Research on Stresses of Narrow Joints Caused by Construction Process of CRTSIISlab Track

A separate finite element model of 1/4 unit track slab of CRTS IIslab track was established for the analysis of the influence of construction process on stresses of narrow joints. When track slabs were connected by tension and when wide joints hardened, the impacts of the longitudinal connection of CRTS II slab on stresses of narrow joints were analysed. The results show that when track slabs are connected by tension, the bonding states between track slab and mortar layer have little effect on track slab expansion displacement and the re-compression of narrow joints caused by the tensioning force cannot be ensured. If track slabs are connected by tensioning force after the concrete hardening of narrow joints, compressive stresses of narrow joints can be increased by 3.03 MPa. Due to the influence of longitudinal connection of CRTSIIslab, the respective track slab temperature for wide joints hardening Tk and narrow joints hardening Tz are difficult to keep consistent. When wide joints hardened, it potentially makes the compressive stresses of narrow joints zero or very large. In order to keep the narrow joints compressed when wide joints hardened, the measures to control Tz and Tk should be taken to make Tk slightly higher than Tz.


Instruction
CRTSⅡslab track mainly consists of track slab, cement emulsified asphalt mortar layer, base plate or support layer. In addition to that the mortar layer, base plate or support layer is the longitudinal continuous structure, track slabs are also connected through joints between slabs to become a longitudinal continuous reinforced concrete structure. Since this structure was used in Beijing-Tianjin inter-city railway in 2008, the overall quality is in good condition, which meets the requirements of high-speed railway for high smoothness and high stability. However, the high-speed railway has been widely constructed in a variety of districts, in which the climatic conditions vary greatly. As a longitudinal continuous structure, the temperature effect of CRTSⅡslab track caused by temperature load is very significant. Affected by the environment, temperature, temperature gradient and so on, the gap under slabs was generated, and joint-defects and arch between slab joints appeared. It brought not only maintenance and repair work, but also adverse effects to normal operation. The uneven stresses in joints are an important cause leading to track slab arch and joint-defects. Therefore, it is very necessary to study the mechanical characteristics of joints between slabs.
In addition to the influence of construction quality, joint-defects and joint-deformation between slabs were mainly influenced by temperature. At present, there have been many researches on behaviour of joint-defects, the stress and deformation and dynamic response of track structure caused by joint-defects [1][2][3]. However, there were few studies on influences of construction process ofⅡslab on joint stresses. Through the analysis of mechanical relationships between track slab and mortar layer, steel bars, joints, the finite element model was established. The influences of construction process ofⅡslab under the action of temperature force on stresses of narrow joints were analysed.

Longitudinal connection of CRTS Ⅱ slab
CRTS Ⅱ track slabs are prefabricated structure in the factory. After the laying of track slabs, they are connected to become a longitudinal continuous structure through joints between slabs. Joints between slabs are shown in Figs. 1~2. Six steel bars with a diameter of 20 mm connect two adjacent track slabs together by the tensioning slack adjusters at the end of slabs. According to the construction process [4], joints between slabs are poured firstly after the strength of emulsified asphalt cement mortar (CA mortar) under slab reaches 7 MPa, which is known as narrow joints with a height of 0.1m; When the strength of CA mortar reaches 9MPa and the concrete strength of narrow joints reaches 20MPa, the six longitudinal steel bars will be connected by the tensioning slack adjusters, and each bar has a tensile load of 50kN. Then the rest of joints will be poured at last, which are known as wide joints. The narrow joints consist of three parts, whose lengths are about 0.2m, 0.4m, and 0.2m respectively [4].  Judging from the construction process, compared with the continuous pouring of reinforced concrete structure, the concrete of narrow joints of CRTS Ⅱ slab are poured firstly, then the concrete of wide joints. Therefore, there is a difference in slab temperatures when the narrow joints and wide joints hardened, and there is also a pre-tension when the longitudinal steel bars are connected. So the longitudinal connection characteristic of CRTSⅡslab track is very obvious. When wide joints hardened, this characteristic made the stresses of narrow joints very complicated, which could be zero or very large. Zhou Min et al.'s research [5] shows that there is indeed some phenomenon on site that when the crack between wide joints and slabs is inexistent, there are cracks between narrow joints and slabs at the same place. This is in conflict with the design concept of Ⅱ slab, which is "the compressive stresses of narrow joints should be always existent when track slabs are connected completely or the wide joints harden". It shows that some improvements are needed for current construction process control measures, so it is of certain engineering significance to carry out the research.

Model assumption
(1) The deformation and stress of track slab are of symmetric distribution under the loads of longitudinal tension, joints between slabs and temperature.
(2) The displacements of track slab cross-section are evenly distributed.
(3) The stresses and strains of steel bars cross-section are evenly distributed.
(4) The stresses of narrow joints cross-section are evenly distributed. (5) Considering that the interfaces between the concrete of joints and the end face of track slab are newold concrete joint surfaces, and the end face of track slab is vertical and its roughness is small, the interface bond stresses are small. Therefore the tensile restraints from the concrete of joints on track slab are neglected.

Finite element model
Track slab is simulated by solid element solid45.Its length, breadth, and height are 6.45m, 2.55m, and 0.2m respectively. Its elastic modulus is 3.60×10 4 MPa. Its Poisson's ratio is 0.2. Its thermal expansion coefficient is 1.0×10 -5 . The top width, bottom width, and height of pre-splitting crack are 38mm, 4mm and 28mm respectively. The constraints of mortar layer and steel bars on track slab are simulated by ANSYS 3D nonlinear spring element COMBIN39, which parameters are shown in sections 2.3 and 2.4 respectively. The longitudinal and horizontal steel bars are simulated by LINK1 and LINK8 respectively. Its elastic modulus is 2.0×10 5 MPa. Its thermal expansion coefficient is 1.2×10 -5 . The length of horizontal common steel bars is 2.45m, and that of horizontal pre-stressed steel bars is 2.55m.The lengths of longitudinal steel bars are 6.2m and 6.35m in the positions of wide and narrow joints respectively. The length of tensioned rebar is 6.45m. The number and locations of steel bars are seen in literature [7]. Narrow joint is simulated by the bar element LINK10 with only compression. The differences in the cross section of joints are neglected. According to the symmetry of the model, a finite element model of 1/4 track slab was established.
In order to consider the constraints of mortar on track slab at joints, the bottom thickness of track slab at wide joints is kept as 20mm. The final separate finite element model of 1/4 track slab is shown in Fig. 3.

Bond slip behavior between track slab and tensioned rebar
The steel bars, which are adopted by CRTSⅡ track slab, all are hot rolled ribbed steel bars [7]. Code for design of concrete structures (GB50010-2010) provides the constitutive relation of the bond stress-slip between concrete and hot rolled ribbed steel bar. For CRTS Ⅱ track slab, whose axial tensile stress f t,r is 3.55MPa [8], the value is not quite different from the average value of tensile strength of C55 concrete, which is 3.60MPa [9]. Then, there are τ cr =2.5f t,r , τ u =3f t,r , τ r = f t,r ,s cr =0.025d, s u =0.04d, s r =0.55d [9],where d is the diameter of steel bar. Taking the tensioned rebar as an example, the relationship between bond stress τ s and relative slip displacement s between track slab and tensioned rebar is shown in Fig. 4. For the rest of steel bars with a diameter of 8mm, 10mm and 16mm respectively, the corresponding slip curves can be obtained by calculating the corresponding s cr , s u , and s r .

Friction characteristics between track slab and mortar layer
The constraint of mortar layer on track slab was influenced by ambient temperature, and gradually decreased with time. Through analysis of the indoor and field tests between track slab and mortar layer at home, the bonding states between track slab and mortar layer are divided into three stages, which are good bond, partial bond and poor bond respectively, and will be simulated by a piecewise linear model.
When mortar layer was stiffened, the bonding state between track slab and mortar layer was little influenced by the environment. At this time, the interlayer state was regarded as good bond, and the selection of parameters were based on the indoor tests. When the bonding state between track slab and mortar layer is in good bond condition, the relative displacement between track slab and mortar layer was very small before the micro cracks were generated. It is considered that the angle of shear is directly proportional to the shear stress. When the bonding state between track slab and mortar layer is good bond, the inter-laminar shear stiffness k c is: Where E c -elastic modulus of mortar, 8000MPa; υ c -Poisson's ratio of mortar material,0.2； h c -thickness of mortar layer,0.03m。 It is known from the indoor shear tests between track slab and mortar layer [2,11] that, the inter-laminar shear strength of 28d age is about 0.44~0.78MPa. When the model simulation was analyzed, the parameter was taken as 0.5 MPa in most of the model. When the bonding state between track slab and mortar layer is in good bond condition, the inter-laminar shear strength is 0.5 MPa.
In the plate pushing test in China, the temperature of mortar was controlled at 20±2℃ after mortar perfusion. The push plate force was about 120t, while the corresponding longitudinal shear stress was about 72KPa, and the corresponding inter-laminar displacement was about 0.02mm [10]. At this time, the bonding state between track slab and mortar layer was less affected by external environment, and the interlayer state was regarded as partial bond.
In the plate pushing test in German, the plate pushing force was about 41t, while the corresponding longitudinal shear stress was about 24KPa, and the corresponding inter-laminar displacement was about 0.5mm [12]. At this time, the bonding state between track slab and mortar layer was greatly influenced by external environment, and the interlayer state was regarded as poor bond.
In summary, the relationship between shear strength τ c and relative displacement y bc between track slab and mortar layer was obtained as shown in Fig. 5. In Fig. 5, A, B and C points are the critical points of good bond, partial bond and poor bond respectively. The curve 0ABCD is a weakening curve of the bonding state between track slab and mortar layer when environmental factors are considered.

Boundary conditions
(1) Displacement constraints were adopted at the end of narrow joints, and the values of displacement constraints took the displacement values of common nodes between track slab and narrow joints when narrow joints hardened.
(2) The shear constraints of mortar layer on track slab were simulated by springs, and the bottom was fully constrained.
(3) Except degree of freedom along the length of steel bars, the remaining two degrees of freedom were restrained, only allowing the steel bars to expand freely along the length direction.
(4) Displacement constraints were adopted at the end of tensioned rebar after track slabs were connected by tension. The values of displacement constraints took the end displacements of tensioned rebar calculated by the corresponding working condition.

Result analysis
Narrow joints are mainly affected by temperature expansion of track slab. The overall temperature rise and fall of track slab were mainly considered. From the mortar layer hardening to the concrete hardening of wide joints, the variation of track slab temperature was mainly affected by monthly temperature difference. For calculation the variation of track slab temperature is 30℃, and the maximum of one-way temperature is 20℃.

Track slabs connected by tension
The main influence factors of stresses of narrow joints are: the maximum of track slab temperature rise or fall ∆T max before concrete hardening of narrow joints, the ascending range of track slab temperature ∆T sl from concrete hardening of narrow joints to the connection between track slabs, and the tensioning force. The initial interlayer states between track slab and mortar layer were divided into three working conditions: good bond, partial bond and poor bond. The corresponding interlayer weakening curves are OABCD, OBCD and OCD respectively in Fig 5. When the stresses of narrow joints were analysed, the initial interlayer state between track slab and mortar layer was regarded as in good bond condition, and the corresponding interlayer weakening curve is OABCD in Fig 5. When calculating stresses of narrow joints, assuming that the narrow joints hardened after ∆T max was exerted on the model, and then ∆T sl and the tensioning force were exerted on the model. When analysing the effect of tensioning force on narrow joints, the above results were applied to subtract results of the model which exerted ∆T max and ∆T sl simultaneously. In the calculation, ∆T max are 0℃,4℃,5℃,6℃,7℃, 10℃,20℃ respectively, and ∆T sl are 5℃,10℃, 20℃respectively. Relationships between end displacements of track slab y bc and ∆T max are shown in Fig. 6. The increments of end displacements of track slab caused by the tensioning force ∆y bd are shown in Fig. 7. Compressive stresses of narrow joints caused by tensioning force σ zl are shown in Fig. 8. Relationships between compressive stresses of narrow joints σ z caused by ∆T sl and ∆T max are shown in Fig. 9.   Figure 6 shows that with the increase of ∆T max , end displacements of track slab y bd increase gradually. Combined with Fig. 5, it is not difficult to see that the bonding states between track slab and mortar layer are weakening gradually. As the initial interlayer states between track slab and mortar layer changing from good bond to partial bond or poor bond, y bd increase slightly, and the increments of y bd decrease gradually with the increase of ∆T max . When ∆T max increases from 4℃to 20℃, the increment of y bd decreases from 0.048mm or 0.088mm to 0.000088mm or 0.0086mm as the initial interlayer state between track slab and mortar layer changing from good bond to partial bond or poor bond. When ∆T max >6℃, the maximum increment of y bd is about 0.0029mm or 0.038mm as the initial interlayer state between track slab and mortar layer changing from good bond to partial bond or poor bond. When considering tensioning force, the increments of y bd decrease slightly. It is indicated that y bd are mainly related to the temperature rise and fall of track slab, and the bonding states between track slab and mortar layer has little effect on track slab expansion displacement. Figure 7 shows that under the action of tensioning force, the end displacements of track slab increase, and the increments ∆y bd are related to the interlayer bonding states. When the interlayer state is the best, namely ∆T max = 0℃, ∆y bd increase gradually as the initial interlayer state between track slab and mortar layer changing from good bond to poor bond. When the interlayer state is weakened, namely ∆T max = 4~20℃, the tensioning force will accelerate interlayer weakening, which leads to the release of energy accumulated in track slab. And the better the interlayer bonding state, the more the release of energy. At the same time, ∆y bd decreases gradually as the initial interlayer state between track slab and mortar layer changing from good bond to poor bond, and then tend to be constant. When ∆T max >6℃, ∆y bd caused by the tensioning force is 0.047~0.051mm、0.047~0.048mm and 0.045~0.046mm respectively as the initial interlayer state changing from good bond to poor bond. Figure 8 shows that under the action of tensioning force, compressive stresses of narrow joints increase. When the interlayer state is the best, namely ∆T max ＝ 0℃and ∆T sl ＝5℃, tensioning force has the constraint of mortar layer on track slab strengthened, which leads to the small increment of compressive stresses of narrow joints σ zl . When the interlayer state is weakened, tensioning force will lead to the release of energy accumulated in track slab, which leads toσ zl very large; When ∆T max =4~5℃, the release of energy accumulated in track slab reaches the maximum, the maximal value ofσ zl is about 3.3 MPa. Then with the weakening of interlayer states, the release of energy accumulated in track slab decreases gradually, and thenσ zl tend to be constant. When ∆T max >6℃, σ zl caused by tensioning force is about 3.01~3.05MPa, and the change rule ofσ zl is basically the same as the change rule of solid line in Fig.  7. Figure 9 shows that with the increase of ∆T sl , compressive stresses of narrow joints increase gradually. When the interlayer state is the best, namely ∆T max = 0℃, the constraint of mortar layer on track slab is strengthened gradually with the increase of ∆T sl , andσ z gets to the minimum values. When the interlayer state is weakened, ∆T sl leads to the release of energy accumulated in track slab. When ∆T max =4~5℃, the release of energy accumulated in track slab reaches the maximum, andσ z reaches the maximum. Then with the weakening of interlayer states, the release of energy accumulated in track slab decreases gradually, andσ z decreases gradually and then tends to be constant. When ∆T max >6℃, σ z is mainly related to ∆T sl . When ∆T sl are 5℃ 、 10℃and 20℃respectively, σ z are 13.65~13.73 MPa 、 24.28~24.41MPa and 45.55~45.77 MPa respectively. The change rule ofσ z is basically the same as the change rule of solid line in Fig. 7.
∆T max is the maximum of track slab temperature rise or fall before the concrete hardening of narrow joints, which is mainly related to diurnal temperature difference and should be more than half the maximum of that. The diurnal temperature difference is usually 10~20℃, so the possibility that ∆T max is less than 6℃is very small. Therefore, the interlayer bonding state had been very weak when track slabs were connected by tensioning force. When ∆T max >6℃, is about 0.045~0.051mm, andσ zl is about 3.01~3.05MPa. Alsoσ z is mainly related to ∆T sl . When ∆T sl is 5℃~ 20℃, σ z is about 13.65~45.77 MPa.
End displacements of track slab caused by the tensioning force are very small. If track slab is cooled down and contracted after the concrete hardening of narrow joints, the pre-compression of narrow joints caused by tensioning force cannot be ensured. Therefore, when track slabs are connected by tensioning force, narrow joints may not be stressed, or they may be subjected to large compressive stresses due to larger ∆T sl .

Wide joints hardened
From the connection between track slabs to concrete hardening of wide joints, the temperature expansion of track slab is affected by mortar layer, narrow joints and tensioned rebar. The main influence factors of stresses of narrow joints are ∆T max , track slab temperature T l when track slabs are connected by tension, track slab temperature T z when narrow joints hardened, track slab temperature T k when wide joints harden.
For calculation simplification, it is assumed that the narrow joints harden when track slabs are connected by tension and T l ＝∆T max . ∆T max are 0℃,-4℃,-5℃,-6℃,-7℃,-10℃respectively, the corresponding values of displacement constraints at the end of tensioned rebar are 0.250235mm,0.377998mm,0.416053mm,0.451592mm,0 .486573mm,0.590754mm respectively. T k are 5℃,10℃,15℃,20℃respectively. After ∆T max and the tensioning force were exerted to the model, narrow joints began to bear force, and then T k was exerted on the whole model. When wide joints harden, the end displacement of track slab y bc is shown in Fig.10, and compressive stresses of narrow joints σ z are shown as Fig. 11.   Figure 11. Compressive stresses of narrow jionts σz when wide joints harden. Figure 10 shows that with the increase of T k , end displacements of track slab y bc increase gradually, but the increments are small. When T l ＝∆T max is 0~-10℃and T k is 20℃, namely the temperature rise amplitude of track slab ∆T z is 20~30℃after the concrete hardening of narrow joints, the increment of y bc is about 0.02157~0.03851mm.. Figure 11 shows that with the increase of T k , σ