Analysis of the seismic stability of foundations according to laboratory soil tests

Seismically hazardous areas are widespread on the territory of Russia. These are the North Caucasus, Altai, Sayan, Eastern Siberia, Kamchatka, Sakhalin. The issues of earthquake-resistant construction in difficult engineering and geological conditions, design in new earthquake-prone zones and construction in already developed territories are important aspects of the increasing intensity of development. Against this background, the problem of assessing the dynamic stability of soils becomes a priority task of modern soil dynamics and geotechnics. The article focuses on highlighting the main stages of the analysis of the dynamic stability of the foundations of structures of increased responsibility, taking into account complex geological conditions. The work contains the theoretical foundations of the methodology for assessing stability under dynamic loads, a description of laboratory equipment and test methods, the process of processing the experimental results. The study uses the results of assessing the dynamic stability of foundations obtained in the course of practical activities of the Scientific and Educational Center “Geotechnics” of the Moscow State University of Civil Engineering..


Introduction
The main goals of earthquake-resistant construction are the construction of foundations, taking into account the necessary safety margins in case of earthquakes, as well as reducing the possible costs of strengthening the foundations to ensure a given level of strength and stability. When designing such foundations, an assessment of the dynamic stability of soils is required. Currently, there are many different methods for such an assessment, both field tests and laboratory ones. Each method has its advantages and disadvantages. In this work, we will use the results of laboratory tests. The task of such tests is to determine the relationship between the load acting during an earthquake and the dynamic strength of soils.

Methods
The most dangerous type of dynamic action during an earthquake is shear stress. The dynamic shear stresses acting in the soil during an earthquake when a shear wave passes from below can be determined using the method proposed in the studies of Sid H.B. and Idriss I.M. [1][2][3][4][5][6]. It is assumed that a soil massif with a height h in an earthquake moves horizontally. In this case, the maximum tangential stress τ max acting on the lower face of such a massif will depend on the horizontal acceleration a max on the massif surface and the specific gravity of soils γ in accordance with the formula: where: a max is the maximum horizontal acceleration at the ground surface during a predicted earthquake, in m/s 2 ; g is the acceleration of gravity, in m/s 2 ; γ is the specific gravity of the soil, in kN/m 3 ; r d is coefficient of stress reduction with depth, taking into account the deformability of the soil mass during an earthquake, the value of which is less than one [7][8].  Since soils are always saturated with water to one degree or another, the pore pressure has a significant effect on the results of determining the effective shear stresses. For water-saturated soil masses, it is necessary to take into account the effective values of the acting stresses. The effective stress values z   are obtained by subtracting the pore water pressure from the total effective stress. Dividing each part of formula (1) by the effective vertical natural stress σ' z , we obtain a modified formula that takes into account the distribution of total and effective stresses in the soil mass where: z h   is the total vertical stress; zz u    is the effective stress, u is the pressure in the pore fluid.
Formula (2) is used in many works [5,6] when calculating the effective shear stress during an earthquake. Of course, it has many disadvantages, such as the lack of taking into account the duration of the earthquake, the spectrum of operating frequencies, the distance from the epicenter of the earthquake. However, it also has a significant advantage, since there is a significant amount of accumulated data on horizontal accelerations on the ground surface in various seismically hazardous regions.
The analysis of the dynamic stability of soils is carried out on the basis of comparing the shear stresses arising in the soil mass during an earthquake and the dynamic strength of the soil corresponding to the maximum shear stresses in the soil sample at the moment of destruction under the action of a dynamic load. The moment of destruction is considered either the physical destruction of the sample, which usually corresponds to vertical deformations of more than 10% [9], or such a level of deformations that is considered unacceptable for the designed structure [10][11]. Another criterion for sample destruction is a sharp increase in pore fluid pressure. To assess this factor, the concept of reduced pore pressure is used, i.e. the ratio of the pressure of the pore fluid u to the lateral pressure on the ground z  . This parameter is called the pore pressure ratio (PPR) and is determined by the formula: If this value reaches 0.9, then we can talk about dynamic liquefaction. Using formula (2), it is possible to determine the stress in the soil acting during a predicted earthquake max z    , and the dynamic strength of the soil max, L z, L    can be determined from the results of laboratory tests of soils in devices of dynamic triaxial compression. Thus, the liquefaction potential L F can be calculated using the formula [12]: If the liquefaction potential L F is less than one, then liquefaction occurs. In all other cases, the soil is dynamically stable [13][14][15][16].
The relative level of tangential stresses acting in the soil max z    is often called the cyclic stress ratio (CSR), and the value of the cyclic strength is called the cyclic resistance ratio (CRR). Most of the field and laboratory dynamic resistance methods are based on comparing CSR and CRR values. Taking these changes into account, formula (4) takes the following form:

Results
Determination of the dynamic strength of soils [4] according to the results of laboratory research consists in the analysis of tests of dynamic triaxial compression. A cylindrical soil sample with a diameter to height ratio of 0.5 is compacted under the action of an isotropic stress corresponding to natural pressure. Then an initial shear stress is applied to the sample, corresponding to the additional vertical pressure from the designed structure. After stabilization of vertical deformations, a vertical dynamic action is applied to the specimen with a predetermined number of "load -unload" cycles. In this case, several series of vertical loads are performed in the absence of drainage of pore fluid with an increasing amplitude. This process is repeated until the specimen failure conditions mentioned earlier are reached. At the moment of fracture, the maximum shear stress is recorded, which becomes the value of the dynamic strength. The frequency of application and the number of loading-unloading cycles during the tests depend on the parameters of the design earthquake and are determined by seismic zoning. In such studies, it should be borne in mind that the possibility of dynamic instability of soils decreases with increasing depth. The generally accepted is the depth of the studied soils up to 20 -25 m [6]. Deeper, as a rule, the danger of dynamic instability does not arise [7][8] due to significant natural pressure.

Conclusions
Based on the results of tests, the following conclusions can be drawn: into account the increased responsibility of buildings cannot be carried out without taking into account the dynamic stability of soils.  To analyze the dynamic stability of soil massifs during earthquakes, it is necessary to assess the level of design impact and the dynamic strength of soil.  Having completed the calculation of the effective shear stresses, it is necessary to correlate them with the dynamic strength obtained from the results of special laboratory dynamic soil tests.  The specified method for assessing the dynamic stability of foundations makes it possible to take into account a significant amount of accumulated data on the characteristics of seismic impact (frequency of impact, frequency, acceleration, magnitude, duration of impact, etc.)  The technique makes it possible to estimate the potential for liquefaction, taking into account the distribution over the depth of the soil massif and to highlight the thickness of the soil, which, during an earthquake, may lose dynamic stability.