Numerical simulation analysis of the shear tests on cemented surface between bedrock and concrete

Based on anchorage foundation of Ganjiang Highway Bridge situated on weakly weathered argillaceous siltstone, numerical simulation analysis of shear tests were carried out to investigate the shear strength of cemented surface, which is between anchorage foundation concrete and bedrock surface. In order to evaluate the effect on shear strength effectively due to the cemented surface roughness, random distribution of parameters is firstly introduced to quantify the roughness and the Monte-Carlo method is employed to simulate the morphology of cemented surface. Secondly, numerical simulation analysis on shear tests is implemented to study the effect of different cemented surface roughness on shear strength. At last, a new evaluation method of cemented surface shear strength is put forward based on the numerical simulation with random contact interface. In addition, the results from numerical simulation method are compared with the field direct shear test, and it is validated that the results are highly consistent.


Introduction
The gravity anchorage of suspension bridge mainly depends on the bonding and friction of the cemented surface between the massive anchorage foundation concrete and the bedrock underlying to transfer the huge tension safely to the foundation, which is derived from the main cable. It is so difficult to evaluate the shear strength of cemented surface between the bedrock and anchorage foundation concrete due to the large base area of anchorage and the great difference in the rock property, weathered degree, roughness and other factors of the underlying bedrock. However, the friction coefficient of cemented surface is often determined according to the classification level of rock mass and the design code. The real roughness of cemented surface and the geometry form of anchorage foundation [1] are usually neglected, which actually will lead to great change. So it seems to be unreasonable for current engineering design.
In order to accurately determine the shear strength of cemented surface between bedrock and concrete foundation, laboratory and field shear tests are often employed in practical projects. For example, Ji et al. [2][3][4] conducted experimental studies on the cemented surface between bridge or dam foundation and underlying bedrock. In addition, in the further study of the cemented surface, Saiang et al. [5] obtained shear strength and shear displacement characteristics of the cemented surface between concrete and rock under different normal stress conditions by experiments. Tian et al. [6] established the constitutive model of shear stress and displacement through direct shear test of the cemented surface between concrete and sandstone. Guo et al. [7] built up the relationship between the China Rock 2020 IOP Conf. Series: Earth and Environmental Science 570 (2020) 022048 IOP Publishing doi: 10.1088/1755-1315/570/2/022048 2 strength parameters of mortar and limestone cemented surface and different size of samples, and the press-shear fracture failure mode was proposed based on the stress intensity factor. Tang et al. [8] studied shear strength of the irregular cemented surface between sprayed concrete and granite under the variation of high temperature by experiments. Apparently, among the many influencing factors, the shape and roughness of cemented surface have the most important influence on shear strength and failure mechanism. Unfortunately, a method to effectively evaluate the influence of the characteristic morphology of cemented surface on shear strength hasn't been established in current research.
At present, there are already many research achievements on the cemented surface and structural surface, but there is still much limitation in practice. For example, laboratory tests are often based on relatively intact rock samples, which differ greatly from rock mass on site. The quantity of field test samples is always limited because of high cost, and test results are usually discrete. Therefore, a new numerical simulation method for shear test on the cemented surface between concrete and underlying bedrock will be proposed based on the anchorage foundation of Ganjiang Highway Bridge, which situated on the weakly weathered argillaceous siltstone. In this method, the characteristic parameters with random distribution will be introduced to quantify the roughness of cemented surface, and the Monte-Carlo simulation method will be adopted to simulate the morphology of cemented surface. And then, a random contacting numerical calculation model will be established to investigate the shear strength of cemented surface with different level of roughness. Finally, this new numerical simulation method will be verified by the comparison of results from physical tests and numerical simulation.

Shear failure mechanism of cemented surface
The shear failure of cemented surface is mainly determined by the relative strength of the upper and lower part on cemented surface, the cohesion between two sides, and the roughness of cemented surface. The shear test of cemented surface between concrete and bedrock is essentially the shear test of cemented surface between one material and another. The roughness of cemented surface will increase the interlock action between two parts, and improve the shear resistance greatly. When the roughness of cemented surface is large enough to exceed the critical value, and lead to high level of interlock between the bedrock and concrete, the shear failure surface will occurs among the weak party (as shown in Figure a and b). When the cemented surface is relatively smooth and the bonding strength between bedrock and concrete is relative low, the failure surface occurs just on the cemented surface (as shown in Figure c). When there are weak surfaces or joints existing in the rock mass, the failure may occur inside the rock mass (as shown in Figure d). A schematic diagram of potential shear failure surfaces under different conditions is shown in Figure 1. The above analysis is based on the ideal situation in which the concrete material or bedrock is isotropic and uniform. In fact, for the same test sample, the rock mass or concrete always has different defects or different structural characteristics. Therefore, the shear failure surface usually doesn't appear as the same as anticipated.

Numerical analysis of shear test on cemented surface
The upper part (concrete) The lower part(bedrock)

Numerical model and calculation method of random contact interface
In reality the morphology of cemented surface is complex and irregular, which has a critical effect on the shear strength of cemented surface. However, the process of field shear tests is complicated. The test results are disperse and not very precise. It also requires lots of labour force, material resources and time. Although the shear deformation characteristics and failure modes of cemented surface can be concluded by experiments, the influence of roughness on the shear mechanism of cemented surface can't be evaluated from the perspective of microscopic mechanism. Therefore, in order to effectively measure the effect of roughness on the shear strength of cemented surface, it is very necessary to quantify the roughness and depict the degree of morphological surface by some variables. Random contact numerical model is proposed by using the Monte-Carlo method [9] in this paper. Some characteristic parameters of random distribution are introduced to describe the convex body size and spatial distribution, and simulate the roughness on cemented surface. And then random contact numerical shearing test will be carried out by DEM to investigate the shear strength, failure modes and the influence of roughness on shear deformation characteristics of cemented surface.

Establishment of the random geometry model
First define a baseline, and make n datum points uniformly distributed on the baseline. It is assumed that each point represents corresponding waving value h which ranges randomly from zero to the maximum waving value hmax. Connect each waving point and a hypothetical curve will appear to model any morphological cemented surface. So there are two random parameters involved, n and h. It is relatively easy to determine the maximum waving value hmax. So it is quite necessary to set the value for n reasonably so that the generated curve can be well fit for the actual cemented surface. After the generation of surface curve, the upper and lower parts on each side can be further built according to the geometry of test sample, which is illustrated in Figure 2.

Generation of random parameters
According to the conception of stochastic modelling, variable h is the key parameter during the establishment of model as well as variable n. For a certain cemented surface, the maximum value hmax is fixed when the variable h randomly in the interval [0, hmax]. It is not difficult to model morphology of the cemented surface when the Monte-Carlo simulation method is used to generate random numbers of variables under relevant distribution rules in any interval to simulate the distribution of random variables conveniently, so variable h can be created by the Monte-Carlo simulation method. Meanwhile, if the value of variable n is larger, it means that there are more datum points on the baseline and it represent that the cemented surface is rougher. Otherwise, the surface is smoother while the value of n is smaller.

Establishment of random contact numerical calculation model
After the above random variables are determined, the geometric model can be generated through the secondary development platform of AutoCAD soft, and then the numerical calculation model can be further established through FlAC3D, as shown in Figure 3.

Baseline cemented surface h max
The upper part(concrete) The lower part(bedrock) The Interface module provided by the FlAC3D program can effectively simulate the interaction between different materials on both sides of the contact surface, including squeeze, separation and relative slip. Since the finite-difference program FlAC3D can only generate regular elements, and cannot divide irregular geometric blocks, the geometric Figures can firstly imported into the ANSYS program by the secondary development of the interface program between AutoCAD soft and ANSYS program. And then, numerical calculation model will be established after meshing in the ANSYS program regardless of the geometry of model. At last, with the help of the Interface program between ANSYS and FLAC3D, the generated computational model can be imported from ANSYS program into FLAC3D program. And then the Interface element with reasonable constitutive model and mechanical parameters can be adopted on the cemented surface. After above steps, the numerical calculation model of random contact interface between concrete and bedrock can be established.

Random distribution of convex body on cemented surface
Random contact interface models with different morphology of cemented surface can be generated according to the above processes. The n value is selected to be 10, 20, 35 and 50 while hmax is 1%~5% of the side length of the concrete test sample. The geometric dimension of concrete on the upper part of the model is 50cm×35cm, and that of bedrock on the lower part is 150cm×35cm. The width of the model is 1cm, and the size of the model is determined by referring to the field shear tests. Finally, Figure 4 clearly illustrates different morphology of the random contact interface model. It can be seen from the Figure that when the hmax is the same, the larger the value n is, the more complicated the cemented surface curve will be. The larger the roughness is, the larger the corresponding cemented area will be.

Contact area of cemented surface
The convex morphology of cemented surface depends on two parameters, n and hmax, which also reflect that the contact area of cemented surface depends on them. Table 1 shows the statistical analysis results of the cemented area generated by different values of n and hmax under different random processes, and 10 random simulations were conducted for each case. In the table, the area of undulating surface of samples is also the cemented area between concrete and bedrock while the width of samples is 1cm.

Geometric properties of cemented surface area
The variation trend of cemented surface area under different values of n and hmax can be obtained by the statistical analysis of undulating cemented surface area, as shown in Figure 5. It is described in the curves that hmax represents the waving height of convex body on cemented surface. The larger the value of hmax is with the same value of n, the more drastic waving difference of the undulating surface will be, and the corresponding cemented surface area will be larger. The value n reflects the distribution frequency of the convex body on the undulating surface. With the same value of hmax, the larger the value of n is, the more convex body on the undulating surface is distributed, and the larger the cemented surface area is. In addition, the cemented surface area increases nonlinearly with increasing of n or hmax, as well as the increasing speed.  Figure 5. Area of cemented surface with different n and hmax.

Constitutive model and mechanical parameters of contact interface
As the main problem of bridge anchorage, the mechanical behaviour of interface between concrete and bedrock directly affects the interaction between engineering structure and subgrade. As for the contact surface between different parts, many scholars have adopted different contact surface element models to study the mechanical properties of contact surface [10,11]. The contact interface element adopted in this paper is the thickness-free element inherent in FlAC3D program. The constitutive relation abides by the linear sliding Coulomb friction criterion, which can reflect the characteristics of shear force, ultimate tensile strength, and dilatancy on the contact surface. Figure 6 is about the schematic diagram of constitutive model elements, and its model equations are as below:  A is the area of each contact node. The parameters involved in the interface element mainly include cohesion, friction Angle, dilatancy angle, normal stiffness, tangential stiffness and tensile strength of the contact interface. The determination of each parameter depends on the mechanical properties of interface element and mechanical properties of the material. The normal stiffness and tangential stiffness of contact interface are related to equivalent stiffness e K , which can be determined by Formula (4): is the normal minimum size of adjacent elements of contact interface, K is the volume modulus of rock mass, and G is the shear modulus. Meanwhile, according to the results of field shear tests, geological survey reports and relevant bridge foundation design codes, the calculation parameters of interface elements, concrete and bedrock are determined comprehensively. The final calculated values of each parameter are shown in Table 2

Statistical analysis of shear strength on cemented surface under random generation
As illustrated in Figure 7 and 8, they are the statistical analysis curves of shear strength results with different variable n and hmax. From the numerical perspective, we are interested in which manner n and hmax influence the shear strength on the cemented surface. According to the numerical calculation results, the shear strength of cemented surface has following characteristics: (1) With the increasing of n or hmax, the contact area of cemented surface gradually increases, and so does the corresponding shear strength of cemented surface. It is also proved that the shear strength is basically in a linear relationship with the contact area.
(2) When the cemented area S is less than 52.5cm 2 , no more than 5% relative to the smooth cementing surface S0 (50cm 2 ), the curve of shear strength is fitting linear very well.
(3) When the roughness of cemented surface is large enough caused by hmax or n, more than 5% of original smooth cemented area, The shear failure will happen not only to overcome the cementation and friction between the upper and lower parts, but also the upper parts should climb over the convex body on cemented surface. And the difficulty completely depends on the distribution and shape of convex body. So In these occasions, the increase of shear strength varies greatly, and it deviates from linear fitting curves greatly.
(4) It is also proved that the shear strength is different with the same cemented surface area. It is indicated that the shear strength of cemented surface depends not only on the area of cemented surface, but also the distribution, location, height and shape of the convex body on cemented surface.
(5) Sliding Coulomb friction criterion is employed for numerical calculation. Therefore, the failure mode of cemented surface is only considered when shear relative slip failure occurs. Under this condition, the shear strength of cemented surface can be fitted by the following formulas.
Where: 0  is the friction coefficient of smooth bonding surface;   is the increase of friction coefficient caused by the roughness of cemented surface; s is the area of undulating cemented surface; 0 s is the area of smooth cemented surface;  is the normal stress applied in the normal direction; A is the correlation fitting coefficient. The fitting parameters of each curve are shown in Table 4.      10 cemented surface when the value of hmax given less than 25 mm and the value of n less than 50. It is illustrated in Figure 9, and the surface fitting equations is as follow:

Evaluation of Numerical Models
As a validation of the numerical approach, comparisons between the experimental shear strength from field tests and the predicted shear strength based on the analytical equations were performed. Table 5 details the measured morphological characteristics of cemented surface for each field experimental sample. Based on these parameters, the predicted shear strength were calculated using equations 7 and 8 as above. Table 6 lists all the results of predicted shear strength, field experimental shear strength as well as error rates with both methodologies. It can be concluded that there is an allowable error rate between the numerical calculation and the experimental results, but it is also verified that Numerical model and calculation method of random contact interface is applicable to model the cemented surface between concrete and bedrock.