Freiesleben Hansen-Pedersen12 functions produced the closest agreement. The reaction of the binder in this concrete was less sensitive to temperature than any of the other concretes, as shown by its lower apparent activation energy in Table 2. Because the reaction was less influenced by temperature, it follows that the early-age strength was only slightly enhanced and the later-age strength was largely unaffected by higher temperatures. The 35% slag cement level was intermediate between the two and its strength development was not particularly well predicted by any of the maturity functions.

The accuracy of the strength predictions of the five maturity functions investigated is shown in Fig. 11 to 15. The accuracy of the maturity functions is dependent on binder type, strength grade, and age. For the Nurse-Saul model7,8 (Fig. 11), the ratio of predicted strength/actual strength increased with age for all concretes except the highstrength portland-cement concrete. For the lower-strength grades of portland-cement concrete, the function was accurate in predicting 1-day strength, but then the ratio predicted/actual increased and the model overestimated the strength by an increasing degree with age. The accuracy of the Nurse-Saul7,8 function in predicting the strength development of portland-cement concrete was dependent on the strength grade of the concrete. For the slag cement concretes, the accuracy of the function seemed independent of strength grade. For the 35 and 70% slag cement concretes, it underestimated the strength development at early ages and overestimated the strength development at later ages. This suggests that the temperature dependence of the Nurse-Saul function is not sufficient to account for the improvement in early-age strength of slag cement concretes caused by higher temperatures.

The Weaver-Sadgrove function9 (Fig. 12) was reasonably accurate for the high-strength portland cement and 35% slag cement concrete but was less accurate for lower-strength grades. The level of agreement was invariant with age for the portland-cement concretes but the predicted strength/actual strength ratio increased with age for the 35% slag cement concrete. The function overestimated strength at all ages from 3 days onward. As with the Nurse-Saul function, the Weaver-Sadgrove function tended to underestimate the strength development of all strength grades of 70% slag cement concretes at early ages and overestimated it at later ages.

The Freiesleben Hansen-Pedersen12 equivalent age function (Fig. 13) tended to overestimate strength development in all cases, except where the ultimate strength was not affected by the curing regime. Its accuracy was better for higher-strength grades of the portland cement and 35% slag cement concretes. The predicted strength/actual strength ratio seemed to be independent of age for all of the concretes. The model is accurate in predicting relative strength development15 but is unable to account for any reduction in later age strength.

The Chanvillard-D'Aloia13 function (Fig. 14) was generally accurate to within 20% and the level of agreement with the experimental data was not highly dependent on age. The only exception is the 70% slag cement concrete with a target mean strength of 70 MPa (10,150 psi), for which the strength was overestimated by approximately 30%. The model was especially good for the low-strength concretes at all slag cement levels.

The Kjellsen-Detwiler14 model was again generally accurate to within 20%, and the level of agreement was mostly independent of age for each mixture. However, the 1-day strengths of the 70% slag cement concretes at the medium- and highstrength grades were overestimated by approximately 50%. Apart from this discrepancy, it seemed to be the best model for predicting the strength of slag cement concretes for a wide range of slag cement/portland cement proportions. It was less suitable for predicting portland-cement concrete strength development as it tended to overestimate the strength of the low- and medium-strength portland-cement concretes, and underestimate that of the high-strength portland-cement concrete.

No single maturity function of the five investigated produced accurate prediction of concrete strength development for all the concretes investigated. The models developed by Chanvillard and D'Aloia13 and Kjellsen and Detwiler,14 however, have been shown to have the highest level of agreement across the full range of mixtures and are therefore to be further investigated. The aim is to modify these models to improve their accuracy. Adiabatic strength development is an extreme case in terms of the temperatures developed due to heat of hydration, and the accuracy of these functions for predicting strength development under more typical inplace temperature conditions will also be investigated.

CONCLUSIONS

The early-age strength of concretes with similar 28-day strengths and cured at 20 °C (68 °F) are adversely affected by increasing levels of slag cement. The early-age strength contribution of slag cement, however, is greatly improved by high curing temperatures; for example, the strength development of slag cement concretes cured under adiabatic conditions have comparable strengths to the portland-cement concrete from either 2 or 3 days onward. If these improved strengths are to be exploited in fast-track construction, then: 1) the expected in-place temperature history will have to be modeled using finite element analysis software-heat of hydration values, which can be obtained from adiabatic tests, will be needed as inputs; and 2) the in-place strength development will have to be predicted using maturity functions. It is worth noting that the improved strengths obtained herein are also relevant to mass concreting, where the temperature conditions may be very close to adiabatic, and slag cement is commonly used at high levels to reduce the temperature rise and, hence, the risk of thermal cracking.

The work presented herein has shown that existing maturity functions for predicting portland-cement concrete strength are unable to predict the strength development of slag cement concrete with sufficient accuracy. Of the functions investigated in this work, those that model a reduction in later-age strength, caused by higher curing temperatures, can predict strength development of concrete for a wide range of strength grades and slag cement levels to within 20%. The other functions investigated only produce good agreement with the experimental results in cases where there was no detrimental effect on the experimental later-age strengths. This occurred in the high-strength portland-cement mixture (and also in high-strength mixtures containing low levels of slag cement).

The functions developed by Chanvillard and D'Aloia13 and Kjellsen and Detwiler14 have the potential to be modified to produce more accurate strength development predictions. For example, in the case of the Chanvillard and D'Aloia model, this could be achieved by modification of the relationship between temperature and ultimate strength. The experimental data show that this relationship is more complex than the linear relationship used in their function.

The determination of dependence of ultimate strength on early-age temperatures is the key aspect to further modification of existing models, or the development of alternative models. The later-age strength of these concretes under adiabatic curing conditions depends on both the binder and the strength grade. In some cases, the ultimate or 28-day strength of the concrete is unaffected by the higher curing temperatures experienced during adiabatic curing.

ACKNOWLEDGMENTS

The authors would like to acknowledge the financial support of the Engineering and Physical Sciences Research Council, UK (GR/R83880/01), and the Appleby Group. The authors are very grateful for the extensive advice received during the project from T. Harrison (Quarry Products Association, UK) and J. A. Bickley (Bickley Associates Ltd, Canada). The authors thank D. Hunter for his assistance with casting and testing specimens.