The concrete repair material was supplied in bags ready for mixing with water. The concrete mix proportions were provided but without any information on the commercially sensitive cement blend proportions apart from an indication that the blend contained a rapid hardening cement and standard Portland cement class I. To produce the concrete, we just had to add water to the dry ingredients (2.25kg of water for each 25kg bag of mix) and mix them in a normal mixer following the mixing instructions described on the bags and the data sheets. Our first investigation therefore was aimed firstly at checking whether the compressive and split cylinder strengths stated in the supplier data sheets could be reached, and secondly to get an idea of the proportions of rapid hardening cement and Portland cement class I in the blend by performing an adiabatic test. Henceforth, the commercial concrete repair material will be simply referred to as RHC.

Standard cube (100mm) and cylinder (100mm diameter, 200mm height) specimens were cast from RHC. The specimens were tested according to British Standard procedures [16–18] at various ages after casting: 60min, 90min, 7h, 24h, and 7 days. The specimens tested at 60 and 90min ages were only air cured, whereas those at later ages were water cured.

The mix was very wet after mixing, but it hardened within minutes in the mould. The results of compressive (fc) and split cylinder (fst) tests are given in Table 2. The compressive strength at all ages is consistently higher than the characteristic value stated in the product data sheets (Table 3).

This test was performed using a large polystyrene block in which a cubical cavity (roughly 150mm side) had been made with a sharp blade. The sides of the cavity were lined with aluminium foil. The cavity was filled with the wet mix and covered first with aluminium foil and then a polystyrene lid. The lid was secured to the block with packaging tape. Five K-type thermocouples (up to 150mm shaft length) were inserted through the lid into the mix within less than 5min of mixing. A typical set up is shown in Fig. 1. The thermocouples were connected to a data logger set to record the temperature readings every minute until steady state conditions had been reached. This rudimentary test set up ensures nearly adiabatic conditions until steady state but not thereafter. A more detailed explanation of several methods for determining the temperature rise in concrete is given in [19] and a procedure for estimation of concrete adiabatic temperature rise by semi-adiabatic temperature rise tests is given in [20].

Figure 1.

Adiabatic temperature test of the mix.

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In our case, several tests with different materials were performed. Fig. 2 shows the response of the most representative RHC mix that we studied in detail. The maximum temperature rise was registered at about 55°C from an ambient temperature of 22°C in 85–95min after mixing. Note that there is practically no delay before the temperature of the mix began to rise.

Figure 2.

Adiabatic temperature rise of RHC mix.

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The hydration kinetics of any binder containing Portland cement can be accurately simulated under fully insulated (adiabatic) conditions using available simulation tools (e.g. LUSAS), provided its chemical composition is known, according to the method of Schindler and Folliard previously described. As mentioned above the suppliers of the RHC mix were only willing to say that the binder is a blend of calcium sulpho-aluminate (CSA) cement and Cem I, but for commercial reasons were not prepared to reveal the proportions of these two components. We had therefore to undertake a forensic investigation in order to gain an understanding of what we had observed in the adiabatic test on RHC mix.

We first simulated the hydration kinetics of Cem I for which the chemical composition is well characterised. We assumed that the mix contained 450kg/m3 of Cem I only. As Cem I is blended with fly ash and therefore contains free lime, we expected it to reach a high temperature but after several hours of hydration following an equally substantial delay in the start of the hydration process. The simulations (Fig. 3) completely agree with the expected behaviour of Cem I. This gave us confidence in trying to reproduce the observed behaviour of the blended binder in the RHC mix (Fig. 2).

Figure 3.

Adiabatic temperature rise in Cem I (450kg/m3) and in RHC mix. The horizontal scale shows time in hours and the vertical scale temperature in °C.

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In the absence of information on the exact proportions of CSA and Cem I in the binder blend of RHC mix, we had to perform many trial simulations in order to reproduce as closely as possible the recorded temperature rise against time curve of RHC mix. The results are also shown in Fig. 3.

Fig. 3 compares favourably with the recorded response (Fig. 2) if the amount of Cem I in the CSA+Cem I blend available for hydration is 280kg/m3.

It would appear therefore that the CSA+Cem I blended binder in RHC mix contains 280kg/m3 of Cem I. As concrete with a 28-day characteristic compressive strength of 55MPa (the 28-day characteristic strength specified in the RHC product sheets) usually contains about 350–400kg/m3 of binder, it appears that the CSA content in RHC mix is between 70 and 120kg/m3 (i.e. the proportions of CSA and Cem I are in the range between 0.2:0.8 and 0.3:0.7).

In this repair option the old concrete sleeper and the surrounding concrete are removed to create a bed (black contour and grey shaded in Fig. 4) for “popping” in the new pre-stressed sleeper (red contour in Fig. 4) and grouting it to the existing concrete (blue contour in Fig. 4) with RHC. The dimensions of the bed and the infill grouting RHC are shown in Fig. 4 and the LUSAS finite element mesh (without the sleeper) in Fig. 5.

Figure 4.

Scheme of the repair option 1.

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Figure 5.

FEM mesh of the repair option 1.

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In the first 90min after the sleeper has been “popped” in and grouted with infill concrete RHC, the latter hydrates releasing heat. As the infill concrete is in frictional contact with the old concrete and the sleeper on the bottom and the sides are exposed to air on the top and at the front, some of the heat is dissipated by convection. The thermal analysis takes this into account through the use of appropriate convection coefficients between the fresh and old concrete and between the fresh concrete and air. The air temperature is assumed to be 27°C. The evolution of temperature with time in the RHC infill is shown in Fig. 6. The temperature profile in the infill concrete 90min after casting is shown in Fig. 7.

Figure 6.

Evolution of temperature due to heat of hydration in the infill grouting RHC in the repair option 1.

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Figure 7.

Temperature profile in RHC mix infill. Note that the maximum temperature at 90min (about 51°C) has dropped below the peak value registered under adiabatic conditions (cf. Fig. 3).

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It is interesting to note that because of the confinement of infill concrete the temperature rise due to heat of hydration (Fig. 6) is only slightly lower than that registered under adiabatic conditions for RHC mix (cf. Fig. 3). Not surprisingly, the coolest regions, albeit still at well above the ambient temperature, are those that are exposed to air at the top and the front.

The contours of maximum and minimum principal thermal stresses (negative sign indicates compressive stress) in the infill RHC at age 90min are shown in Fig. 8.

Figure 8.

Maximum (a) and minimum (b) principal thermal stresses in infill RHC mix at 90min age. The black diamonds indicate damage which is confined to corners.

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After 90min, the first axle traverses the sleeper applying a quasi-static equivalent load of 209kN to it. Assuming that the sleeper is in full contact with the bed of infill RHC, this concentrated load can be replaced by a uniform pressure on the bed applied in the negative z-direction, as shown in Fig. 9. At this stage we are considering only the most favourable load scenario which does not include any lateral loads in the x- and y-directions (Fig. 5). Moreover, as the hydration reaction in the infill RHC is still continuing, we perform a coupled thermo-inelastic analysis from 90 to 120min. In this coupled analysis, apart from the frictional contact (interface) between the old and infill concrete, we now allow a certain movement between the infill concrete and the sleeper. Thus, the surfaces A and B in Fig. 9 in contact with the sleeper are free to translate in the y-direction, whereas the surface C is free to translate in the x-direction. The contours of maximum and minimum principal thermo-mechanical stresses in the infill RHC at age 120min are shown in Fig. 10.

Figure 9.

Loading scheme in the repair option 1 due to the train wheels.

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Figure 10.

Maximum (a) and minimum (b) principal thermo-mechanical stress contours in the infill RHC at 120min age. Black diamonds which indicate areas of damage are confined to corners.

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As observed in Fig. 10, the minor damage generated is the same as at 90min age (Fig. 8). Thus the axle loading does not seem to have induced any additional damage.

Our coupled thermo-inelastic analysis of the hydrating infill RHC mix under vertical axle loading shows insignificant damage at 90min or 120min age. The minor damage apparent in Figs. 8 and 10 is because of the stress concentration at sharp corners. The situation may however change if lateral loads are also applied (see below).

In this repair option the old concrete sleeper and the entire concrete seat are removed to create a bed which is infilled in one continuous pour with RHC mix in readiness for a new pre-stressed sleeper (Fig. 11).

Figure 11.

Geometry of the infill concrete block used in the analysis of repair option 2.

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The thermal and thermo-inelastic analysis of the infill RHC concrete in the repair option 2 followed the same sequence as in the repair option 1 above. The evolution of temperature due to the heat of hydration was followed up to 90min age. Following that the vertical axle loading was applied to the sleeper and the thermo-inelastic analysis continued up to 120min age. Frictional contact was assumed between the old concrete and cast iron tunnel lining and the infill RHC concrete as shown in Fig. 12. The same boundary conditions between the infill RHC concrete and the sleeper (Fig. 13) were assumed as in the repair option 1.

Figure 12.

FEM mesh of the repair option 2.

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Figure 13.

Loading scheme and contact conditions in the repair option 2 due to the train wheels.

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The principal thermal stresses at age 90min in the infill RHC concrete are shown in Fig. 14.

Figure 14.

Maximum (a) and minimum (b) principal thermal stresses in RHC infill concrete at 90min age. There is some minor top surface damage (black diamonds).

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The principal thermo-mechanical stresses induced in the infill RHC concrete by both the temperature and the vertical axle loading at 120min age are shown in Fig. 15. A comparison with Fig. 14 shows that the vertical axle loading does not induce any damage additional to the minor thermal damage already present at 90min age.

Figure 15.

Maximum (a) and minimum (b) principal thermo-mechanical stresses in RHC infill concrete at 120min age. Note that there is practically no change in the minor thermal damage from 90min age (cf. Fig. 14).

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Our coupled thermo-inelastic analysis of the hydrating infill RHC concrete shows that the performance of RHC mix in the repair option 2 almost mirrors its performance in the repair option 1. It suffers very minor damage at both 90min and 120min age (Figs. 14 and 15). However, the situation is likely to change when lateral loads are also applied (see below).

Repair option 3 is a modification of option 2 above. The infill RHC concrete block is cast in two pours, the first to level that just covers the sleeper re-bar and the second to final level with 3 days between pours. In this option, the wheel load is applied 90min after the second pour and there is an interface between the 3-days old first RHC pour and fresh second RHC pour. The geometry and the boundary conditions between the second pour and the sleeper are shown in Fig. 16.

Figure 16.

FEM mesh of the two-pour repair option 3 (a) and loading scheme and contact conditions due to the train wheels (b).

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The thermal and thermo-mechanical analysis in this repair option mimics the casting steps. First, a thermal analysis of pour 1 is performed until 72h age. Next, the thermal analysis of this pour and pour 2 is performed for a further 90min. Finally, a thermo-mechanical analysis is performed until pour 2 reaches 120min age. The temperature profile in pour 1 at 72h age is shown in Fig. 17. Note that the maximum temperature has already reduced to less than 34°C. The corresponding thermal stresses at this age are shown in Fig. 18.

Figure 17.

Temperature profile in infill RHC concrete pour 1 at 72h age.

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Figure 18.

Maximum (a) and minimum (b) principal thermal stresses in infill RHC concrete pour 1 at 72h age. Note that there are a few thermal cracks in this infill concrete.

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We present next the temperature profile (Fig. 19) in the RHC infill mix when the pour 2 is 90min old (pour 1 is 73.5h old) and the corresponding thermal stresses in Fig. 20.

Figure 19.

Temperature profile in RHC infill concrete pours 1 and 2 at 73.5h. Pour 2 is only 90min old.

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Figure 20.

Maximum (a) and minimum (b) principal thermal stresses in RHC infill concrete at 73.5h. There are a few thermal cracks in both pours 1 and 2; those in pour 1 are shown by broken pyramids.

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Finally, we show in Fig. 21 the thermo-mechanical stresses when the age of pour 2 is 120min and that of pour 1 is 74h.

Figure 21.

Maximum (a) and minimum (b) principal thermo-mechanical stresses in RHC infill concrete at 74h.

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The minor cracking in both pours 1 and 2 is very nearly the same as at 73.5h (Fig. 20) which again suggests that cracking is primarily induced by thermal stresses.

In order to demonstrate the importance of thermal stresses induced by the heat of hydration to the early age performance of the infill concrete elements, we have performed an inelastic analysis of the repair option 3 without thermal stresses. We were now able to include also the 4 rebars of the sleeper in this option, as shown in Fig. 22.

Figure 22.

FEM mesh of the repair option 3 with rebars.

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The principal mechanical stresses in the infill concrete at 120min age of pour 2 (pour 1 is 74 hour old) under the vertical wheel loading are shown in Fig. 23. A comparison with Fig. 20 clearly shows that the thermal stresses are responsible for most of the minor damage. Indeed, it would appear from Fig. 23 that the vertical wheel loading hardly causes any damage even at this young age.

Figure 23.

Maximum (a) and minimum (b) principal mechanical stresses due to vertical wheel loading in the infill concrete when pour 2 is 120min age (pour 1 is 74h old). To get an idea of the role of thermal stresses in the early age performance, this figure should be compared with Fig. 21.

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In the above thermo-mechanical analysis from 90 to 120min age of infill RHC concrete in all three repair options we considered only the most favourable mechanical loading scenario, i.e. when the wheel loading was vertical (total static equivalent vertical load=209kN). It is of interest to investigate the performance of RHC infill concrete when the full shear loading in the lateral (65kN) and longitudinal (1.6kN) directions are applied, besides the vertical loading. In our co-ordinate system (Figs. 5 and 11), the longitudinal, lateral and vertical directions correspond to x, y, and z axes. We shall demonstrate the influence of the full lateral and longitudinal shear loads on the repair option 2. Fig. 24 shows the principal thermo-mechanical stresses at age 120min, i.e. 30min after the application of the wheel loads. A comparison with the corresponding thermo-mechanical stresses under vertical wheel loading only (Fig. 15) shows that the lateral loads do indeed induce additional damage to the infill RHC concrete.

Figure 24.

Influence of lateral loads on the thermo-mechanical performance of RHC infill concrete at age 120min in the repair option 2. Maximum (a) and minimum (b) principal stresses.

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