Stress-strain state of the structure in the service area of underground railway

The paper focuses on numerical study how vibration due to underground trains influences the load-bearing building structures. Diagrams of vibration levels for monolithic floor slab depending on frequency are obtained. Levels of vibrations on floor slabs and columns are measured. The simulation of dynamic load from underground railway onto load-bearing building structures is presented as an example with account of load transmission through the soil. Recommendations for generation of design model in dynamic analysis of structure are provided.


Introduction
In recent years, many scientists have come very close to developing adequate static-dynamic design models for account of the interaction of buildings and structures with soil under dynamic loads [1][2][3][4]. Using such models to study the stress-strain state of building structures throughout their life cycle is of particular interest. Such models include both buildings designed and built in the metro area and buildings that have been deformed in the course of long-term operation and subject to new dynamic loads transferred to buildings through the soil. Practically across the whole area of Ukraine there is a high density of residential development in large cities, the complexity of engineering and geological conditions, as well as the long life cycle for most buildings. That's why, the issue of how main loadbearing structures of buildings take considerable loads and actions (that arise from the nearby thoroughfares, mainline railroads and underground railway) has come to the fore.
Protection of structures against vibration caused by underground trains has become highly critical in recent years when shallow tunnels are used for the new underground lines.
Numerical simulation of the stress-strain state in such structures is the only tool that could provide qualitative and quantitative evaluation for behaviour of geomechanic system "soil body -elements of surface and underground structures" [5].
For that matter, numerical study of structures of the office & shopping centre under construction at 7, B. Khmelnitskogo Str. was carried out. The purpose of this work was to determine adequacy of the static-dynamic design model used in dynamic loads transferred through the soil stratum.

Theory
In Ukraine there are no regulations that stipulate allowable vibration in buildings and structures caused by transport vibration. The only document in this field is DSN 3.3.6.039-99 "State Sanitary Code for General and Local Vibration in Industry". Regulations for vibration load for people inside buildings are stipulated in this document.
However, there are several international documents that stipulate frequency dependent criteria for vibration evaluation. In National Code of Germany DIN 4150-3:1999 "Structural vibration -Part 3" ultimate values are stipulated for short-term vibration for extreme values of speed on foundation of buildings for three categories of buildings: business structures, industrial buildings and structures that have similar design (category 1); civil structures and structures that have similar design or purpose (category 2); structures that are not included into categories 1 or 2 and that have high social significance (for example, protected as historic monuments, category 3).
In National Code of Great Britain В3 7635-2:1993 BS 7635-2:1993 "Evaluation and measurement for vibration in buildings -Part 2: Guide to damage levels from groundborne vibration" ultimate values (figure 1) are stipulated for short-term vibration for extreme values of speed on foundation of buildings for two categories of buildings: business and industrial buildings that have framework or reinforced concrete structures (category 1); civil and business structures that have light-weight design, design with no reinforcement or with light-weight framework (category 2).
It is supposed that moderate damage may take place if ultimate values are two times higher than the values mentioned in figure 1, and serious damage -if they are four times higher.
In case of low frequency signal that has significant components on frequencies low than 4 Gz, it is recommended to measure displacements. Ultimate extreme value of displacement for frequencies low than 4 Gz is equal to 0.6 mm.
In case of continuous vibration that could cause resonance of structure (especially in low frequencies), it is recommended to reduce ultimate values mentioned in figure 1 by half. If the earthwork may cause vibration of structure at resonance frequency (for example, when vibration machines are used or in permanent or short intervals between start of electronic ignition system during explosion at construction work), then to evaluate whether arising vibrations are allowed, it is necessary to carry out additional research. Unfinished building structure by structural elements that should be erected according to [9] is considered as specific permanent structure (I group of importance) with normative lifetime of 175 years.
Purpose of the work is to determine technical state of the framework structures of the building in order to continue construction works. Instrumental verification of geometrical parameters of the building at 7, B. Khmelnitskogo Str. for columns, walls, floor, ceiling, lift shaft is carried out in order to find out vertical and horizontal displacements of erected structures from design location.
To determine numerical values of vibration with the help of vibrometer, measurements were taken with three vibrator inverters in the mode of automatic registration of mean-square and max levels of vibration acceleration with the averaging time of 1.5 and 10 s.
According to [9], technical state of the framework structures is considered as unserviceable (state III). Concrete strength in RC monolithic structures was determined by nondestructive sclerometric method.
Measurement results of concrete strength in monolithic RC walls and floor slabs were applied to computational investigation in order to define real stiffness parameters for structural elements.
Destruction of foundations and underground walls is 15-20 % and in some places 50-80 %, which is much higher than in similar buildings located inside blocks. It is mainly related to low-damped settlements on soft water-saturated soil in permanent action of considerable vibrations caused by underground railway. [7,9,11,12].
Reaction of building and its elements depends not only on level and spectral content of vibrations transferred by the soil but on dynamic parameters of load-bearing and enveloping structures. This  Traffic analysis of underground trains shows that as number of passengers is increased (rush hour between 17 and 19 hours), the levels of vibration acceleration are 3...3.5 dB higher relative to the time from 19 to 22 hours. Levels of vibration acceleration also depend on technical state of rail track and railway vehicles, train speed (in rush hour speed is higher). All above-mentioned factors also influence the frequency distribution of level of vibration acceleration.
The main source of vibration is the impact when the wheel of the train passes through the rail joint. The resulting vibration of the tunnel lining reduces up to the time when the next wheel passes the rail joint.
In addition, there is a polyfrequency vibration from the imperfectly smooth surface of the wheel and rail material, from the deformed wheels as well as from the effect of the 'wheel wobble' in trains during motion. Of the loads mentioned above, vibration load in the frequency range of 25-50 Hz prevails. If this frequency of vibrations is close to the natural frequency of the tunnel lining, even with account of the filtering features of the soil, the very structure of the path, regardless of the fact wether the path is vibrated or not, the wave radiation can be increased [2,3]. Therefore, with regard to metro, in general, one can not speak of one prevailing frequency. Thus, rather than going into design features of the lining and the upper structure of the track, we could take the operating frequency range of vibration from the metro 20-70 Hz. A typical feature of this range is that natural frequencies of the floor slabs in buildings usually fall within this range [2][3][4]. It can be seen from obtained data (figure 3). The highest levels of vibration acceleration of the floor slab are obtained in vertical vibration for the frequency range from 16 to 80 Hz and exceed values in other directions by more than 15 dB (more than 6 times). For comparison, the intensity of soil vibrations near the metro corresponds to 6, 7 units of magnitude. The map at the Institute of Geophysics shows that an earthquake of magnitude 5 -in most parts of Ukraine occurs every 100 years. Earthquake of magnitude 6 units -every 5 thousand, that is, the probability of an earthquake in the zone of Kiev and the Kiev region is quite small. In this case, the permanent vibration from a moving vehicle (but with relatively small amplitude of vibrations) may cause damage of the load-bearing structures, crack propagation and, if measures are not taken, even to destruction.
The problem under consideration has the following main tasks: -to study the soil dynamics and vibration of protected structures from various types of dynamic loads; -to estimate the risk level as to whether parameters of the stress-strain state in load-bearing structures of nearby buildings may estimate the normative values; -to develop design methodology for similar buildings. Thus, there are principal lines in this paper: 1. To develop methodology for analysis and design of a building in external vibration caused by the underground rolling stock. The work is carried out using LIRA-SAPR program based on FEM. This program enables the user to analyse buildings of all types in order to evaluate and then forecast behaviour of structure.
2. To develop methods for preliminary assessment and evaluation of dynamic phenomena in highrise buildings at the stages of design, construction and maintenance in order to prevent negative effects on structural elements and people from vibrations caused by the underground train.

Mathematical relations
Vertical and horizontal components of vibration velocity at the soil surface are determined by formula: where v R -vibration velocity caused by Rayleigh wave and calculated by formula In this case H 0 -depth at which the trough part of the tunnel lining is located; x -distance from longitudinal axis of the tunnel; R0 -characteristic dimension that represents min from D/2 -half width of the tunnel; To determine stress-strain state of the building with account of pulse processing during pulse transition from the soil to foundation of building, the structure and soil body were simulated in the LIRA-SAPR program.
To transfer dynamic loads through the soil to the load-bearing structures, it is possible to perform computer simulation in several ways. In this paper it is proposed to simulate the soil with solid finite elements. This simulation type provides min error in transmission of parameters of dynamic loads in comparison to results of measurements. The subway tunnel with reinforced concrete sheeting is simulated with plate FEs. Dynamic loads are applied at the place of their origin, that is, in the tunnel. The plan view of the structure and diagonal location of underground railway tunnel are presented in figure 5.
3D soil body is simulated in the SOIL module according to data from engineering-geological survey (see figure 5). Such method of generation for system 'soil body -elements of surface and underground structures' represents quite a promising solution in terms of forecasting behaviour of buildings and structures when permanent dynamic loads are transferred through the soil.
Time period for which dynamic loads were determined is taken as equal to 10 seconds. Parameters of vertical and horizontal vibrations at check points (where in-situ measurements were made) were obtained in analysis.
Natural frequencies of vibrations thus obtained are compared to experimental data and presented in table 1.