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1
DOI:10.22337/2587-9618-2023-19-4-116-123
CALCULATION MODEL OF DEFORMATION OF THE SOIL FOUNDATION OF A HIGH-RISE BUILDING, TAKING INTO ACCOUNT THE LOADING HISTORY
Ilizar T. Mirsayapov, Irina V. Korolev
Kazan State University ofArchitecture and Engineering, Kazan, RUSSIA
Abstract: While designing high-rise buildings, it is necessary to take into account the influence of stages oftheir erection, this is the sequence of loading, on the change in physical-mechanical properties of soils. The calculation of deformations of subgrade is made with due regard for the change in soils properties comparing with the initial (natural) state. On the basis ofthe results ofexperimental studies, the authors substantiate the necessity for introducing the new parameter which makes it possible to characterize the mechanical condition of the soil at any stage of loading and can be used for creating calculation models. An analytical diagram of soil deformation in coordinates «oi-ei» for triaxial compression (where oi - vertical stresses (deviator), ei - linear deformations under the triaxial compression) is adopted as this parameter. The procedure for constructing transformed diagrams of the soil state under the long performance triaxial loading is described. The procedure obtained was approbated when calculating deformations of the foundation base of the high-rise building with due regard for the influence of staging of construction and rheological properties of soils on the change in the base rigidity and, as a result, on the redistribution of stresses among separate elements of the system "subgrade -foundation - upper part ofthe building.
Keywords: long regime triaxial loading, analytical diagram ofsoil deformation, coefficient of subgrade resistance, settlement calculation, high-rise building
РАСЧЕТНАЯ МОДЕЛЬ ДЕФОРМИРОВАНИЯ ГРУНТОВОГО ОСНОВАНИЯ ВЫСОТНОГО ЗДАНИЯ С УЧЕТОМ ПРЕДЫСТОРИИ ЗАГРУЖЕНИЯ
И. Т. Мирсаяпов, И.В. Королева
Казанский государственный архитектурно-с^оительный университет, г. Казань,РОССИЯ
Аннотация: при проектировании высотных зданий необходимо учитывать влияние этапов их возведе-
-
тов оснований. Расчет деформаций оснований фундаментов следует выполнять с учетом изменения свойств грунтов по сравнению с первоначальным (природным) состоянием. По результатам экспериментальных исследований авторами обоснована необходимость введения нового параметра, который позволил бы охарактеризовать механическое состояние грунта на любом этапе нагружения и мог использоваться при создании расчетных моделей. В качестве такого параметра принимается аналитическая диаграмма деформирования грунта в координатах о1-е1 для трехосного сжатия (где о1 - вертикальные напряжения (девиатор), е1 - линейные деформации при трехосном сжатии). Описана методика построения трансформированных диаграмм состояния грунта при длительном режимном трехосном нагружении. Полученная методика была апробирована при расчете деформаций основания фундамента высотного здания с учетом влияния этапности строительства и реологических свойств грунтов на изменение жесткости основания и, как следствие, на перераспределение усилий между отдельными элементами системы «грунтовое основание - фундамент - надземная часть здания».
Ключевые слова: длительное режимное трехосное нагружение, аналитическая диаграмма деформирования грунта, коэффициент постели, расчет осадки, высотное здание.
INTRODUCTION
Soil bases of foundations of buildings and structures are exposed to various static and dynamic loads under various combinations of these loads. The existing methods of deformation calculation of foundations are developed for a single short-term static loading with constant parameters for the entire period of operation. In real conditions of construction and operation, the loads on the soil foundation are applied in stages as the building or structure is erected [1-5]. In this case, the stages of active loading during the construction period pass into the stages of long-term holding under loading. Experimental studies (Fig. 1, 2) carried out by the authors [6-7] show that the nature of changes in soil deformations under long-term regime loading differs significantly from the results obtained under short-term static loading, which are the basis for the existing methods of settlement calculation. In this regard, there is a need to improve the methodology for calculating settlement of foundations of buildings with a developed underground part. This task is especially relevant for the foundations of high-rise buildings composed of clayey soils, the stress-strain state of which changes in time and depends on the history of previous loading [1-5]. In addition, in accordance with modern requirements, the calculation of the bases of high-rise buildings should be performed taking into account the joint deformation of the system "subgrade - building", i. e. deformations (settlement) of the subgrade of such a building should be calculated taking into account the influence of the stiffness of the elevated part of the building.
Oi, MPa
(a)
<Ti,MPa
<b>
Figure 1. Results ofexperimental studies: a -regime ofloading; b - dependence between average stresses ai and relative linear strains si; c - development ofrelative linear strains in time
MATERIALS AND METHODS
To calculate the settlement of a high-rise building taking into account the joint deformation of the above-mentioned system, the modified Pasternak method [8] was used as a basis, taking into account the spatial stress-strain state of the
base soils and changes in the rheological properties of soils under long-term regime loading. As it is known, Pasternak's method [9] describes the performance of the soil by means of compression coefficient Ci, which relates the intensity of vertical soil pushback to its settlement, and shear coefficient C2, which characterizes the vertical shear forces arising in loose and loosely cohesive soils due to entanglement and internal friction between its particles. These coefficients were determined according to the equation:
-gr
Hc(l-2ngr)
;C2
Ci-Hc(l-2ngr)
6(1+Hgr)
Where is the Poisson's coefficient within the compressed layer:
^gr =
Z?=lf
lH-i-hj
(2)
When using the modified Pasternak method [6], the coefficients of subgrade resistance Ci and C2 were also determined according to equation (1), but to determine the average strain modulus, a correction factor u was introduced to the value of the strain modulus of the i-th sublayer. This coefficient varied according to the law of a square parabola from u = 1 at the level of the foundation footing to u = 12 at the level of the already calculated boundary of the compressible strata and was determined by the equation:
into account in the model by means of coefficients of subgrade resistance Ci and C2 variable in time, depth and in plan:
Ci =
£i(t,T) ; HC(l~2ßgr) ;
C2 =
6(l+i" gr)
(5)
■ (1)
1,8
CL 1,5-
==
S 1,2-
0 JC, 0,9-
<L> 0,6"
0,3-
0
_L_
_L_
_L_
_L_
_L_
12 24
132
200
62 100 Time, day
_One-time short-term static loading
_ . Long-term static loading
„_ Short-term cyclic loading e Long-term static regime loading
Lorg-term static and cyclic regime I lading
Figure 2. Variation ofsoil strength under different loading regimes
It is proposed to determine the deformation modulus at each point of the compressible layer on the basis of transformed deformation diagrams by the expression:
Ei(t,r) =
Affii(t/Q £li(t/0 '
(6)
Then the soil deformation modulus for determining the variable bedding coefficient should be calculated by the equation:
nz2 , t
u = —^ + l
2
(3)
El(t,r) =
Hr
(V)
¡^El^T)
At the same time, the modulus of deformation of the base was calculated:
F =
Hr
En
/=1
(4)
UfEf
The authors propose to modify the modified Pasternak model. In this case, the pliable properties of base soils under such regimes are taken
Variability coefficients of subgrade resistance is substantiated by the results of experimental studies (Figs. 1, 2) and the calculation model developed by the authors [6-7]; it was found that under step-by-step loading, all the bases of parameters characterizing the stressed and deformed state of soils change in time, which allows us to conclude that it is necessary to develop a new parameter that would characterize the mechanical state of the soil at any stage of load-
ing and could be used to create calculation models. The analytical diagram of soil deformation in coordinates o -e for triaxial compression is taken as such a parameter(where 01, si are vertical stresses (deviator) and linear strains in triaxial compression).
Based on the obtained graphs (Fig. 1), the initial diagrams (state diagrams) of soil deformation under short-term triaxial static loading are constructed. The value of temporary resistance ai =Rgr,u (deviator) of the soil is taken as the limit point in coordinates (o). Under triaxial short-term static compression.
The limit point on the ordinate axis (s) is taken as the value of linear strain Sui=0,0869. Types of diagrams are presented in Fig. 3. When considering the state diagrams of clayey soil under triaxial long-term static loading, the deformation diagrams ai-ei for the case of triaxial short-term static loading are used as initial ones. By transforming the initial state diagram under triaxial short-term static loading, we obtain analytical dependences to describe the deformation diagrams of clayey soil under triaxial long-term static loading. In form, the transformed diagrams are assumed to be similar to the original state diagram on the basis of the following provisions (Fig. 3).
Figure 3. Initial (short-term static) and transformed (long-term static) analytical diagrams
The limiting point of vertical pressure at the top of the diagram is taken to be the stress in the soil, which is equal to the limit of long-term resistance under triaxial load action Rgr,long=(t,x) and deformations corresponding to the defor-
mations at the top of the state diagram under triaxial short-tern static loading Sgru,red=Sgru; For the limiting point defining the boundaries of the state diagrams along the ordinate axis, the deformations are equal to the limiting deformations under triaxial short-term static loading Sgr,red £gr,R, and the basic dependencies are used to calculate the stresses in the soil; The start of the diagram coordinates is assumed to be shifted by the value equal to the creep deformation at the considered time Spl (t) - at long static loading;
The obtained slope angles of deformation diagrams are taken into account the change in the deformation modulus of clayey soil under triaxial long-term static loading. In the next step, the diagram is transformed for each block long-term loading block (Fig. 4). When describing soil deformation modes under triaxial loading, it is necessary to take into account the effect of vertical pressure (ai) of the previous block on the strength, strain modulus and relative strains at the top of the diagram during subsequent loading after the regime change.
transformed (regime long-term static) analytical diagrams
On the basis of the obtained transformed analytical deformation diagrams, a method of calculating settlements of foundations of high-rise buildings has been developed, which is based on the method of layer-by-layer summation taking into account changes in the spatial stress-strain state of soils in the process of triaxial regime long-term static loading.
Based on the values obtained from the diagrams, the modulus of total soil deformations at each point of the foundation is determined (Fig. 5), and then the value of coefficient of subgrade resistance for each point is specified.
Taking into account that after 35 and 45 months from the beginning of construction the load from the building was 75% of the full load, the following loads were taken into account in the calculation: standard load on the typical upper floor taking into account the weight of load-bearing structures 13.65 kPa; standard load on the underground floor taking into account the weight of load-bearing structures 14.35 kPa; total weight of the building without taking into account the weight of the foundation 82620 t; average pressure at the bottom of the foundation without taking into account its weight 60 t/m2; average pressure under the bottom of the foundation taking into account the weight of the foundation and the floor 64.59 t/m2. Wind pressure was not taken into account.
The settlement was calculated using the LIRASAP 2014 software program, which implements
The proposed methodology was used in the calculation of the foundation settlement of a high-rise building, which has a frame-wall system, made of monolithic reinforced concrete and has the following parameters: total height 144.9 m (39 floors); number of underground floors 4; foundation depth 15.15 m; area of foundation 1377 m2; columns, internal and external walls of the underground part are made with concrete class B40, floor slabs B30, staircases and flights - B25; the building has a distributing technical floor with a 2100 mm thick floor slab, providing load transfer from the above-ground part to the underground part; the thickness of the foundation slab is 2000 mm (Fig. 6). Physical and mechanical characteristics of engineering and geological elements of the base are given in Table 1.
Tablel. Characteristics offoundation soils
the finite element method [7]. At the same time, a spatial model of the whole building was created in the program structure to automatically transfer the load "base".
In the vicinity of the investigated building there is an enclosing structure in the form of a monolithic reinforced concrete "wall in the soil" 0.8 m thick and 35 m deep, providing stability of the excavation walls during the zero cycle works (Fig. 6). Taking into account that the soils below the foundation footing in the wall-in-soil zone are in constricted conditions and are subjected to greater lateral pressure during the application of vertical loads from the building, it can be assumed that the compressibility parameters of the soils will be variable. In the calculation, this was taken into account by introducing different bedding coefficients under the main area of the foundation and the zone of influence of the wall.
№ layer Type of soil p, kg/m3 E, MPa (p, grad C, kPa
Layer-6 Dense dusty sands 2030 32 36 4
Layer-7 Semi-solid clay I960 23 23 67
Layer-8 Tightly plastic clay 1940 22 26 43
Layer-9 Solid clay 1720 25 19 86
N Sav, mm Smax, mm Smin, mm i
1 137 145 129,7 0,00026
2 135,96 147,29 124,63 0,00038
3 215 226 205 0,00035
4 214 235 193 0,00073
5 242,3 254,7 231,04 0,00035
6 241,18 264,85 217,5 0,00073
tion; 1 - in 45 month without taking into account the slurry wall and 75% of load; 2 - in 45 month with taking into account the slurry wall and 75% ofload; 3 - in 45 month without taking into account the slurry wall and 100% ofload; 4 - in 45 month with taking into account the slurry wall and 100% of load, 5 - in 100 years without taking into account the slurry wall and 100% ofload; 6 - in 100 years with taking into account the slurry wall and 100% of load.
(b) e,
\
JL
Figure 6. High-rise building of a residential (plan and section)
RESULTS AND DISCUSSIONS
The above-mentioned soil model under triaxial loading was used, taking into account the change of horizontal stresses ax and ay due to the influence of the excavation enclosing wall. The obtained calculation results are shown in Table 2 and Fig. 7.
Table2. Settlements and inclinations
offoundation
Where Sav, Smax, Smin, i - average, maximal, minimal settlement and inclination of founda-
Figure. 7. Calculation results: a - calculated distribution of coefficients of subgrade resistance without taking into account the "slurry wall"; b - the same with taking into account the "slurry wall"; c,d- characteristicpicture of vertical displacements of thefoundation slab and the base without and with taking into account the influence of the "slurry wall"
The analysis of the results showed that the picture of foundation deformation changes qualitatively when the "slurry wall" operation is taken into account. At the same time, there is a good convergence of the calculated results with the data of geotechnical monitoring. In 45 months since construction, the deviation of the calculated values from the monitoring data on the average settlement was no more than 13%.
CONCLUSIONS
1. The methodology of calculation of deformations of high-rise buildings foundations taking into account the stage of building erection with the use of analytical diagrams of soil deformation under long-term triaxial regime loading has been developed.
2. The testing of the proposed methodology for calculating foundation settlement of a high-rise building on the basis of analytical diagrams of soil deformation allowed us to obtain calculation results with good convergence with the monitoring data. The deviation of the calculated average settlement from the real one was no more than 1% and no more than 13% with the data obtained for 35 and 45 months of monitoring, respectively.
REFERENCES
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СПИСОК ЛИТЕРАТУРЫ
1. И.Т. Мирсаяпов, И.В. Королева (2021) Геотехнический прогноз влияния устройства свайного фундамента в овраге на существующую застройку, Жилищное строительство, №8, С. 3-11. doi:10.31659/0044-4472-2021-8-3-11.
2. Ter-Martirosyan A., Sidorov V. (2021) Studying the influence of taking into account the elastic-plastic behavior of strut elements on the retaining system equilibrium. IOP Conference Series: Materials Science and Engineering: 7, Tashkent, 11-14 November 2020. Tashkent, p. 012030. doi:10.1088/1757-899X/1030/l/012030.
3. Мангушев P.A., Пеньков Д.В. (2021) Сравнение результатов численных расчетов с использованием современных моделей грунта (Hardening Soil, Hardening Soil Smalln Generalized Hardening Soil) с результатами мониторинга. Вестник гражданских инженеров, № 2(85),с. 85-93. doi: 10.23968/1999-5571-2021-18-2-85-93.
4. И.Т. Мирсаяпов, Н.Н. Айсин (2022) Оценка влияния устройства глубокого котлована на дополнительные осадки зданий
окружающей застройки. Известия Казанского государственного архитектурно-строительного университета,^ 3(61), С. 6-13.doi:10.52409/20731523_2022_3_6.
5. Mirsayapov I.T., Koroleva I.V. (2020) Seismic and wind impacts on subgrade deformations of high-rise buildings. Proceedings of the 12th International Conference on Contemporary Problems of Architecture and Construction, ICCPAC 2020 (Санкт-Петербург, Россия, 25-26 Ноября, 2020 г), С. 221-224.
6. Mirsayapov I.T., Koroleva I.V. (2016) Strength and deformability of clay soil under different triaxial load regimes that consider crack formation. Soil mechanics and foundation engineering. 2016. No. 1, pp. 5-10.
7. Mirsayapov I.T., Koroleva I.V. (2014) Bearing capacity and deformation of the base of deep foundations' ground bases, Ge-otechnical Aspects of Underground Construction in Soft Ground: Proc. intern, symp., Seoul, Korea, 25-27 August 2014. Lieden: Balkema, Pp. 401-404.
8. Пастернак П.Л. Основы нового метода расчета на упругом основании при помощи двух коэффициентов постели. М.: Гос-стойиздат, 1954. 56 с.
9. Городецкий А.С., Евзеров И.Д. Компьютерные модели конструкций. М.: АСВ, 2009. 360 с.
Ilizar Talgatovich Mirsayapov — doctor of technical science, professor, head of department "Bases, Subgrades, Structure Dynamics and Geology", Kazan State University of Architecture and Engineering, 1, Zelenaya st, Kazan, 420043, Russia, mirsayapovl@mail.ru, +7 917 852-14-59
Irina Vladimirovna Koroleva — Candidate of technical science, professor, Associate Professor of department "Bases, Subgrades, Structure Dynamics and Geology", Kazan State University of Architecture and Engineering, 1, Zelenaya st, Kazan, 420043, Russia, prepod-irina@yandex.ru, +7 917 871-12-18
Мирсаяпов Илизар Талгатович — доктор технических наук, профессор, заведующий кафедрой «Основания, фундаменты, динамика сооружений и инженерная геология», Казанский государственный архитектурно-строительный университет», Казанский государственный архитектурно-строительный университет, Россия, 420043, г. Казань, ул. Зеленая, 1, mirsayapovl@mail.ru
Королева Ирина Владимировна — кандидат технических наук, профессор, доцент кафедры «Основания, фундаменты, динамика
сооружений и инженерная геология», Казанский государствен-
Казань, ул. Зеленая, 1, prepod-irina@yandex.ru
