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Determination of viscosity parameters in rigid body-soil interaction
Xojimetov Gaibnazar Xadjievich, Institute seismic stability of structures, Academy of sciences of Uzbekistan, Doctor of Technical Sciences, Professor Bekmirzaev Diyorbek Abdugapporovich, Institute seismic stability of structures, Academy of sciences of Uzbekistan, s. r. c. E-mail: diyorbek_84@mail.ru Yuvmitov Anvar Sayfullaevich, Tashkent architecture and construction institute, s. r. c.
E-mail: anvar.sayfullaevich@mail.ru
kj = akx, (2)
where kx - is a coefficient of interaction under longitudinal displacement of the pipeline relative to soil, a. = 2 (l + pmil) if k. = k ; at
10
at = 8l /PDH ; ' '
k. = k
at k = k.
' l V
ß =
1 —
DB
Di
v Dh y
Determination of viscosity parameters in rigid body-soil interaction
Abstract: The paper is devoted to the determination of viscosity parameters of the interaction of rigid bodies (such as foundations and underground pipelines) with soil under arbitrary action of load on the former. Here on the bases of developed methods and tests results the viscosity coefficients are determined in the contact of body-soil interaction. They may be used in design of buildings and underground pipelines on seismic effects, utilizing Voigt or Maxwell-Kelvin's models.
Keywords: underground pipeline, foundation, soil, elasticity coefficients, viscosity parameters, model, seismic load.
As an example, consider the tests with underground pipelines, which are also true in the study of properties at foundation-soil interaction.
Assume that seismic load is arbitrary directed towards the axis of underground pipeline. Then, it would sustain longitudinal ( N ), transverse ( Q ) loads, and bending ( Mu), torsional ( Mk) moments. In [1], assuming that the relation between displacements and loads subject to a linear law, one may write the following:
q. = k®.1, (1)
u . ^
where qt - is one of the loads N,Q,Mu, Mt; k - one ofproportion-ality coefficients of pipe-soil interaction; ©; - one of the displacements of these loads.
The methods of determination of coefficients k (kx ,k ,k^,ka~j depending on various factors (diameter, length, depth of a pipeline bedding, soil characteristics, etc.) are given also in [1], based on tests results. Using dimensional theory and the principle of superposition, it is shown that if one of the coefficients kx ,k ,k^,ka is known, the others may also be determined:
DB, DH - internal and external diameters of the
pipe; - Poisson ratio and l - the length of a single pipe.
The tests show that the range of linear connection (1) is not wide. Figures 1 a, b present experimentally obtained graphs of longitudinal interaction ofloamy soil (a) and gravel (b) with steel pipeline ( DH = 0.089 m., the length 3.869 m., the depth of bedding from the pipe top for a loamy soil 0.7 m., for gravel 0.4 m.) at different velocity of displacements. The time to reach a maximum load for the curves 1-3 is 240, 21 and 12 sec., respectively for a loamy soil and 180, 9 and 6 sec for gravel. At small displacements the relation between za and u may be considered as nearly linear. Results of these tests show that even at small changes in velocity of displacements, the graphs of interaction Ta - u vary considerably.
Ta,kN! m2
0,0015
T„,kNhrf
0.0004 0.0008 0.0012 u,m
b
0.0004 0.0008 0.0012
il, m
Fig.1. Graph of longitudinal interaction (a, b)
The effect of displacement velocity on the dynamics of underground structures may be considered by the application of linear-viscous-elastic law to record the stresses at structure-soil contact through relative displacement. If elastic characteristics are determined through coefficients of interaction, viscous properties of interaction may be characterized by a coefficient of viscosity,
its values essentially effecting on the dynamics of underground structures.
When considering concrete problems in linear-viscous-elastic statement and to obtain numeric results which determine stressstrain state ofunderground pipelines it is necessary to know the values of viscosity coefficients of the interaction depending on differ-
a
Section 7. Technical sciences
ent factors which may be stated by tests results, using the methods discussed in [2].
Let the interaction of a pipeline with soil subject to deformation law of viscous-plastic medium. Simulating the medium element in the form of two springs and a damper (Fig. 2), their displacements will be written in the following form:
u = u + u2, (3)
where u1 and u2 — are the displacements of the 1st and 2nd springs.
The relation between tangential stress and spring displacement is determined at loading as:
- W' % > * f > ° , -(- )■ £ > * i > » '
At un-loading the relation betweenro and u1 is:
T a = f (« ), f > 0, dUf > 0, f («. («0,
(4)
(5)
(6)
And between ta and u2 it is determined by equation (5), till the state u2 = u2max. Under further un-loading u2 = const. Damper resistance is taken in the form:
T = u(T . (7)
The displacements of the 1st spring are partially reversible, and of the 2nd spring and the damper- irreversible. If for the spring and damper Ta =$2 (u2) + ^ (ra )U2 then displacement velocity of the
dT
medium from (3-5), (7) is determined at —- > 0 :
dt
U
dt
dz
at —^ < 0, u, < u,
dt 2 2m
Ta -fa (U ) ta w ,
- " /V' =-tt~ + f (ta ,U - Uj ,
dt
u=dR+f ( ,u - u>), dt
(8)
(9)
dTa n
at if < 0' U2 = U2max ! dt
u =
dt
(10)
Functions and ocmay be determined from tests results
at different«, comparing then with design data.
Fig. 2. Viscous-elastic model When considering seismic waves rather distant from the blast site, load increase and decrease may be presented by the equations:
t
Ta = t-, 0 < t <t,
t, -1 ^ ^ t„=t„„ —1-, t < t <t,
(11)
ra = 0, t < t.
Let the relation between the load and the displacement of the pipeline relative to soil have the form:
t = kDu., t = kSu,
= kR( . t (12) Ta -TaK = k,, (u -uK), ¡j, = const.
corresponding to dynamic and static loading and un-loading (taK and ur — are the maximums of stresses and displacements u1). Under continuous increase of load and its decrease, but at growing u2, substituting (12) into (8) and (9), we get:
u = k--
i \ t
k - u
V /
u=kR-n
kDkR - kSkR+kSkD
■ + t„
kR - kD
--u
(13)
(14)
where n =
kDkS
kSkDkR aK kDkR /V /V /V /V /V
xxx xx y
- is a viscosity parameter. At u2 = const
- K)
from (8) kRu -ra = 0.
Now substituting the 1st and 2nd from (11) into, respectively, (13) and (14), we obtain a differential equation:
u + + At + B = 0, (15)
differing only in the constants A and B, which are: at t <T :
A = -t, b = ,
tkSS tkD '
at t >T :
_nTgK (kR - K2 ) R _ Ta
A _
_ vtgK (kR + kx2 )t - kR - kR
(t-t)kRK2'~ -t)kR (t-t)kRK2 kRkR
nT.
(16)
(17)
Integrating (15), we would find:
u(t ) = -- - 4 (nt -1) + Ce ~nt, nn
where:
A B
C = —-^ at 0 < t <t , n n
C = u(t) +—(riT -1) en at t >t.
_ n _
Displacement maximum under the load of the form (ll) may be reached at t >t . The value of maximum time tmax is found from the equation:
A
u (t ) =---nCe = 0,
n
hence:
1, f A
tmax =--In I - —
n \ n c
Determine approximate numeric values n of pipeline-soil interaction. For that we would compare tests values u(j),tmax and u (tmax) with results, obtained from the model of viscous-plastic medium (see Table l).
In relation to tests data for gravel soil in design it is taken as:
kR = 37 • 103 kN/m 3, kR = 25 • 103 kN/m 3, kR = 90 • 103 kN/m 3, T1 = 15 sec; And for loamy soil:
kR = 74 • 103 kN/m 3, ksx = 33 • 103 kN/m 3, kR = 61-103 kN/m 3, t1 = 30 sec.
Comparison of these data shows that they are most identical at n = 0.1 sec-1. Viscosity coefficient oc of pipeline-soil interaction at n= 0.1, equals to 945 -103 kNsec/m 3 — for gravel and 595 -103 kNsec/m 3 for loamy soil.
If load-displacement relation is written in the form:
u + n = T + Vjj. (18)
Then, for the determination of viscosity coefficient, with u = const and u = ut, from (18) we get:
kD b t + az = bt + c, a = "HS, b = nkDu, c = —. (19)
K n
Role of the acid-base nature of interphase interactions in structurization of composite construction materials
Integrating (19) at initial condition Ta (0), we would get
b - ac
e , C = —:—.
bc Ta (t) = — (at -1) + - + C
(20)
Considering t = U, we would find: u
bu ac - b . Ta (u) = — + —— I 1 - e
an
- kSu
1 - e
a
ku
n
1 - k. kD
(21)
Fig. 3. Addiction kD /k;
Solving the equation (21) graphically, we find the valuen. Figure 3 shows the dependences a from the relationship k^D / ksx built by determined values of n from (21). The curves 1 and 2 are built using tests results with loamy soils (presented in the Table), and the curves 3 and 4 at the values t = 13.30 kN/m 2, t= 12 sec., u = 0.180 mm. and Ta = 6.55 kN/m 2, t = 15 sec., u = 0.180 mm., respectively. Results of the study show that the values of for carried out tests are within the range (40 ^ 400)-103 kNsec/m 3 or ft = = (78 - 800) kNsec/m 2.
The values of oc for other cases (under the effect of transverse force, bending and torsional moments) may be found by similar way. It is suffice to know the values of interaction coefficient under the effect of dynamic load with different velocity of loading. However the experimentations present a lot of difficulties. So, considering that, it is proposed to make use of the data found under the effect of longitudinal force N, when determining viscosity parameters under the loads Q, Mu and Mk. Here the expression (2) may be used with a high degree of accuracy in the following form:
& = ajVx, (22)
where a - is one of viscosity coefficients under the effect of loads Q, Mu, Mk; a -viscosity coefficient under longitudinal force N; a^-the same as in (2).
In [3], when investigating horizontal oscillations of buildings under seismic effect and using Voigt and Maxwell-Kelvin linear-viscous-elastic model, it is shown that even two order change in viscosity parameters insufficiently effects on design results. This is true for above given statements.
Тable 1.
or:
D
uk
Soil Tests data Design data
t au, kN/m 2 t, sec u (r), mm n, sec-1 u(r), mm tmax sec u (t ), mm \ max )
Loamy soil 9.4 18 0.200 0.01 0.600 144 0.747
0.1 0.207 14 0.130
Gravel 7.55 3 0.220 0.01 2.676 120 1.267
0.1 0.203 17 0.48
References:
1. Rashidov T. R., Khozhmetov G. Kh. Seismic Stability of Underground Pipelines. - Tashkent: Fan, 1985. - 153 p.
2. Lyakhov G. M. Bases of the Dynamics of Explosive Waves in Soils and Rock Mass. - Moscow: Nedra, 1974.
3. Khojmetov G. K., Khodjimetov A. I., Yuvmitov A. S. Influence of Soil-Foundation Interaction Properties on Oscillations of the System "Building-Building" and "Building-Stack-Like Structure"//World Journal of Mechanics. USA. - 2015. - № 5. - P. 106-117.
Adilxodjayev Anvar Ishanovich, Soy Vladimir Mixaylovich, Tashkent Institute of Railway Transport Engineers E-mail: volodya_tsoy@inbox.ru
Role of the acid-base nature of interphase interactions in structurization of composite construction materials
Abstract: Modern ideas of polystructural theory of composite construction materials are presented in the article. Keywords: polystructural theory, composite materials, acid-base centers, microstructure, mesostructure, macrostructure.
The modern perceptions following from the polystructural theory of the composite construction materials (PT CCM) with mineral, combined and polymeric binding agents are based on the concept of their structurization based on the community of the levels of structure created by the founder of PT CCM academician Solomatov V. I. [1].
In construction mastics, glues, solutions and concrete on the basis of various binding agents are most of use. On the basis of PT
CCM, it is expedient to consider their structure in the following large- scale levels:
- microstructure (mastics, glues, sealants, etc.);
- mesostructure (solutions);
- macrostructure (concrete).
From the standpoint of structurization of CCM the greatest scientific interest is represented by the microstructure since the surface area of its disperse phase makes 90 and more percent [1].
