CC BY
19Magazine of Civil Engineering. 2020. 99(7). Article No. 9907
Magazine of Civil Engineering issn
2712-8172
journal homepage: http://engstroy.spbstu.ru/
DOI: 10.18720/MCE.99.7
Transition factor between elastic and deformation moduli for dispersive soils
V.V. Antipov*, V.G. Ofrikhter
Perm National Research Polytechnic University, Perm, Russia * E-mail: seekerva@mail.ru
Keywords: Multichannel Analysis of Surface Waves, MASW, elastic moduli, deformation modulus, experimental investigations, Plate Load Test, PLT, Triaxial Test, numerical models
Abstract. The paper is devoted to the perspective trend of researches on estimation of physical and mechanical characteristics of dispersive soils by means of non-destructive methods of in-situ testing by wave analysis. The paper presents the results of comparison of the values of the transition coefficient between the soil dynamic elastic modulus, which can be calculated from the results of in-situ tests by means of nondestructive technique of Multichannel Analysis of Surface Waves, and the soil deformation modulus. Application of such a transition factor makes it possible to estimate the soil deformation modulus according to the soil elastic characteristics determined using modern non-destructive express techniques of wave analysis of the low velocity zone of the upper part of the profile. Due to the application of such express methods, labor and time costs of field investigations are significantly reduced during preliminary geotechnical site assessment. Comparison of different values of the transition factor was made on the basis of the results of laboratory standard triaxial tests and numerical experiments with the values calculated on the basis of dependencies proposed by the results of in-situ tests with Plate Load Tests and Multichannel Analysis of Surface Waves in previous in-situ studies. The results of standard triaxial tests on samples of cohesive and non-cohesive soils confirm the dependence of the transition factor on the soil unit weight, obtained in the previous stage of in-situ researches. The values of the transition factor based on the results of numerical experiments do not exceed the results obtained by field research methods. The results of the research will be useful in estimating the physical and mechanical properties of the soil during preliminary geotechnical calculations of the foundations. All in-situ investigations are carried out using non-destructive technique. No permits or approvals are required to perform the work according to the proposed methodology.
1. Introduction
At present, obtaining initial data about soils strata and also physical and mechanical characteristics for geotechnical calculations can take quite a long time, and application of conventional test methods requires relatively large labor costs at the preparation and execution stages. These disadvantages are clearly apparent when conducting an express preliminary geotechnical assessment of the soil base of a future or existing building or structure. The task of reducing the labor and time required to conduct a preliminary geotechnical situation assessment at the pre-design stage is relevant. To solve this problem, modern non-destructive wave methods can be used, in particular, Multichannel Analysis of Surface Waves (MASW).
MASW is a modern non-destructive technique of wave analysis of the low velocity zone at the upper part of soil profile, which allows obtaining a velocity profile of the surface wave distribution in the upper section. MASW was first presented in the Park et al paper. [1]. Different researchers (C.B. Park, J. Xia, S. Foti, J.N. Louie, N. Ryden, K. Suto, R. Miller, M. Carnevalle, Z. Lu, B. Mi, A. Levshin, C. Li et al. [2-14]) continue to improve the technique, increasing the speed of the in-situ procedure and the resolution of velocity profiles. The results of MASW are generally used for dynamic (elastic) soil calculations [15-19], but they can also be used for preliminary geotechnical assessment of soil bases. In the Russian Federation, the Regulation SP 11105-97 "Engineering geological site investigations for construction. Part VI. Regulations for geophysical surveys" presents several empirical dependencies to determine the deformation modulus (calculated by service limit state) as well as cohesion and the internal friction angle (calculated by ultimate limit state) based
Antipov, V.V., Ofrikhter, V.G. Transition factor between elastic and deformation moduli for dispersive soils. Magazine of Civil Engineering. 2020. 99(7). Article No. 9907. DOI: 10.18720/MCE.99.7
I This work is licensed under a CC BY-NC 4.0
Magazine of Civil Engineering, 99(7), 2020
on longitudinal and/or transverse wave velocities for different types of dispersed soils. No such dependencies are given for the surface wave velocity that can be determined using MASW.
Conventional Plate Load Tests (PLT) are used in the Russian Federation to determine the deformation modulus of the soil base during engineering and geological surveys. Deformation modulus corresponds to the straight-line section of the load-settlement curve of PLT in accordance with the State Standard GOST 202762012 "Soils. Field methods for determining the strength and strain characteristics". The straight-line section ends at the fourth point of the load-settlement chart, counting from the point of accepted initial pressure. In previous papers of the authors [20, 21], based on comparison of the in-situ PLT and MASW tests, the dependence (1) was proposed to estimate the deformation modulus E using the initial shear modulus G0 and transition factor ko. Non-dimensional transition factor ko can be calculated by means of empirical relation (2) as a function of the soil unit weight.
E - AgGq (1)
kG = —0.005286y3 + 0.314254y2 — 6.248539/+ 41.723895 (2)
where E is deformation modulus, corresponding to the PLT deformation modulus Eplt for a 5000 cm2 round plate, MPa; G0 is the initial shear modulus, MPa, it can be estimated using (3) [22] via density (unit weight) and surface wave velocity based on MASW results [20, 21]; y is the soil unit weight, kN/m3, it can be estimated using (4) [22] via surface wave velocity, proposed on the basis of known empirical relationships for shear wave velocity [23, 24].
G0 = 1.096 • 10—6 pVR, MPa (3)
y = ln
f V 3.6O
VR
z0-1 V z y
+ 0.166372,kN/m3 (4)
where p is soil density, kg/m3, calculated via soil unit weight; Vr is surface wave velocity, m/s; z is soil base depth, m.
To increase the accuracy of dependence (2) inferred from in-situ tests it is necessary to compare it with the results of deformation modulus determination on the basis of triaxial tests, because of all laboratory tests only triaxial tests simulate the behavior of soil under load most closely to the actual behavior [25]. In addition, it is also necessary to carry out numerical experiments based on the results of triaxial tests, since the numerical modeling at preliminary geotechnical assessment of soil bases allows us to eliminate the need for costly and lengthy field tests and, at the same time, to calculate the parameters required for engineering calculations.
The purpose of the paper is to compare the values of transition factor between the elastic modulus and the deformation modulus obtained by means of field tests [20, 21], laboratory triaxial tests and numerical experiments.
2. Methods
2.1. Triaxial tests
Comparison of the values of transition factor between the elastic and deformation moduli was performed based on the results of standard drained triaxial tests of cohesive and non-cohesive soil samples with predescribed parameters at a full water-saturated state (Table 1, soils a and b). The tests were carried out with a triaxial compression unit GT 2.0.9 manufactured by NPP Geotek, LLC (Penza City, Russian Federation), and pressure control panel GT 2.0.11 with static and kinematic loading modes, maximum load of 1 ton (10 kN). Tests were performed in the triaxial compression cell GT 2.3.8 of type A (isotropic compression), the test data was processed using the ASIS automatic software.
To reduce the amount and time of triaxial tests, an analysis of the provided results of triaxial tests on the samples of cohesive soils was performed. The results were provided by NPP Geotek, LLC and the "MIKS" Center for Technological Innovation and Modernization in Construction at PNRPU (Table 1, soils c - g).
The summary list of soils studied in laboratory conditions:
a is fine, saturated, dense sand;
b is heavy, tough clay;
c is medium-hard, light, silt clay;
d is very soft sandy clay;
e is very soft sandy clay; f is soft, silt clayey sand.
Table 1. Physical parameters of the studied soils.
Soil z* (m) W Wl Wp Ip Il p (g/cm3) ps (g/cm3) Pd (g/cm3) e Sr
a 1.5 0.22 - - - - 2.01 2.66 1.68 0.58 1.00
b 1.5 0.24 0.39 0.11 0.28 0.47 1.85 2.74 1.65 0.66 1.00
c 6.5 0.25 0.40 0.22 0.18 0.15 1.98 2.73 1.59 0.72 0.94
d 2.5 0.22 0.27 0.11 0.16 0.69 1.79 2.54 1.47 0.73 0.77
e 4.5 0.23 0.27 0.12 0.15 0.73 1.85 2.54 1.50 0.69 0.84
f 3.9 0.24 0.26 0.23 0.03 0.33 1.97 2.58 1.59 0.62 0.99
z* is sampling depth, for soils a and b the depth is specified; W is water content; Wl is liquid limit; Wp is plastic limit; Ip is plasticity index; Il is liquidity index; p is density; ps is particle density; pd is dry soil density; e is void ratio; Sr is degree of saturation.
The samples with prescribed parameters were formed according to State Standard GOST 304162012 "Soils. Laboratory testing. General". Before installation on the cell base the samples of sandy soil were previously stabilized at a negative temperature for 1 hour. The formed sample was squeezed out of the holder using a special device and installed in the triaxial cell.
To restore the assumed natural state of the studied soils, the reconsolidation of the prepared samples was carried out by the phase state restoration method (a special case of the backpressure method) in automatic mode, according to Appendix E of State Standard GOST 12248-2010 "Soils. Laboratory methods for determining the strength and strain characteristics".
Cell pressure increment and stabilization period were assigned according to Table 5.4 of State Standard GOST 12248-2010 (Table 2). Due to the fact that in-situ tests were conducted at a shallow depth in the low-velocity zone, a "sensitive" model at low cell pressures was adopted for triaxial tests.
Table 2. Parameters of triaxial tests.
Parameters a b
Vertical overburden pressure 01 (kPa) 30 30
Cell pressure 03 (kPa) 30 30
Cell pressure increment (kPa) 30 30
Stabilization period of PSR method (min) 5 30
Stabilization period (h) 0.5 18
Loading/unloading rate (mm/min) 0.001
Unloading stages by deformation value (%) 0.05; 0.10; 0.15; 0.20; 0.30; 0.40; 0.50; 1.00; 2.00; 3.00;
4.00; 5.00
Sample sizes, h * d(mm * mm)_100*50_
The deformation curve obtained as a result of triaxial tests was used to determine the soil deformation modulus E. The deformation modulus is not a constant value. Its values depend on the loading interval [25] determined by the future load on the soil from the foundation. At a preliminary estimation of the deformation modulus, the future loads are not yet known, therefore, like the assumption about the first four points of the load-settlement curve in State Standard GOST 20276-2012, deformation modulus was determined for the initial linear section of the deformation curve directly from the charts. The first point of the deformation modulus interval corresponds to overburden pressure in accordance with State Standard GOST 20276-2012, so when defining the deformation modulus from deformation curves, the initial point was taken as zero deviatoric load ffdev = 0. The end point of linear approximation by the deformation modulus is taken for relative deformation £1 = 0.005. The deformation modulus was calculated according to formula (5).
E = ^^ (5)
S1
For further calculation of the transition coefficient, the static elastic modulus Eo,st was also determined. For this, an unloading-reloading of the samples was carried out at different relative deformations (Table 2) to determine the values of recovering strains at specific pressure, and the unloading modulus was taken equal
Magazine of Civil Engineering, 99(7), 2020
to the static elastic modulus, similar to [26], at a relative strain of the order 10-3 (restored strain being not more than 10-4).Then the dynamic elastic modulus £b,dyn was estimated based on the value of static elastic modulus using coefficient K which is the ratio of dynamic and static moduli of elasticity according to (6) and Fig. 1 proposed in [26]. The dynamic modulus of elasticity was taken for deformations of less than 10-6, which occur during the field tests by MASW method.
K = ^ (6)
E0,st
! -i- Rocks
S oi Is - •A. ...............
:::: < iohe )S\\ /e j 4...............
t
lar
10 102 103 104 Static moduls of elasticity (Eo.st) [kg/cm2]
Figure 1. Empirical curve of dynamic and static elastic moduli ratio proposed in [26].
To shorten the test time, the kinematic loading mode was adopted. To create a "sensitive" model, the smallest loading rate of 0.001 mm / min possible for the device was taken (Table 2). Tests were carried out until the destruction of the sample or up to the maximum relative deformation of the sample of 0.15 according to paragraph 5.3.6.13 of State Standard GOST 12248-2010.
Provided results of triaxial tests on cohesive soils (Table 1, soils c-g) did not contain unloading stages, so it was not possible to determine the static modulus of elasticity directly, and the dynamic elastic modulus could not be estimated from Fig. 1 either. Therefore, the dynamic modulus of elasticity was estimated indirectly. First, the surface wave velocity Vr was estimated using formula (4). Further, the initial shear modulus G0 was calculated from the theory of elasticity using a well-known formula (3). Finally, the dynamic elastic modulus E0,dyn was estimated via formula (7) using dynamic Poisson's ratio.
E0,dyn = 2G0 i1 + Vdyn ),MPa (7)
where G0 is the initial shear modulus, MPa; Vdyn is the dynamic Poisson's ratio assumed by Appendix G of Regulations SP 23.13330.2018 "Foundations of hydraulic structures".
2.2. Numerical modeling
Numerical modeling to determine transition factor values was carried out by modeling in-situ PLT tests by a plate of 5000 cm2 (diameter D ~ 80 cm) in the conditions of natural soil occurrence at the depth of sampling. It was performed in the PLAXIS 2D software package. The geometric model is axisymmetric, 3.0x3.0 m, boundary conditions are standard. The finite element mesh is very fine. Two vertical distributed loads were applied to the geometrical model: the first was the overburden pressure; the second was a variable step load applied to the plate. Loading was made by stages accepted in accordance with State Standard GOST 20276-2012 depending on the soil type and void ratio.
Numerical experiment was carried out using the model of Hardening Soil [27] with Small Strains (HSSS) [28, 29]. The initial shear modulus G0 was estimated using formula (7) through the dynamic elastic modulus E0,dyn, which in turn was calculated using formula (6) through the ratio K of the dynamic and static moduli of elasticity. The ratio K was estimated using the empirical chart in Fig. 1 [26]. The unloading/loading modulus Eur was assumed to be equal to the static elastic modulus £b,st, which in turn was taken for abraded soils according to the results of triaxial tests, and for intact soils was E0,st = 6-7 E50 (E50 was taken from triaxial tests) according to recommendations [30]. The power coefficient m of HSSS model [29] was adopted according to recommendations [29] and [31], depending on the soil type. According to [31], the coefficient m
is usually assumed to be 0.5 for sand; 1.0 for clay; and intermediate values are assumed for sandy clay and loam.
To improve the accuracy of soil behavior modeling, the parameters of model deformation curves were calibrated in the PLAXIS software module SoilTest on the parameters of triaxial test curves according to the method proposed in [32]. The calibrated soil model parameters are presented in Table 3.
Table 3. Parameters of numerical soil models.
Parameter a b c d e f
Soil model HSSS HSSS HSSS HSSS HSSS HSSS
Material type Drained Drained Drained Drained Drained Drained
yunsat (kN/m3) 20.075 20.069 19.404 17.542 18.130 19.306
ysat (kN/m3) 20.075 20.069 19.653 18.534 18.713 19.342
e 0.58 0.66 0.72 0.73 0.69 0.62
E5oref (kN/m2) 14000 10000 7100 4300 7000 8800
Eoedref (kN/m2) 14000 26400 7100 4300 4000 8800
Eurref (kN/m2) 160000 60000 49700 25800 24000 61600
m 0.5 0.9 0.9 0.8 0.8 0.6
c (kN/m2) 12 13.5 83 10 39 30
9 41 7 22 19 21 23
y 0 0 0 0 0 0
Go (kN/m2) 140000 170000 66400 45000 43000 77000
yo.7 2.00E-04 1.00E-05 1.00E-05 8.84E-05 3.51E-04 1.47E-04
pref (kN/m2) 30 30 150 100 100 77
Rf 0.9 0.9 0.9 0.9 0.9 0.9
yunsat is soil unit weight; ySat is saturated soil unit weight; e is void ratio; Esoref is the secant deformation modulus at 50 % of the maximum deviatoric stress; Eoedei is tangent modulus for primary oedometer loading; Euriei is unloading/reloading modulus; m is power coefficient; c is cohesion; y is angle of internal friction; y is angle of dilatancy; Go is initial shear modulus; yo.7 is shear strain level at which shear modulus is reduced to about 70 % of Go; pref is reference pressure; Rf is failure ratio [23].
The deformation modulus E was calculated according to State Standard GOST 20276-2012 using formula (8) from load-settlement curves obtained during numerical experiments.
E = (l - v2 ) KKD — V ' p 1 AS
(8)
where v is Poisson's ratio; Kp is the specific-conditions-of-use factor according to paragraph 5.5.2 of State Standard GOST 20276-2012; Ki is the coefficient that depends on the plate shape, for a round plate Kp = 0.79; D is the plate diameter, cm; AP is pressure increment Pn - Po, MPa, Pn is the end of the chosen load interval, Po is the initial point of the chosen load interval, according to State Standard GOST 20276-2012, Po is usually taken equal to the overburden pressure; AS is settlement increment that corresponds to AP, cm.
2.3. Transition factor kE
After determining deformation and elasticity moduli, the transition factor was calculated. For ease of comparison, instead of the transition factor ko, the transition factor kE (9) between the dynamic elastic modulus Eo,dyn and the deformation modulus E was calculated in the same way [26]. Dynamic elastic modulus can be calculated using the well-known formula (7). The relationship between transition factors ko and kE is represented by the formula (10).
E
kEE0,dyn
kE = kG
2 i1 + Vdyn )
(9) (10)
1
Magazine of Civil Engineering, 99(7), 2020
where Vdyn is dynamic Poisson's ratio that can be evaluated by means of wave analysis or estimated using Appendix G of Regulations SP 23.13330.2018.
3. Results and Discussion
Deformation curves obtained from triaxial tests are shown in Fig. 2. Elastic parameters of soils determined and evaluated during standard drained triaxial tests are presented in Table 4. Accepted loading intervals for the calculation of deformation modulus and its values, as well as obtained values of the transition factor Re are given in Table 5.
o.uo
1 0.100
o 0.080
S 0.060
y
s
0.040
s
—
0.020
0.000
E= 17.68 MPa .
^Ost " J-1*»" ivura
0.00J
Vertical relative strain, E]
& rf
I 0.040 D
| 0.030
'J
| 0.020
0.010
0.000 0 000
= isroU _.36MP|l
O.010 0.020 0.030
Vertical relative strain. Sj
|
-i: 0.100
i
C 0.050
o.™
(1.300
£ = 9,282 MPa
0.015 0 020 (1.025 Relative verticil '.Train, r-
0.035 O.OJO
2 0.0J0 g O.OiO 0.010 0,[Kl(l
E = 5.571 MPs
0.020 0.030 0.MO
Relative venial snaii],t'.i
0 0.150
1
C
n 0.050
0.00« 0000
£ = 9.167 MPa
H
0 ODfiO 0.050
Relative vertical strain, e.
0.200 (ISO
o.m (.140 I
o (.120 | (.100
■S (.080 ■■■
■3 (.M0 &
Q (.040
(.000 0.(0(
E~ 10,352 MPa
0.060 0.010 0.100 Relative vertical strain, E:
0.120 0140
b
a
d
c
f
e
Figure 2. Deformation curves obtained by means of standard drained triaxial tests, the figure letters correspond to soil type letters.
Table 4. Estimation of elastic parameters based on triaxial tests.
Soil Oov (MPa) Y (kN/m3) Eo,st (MPa) K Eo,dyn (MPa) Vdyn G0 (MPa)
a 0.030 20.075 154.000 2.5 385.000 0.48 130.068
b 0.030 20.069 187.000 2.5 467.500 0.45 161.207
c 0.150 19.404 - - 550.915 0.46 188.669
d 0.045 17.542 - - 121.083 0.44 42.043
e 0.082 18.130 - - 217.542 0.44 75.535
f 0.077 19.306 - - 423.139 0.45 145.910
Cov is overburden pressure; y is soil unit weight; Eo,st is static elastic modulus; Kis ratio of dynamic and static elastic moduli according to (6) [26]; £o,dyn is dynamic elastic modulus; Vdyn is dynamic Poisson's ratio estimated using Appendix G of Regulations SP 23.13330.2018; Go is initial shear modulus.
Table 5. Estimation of elastic parameters based on triaxial tests data Ue from triaxial tests.
Soil a £1 E Eo,dyn Re
(MPa) (MPa) (MPa) triaxial
a 0.0884 0.0050 17.680 385.000 0.046
b 0.0268 0.0050 5.360 467.500 0.011
c 0.0439 0.0047 9.282 550.915 0.017
d 0.0279 0.0050 5.571 121.083 0.046
e 0.0550 0.0060 9.167 217.542 0.042
f 0.0557 0.0054 10.352 423.139 0.024
a is deviatoric stress; £i is axial strain, corresponding to the deviatoric stress a.
The total calculation of the deformation modulus from numerical experiments is shown in Table 6. It was assumed that the tests were performed in the borehole, so, according to State Standard GOST 20276-2012, the Kp coefficient is assumed to be 1.0. Calculation of transition factor Re values based on the results of numerical experiments is presented in Table 7. Final comparison of obtained transition coefficient Re values based on the triaxial tests and numerical experiments with the values according to proposed formulas (1) and (2) on the results of PLT and MASW is presented in Table 8 and Fig. 3.
Table 6. Calculation of deformation modulus E from numerical experiments.
Soil hpLT Pi P4 Si S4 E
v
(m) (MPa) (MPa) (cm) (cm) (MPa)
a 1.5 0.30 0.030 0.180 0.18 0.67 17.61
b 1.5 0.42 0.030 0.060 0.29 0.37 18.37
c 6.5 0.42 0.150 0.300 5.80 6.66 9.11
d 2.5 0.35 0.045 0.120 1.08 1.78 5.98
e 4.5 0.35 0.082 0.157 4.15 4.94 5.31
f 3.9 0.30 0.077 0.227 2.23 3.09 9.98
hpLT is plate depth; v is Poisson's ratio; Kp is specific-conditions-of-use factor; Pi and P4 are first and fourth points of load-
settlement curves; Si and S4 are settlements at Pi and P4 respectively; E is deformation modulus.
Table 7. Evaluation of transition factor Ue from numerical tests.
Soil Go vdyn Eo,dyn E Re
(MPa) (MPa) (MPa) numerical
a 140.000 0.48 414.400 17.606 0.042
b 170.000 0.45 493.000 18.371 0.037
c 66.400 0.46 193.888 9.111 0.047
d 33.000 0.44 95.040 5.985 0.063
e 36.300 0.44 104.544 5.305 0.051
f 77.000 0.45 223.300 9.985 0.045
Table 8. Overall comparison of different values of transition factor Ue.
Deviation of the Deviation of the
Re Re triaxial Re numerical
Soil PLT triaxial Re from the PLT one numerical Re from the PLT one
(%) (%)
a 0.050 0.046 -8.5 0.042 -15.3
b 0.051 0.011 -77.6 0.037 -27.3
c 0.056 0.017 -69.7 0.047 -15.6
d 0.091 0.046 -49.3 0.063 -30.7
e 0.075 0.042 -43.8 0.051 -32.4
f 0.057 0.024 -57.1 0.045 -21.6
0.100
0.090
0.080
0.070
o 0.060
sa
ö 0.050
o
1 0.040
£
0.03 0
0.020
0.010
0.000
•
A A A X
X
A '--• _
A A
• PL T correlation
* Numerical modelling
A Triaxial tests ....... Exponential (FLT)
— - — Exponential
(numerical)
— ■ —Exponential
(triaxial)
17.000 17 500 18 000 18.500 19.000 19 500 20 000 20.500 Unit weight kN/m3
Figure 3. Overall comparison of different values of transition factor Re.
The comparison of different values of the transition factor confirms its dependence on the soil unit weight.
The lowest values of the transition factor Re (and, accordingly, the deformation modulus E) were obtained for the triaxial tests, and the highest values were obtained for formula (10) on the basis of the dependencies derived from in-situ tests with PLT and MASW. The deviation of the triaxial test results from the in-situ dependencies does not exceed 78 %.
The results of numerical simulation do not exceed the calculated in-situ dependencies, and the deviation of numerical values from the calculated in-situ ones does not exceed 33 % to the lesser side.
A comparison with the results of experiments performed by other researchers is not given in the article because the transition factor between the elastic modulus and the deformation modulus are determined by the results of MASW for the first time.
4. Conclusions
1. Standard drained triaxial tests allow evaluating dynamic and static modulus of elasticity during a single experiment.
2. The triaxial tests on cohesive and non-cohesive soil samples confirm the dependence of the transition factor on the soil unit weight.
3. The deviation of triaxial test results from in-situ dependencies is not more than 78 %.
4. The comparison of the transition factor Re from the dynamic modulus of elasticity to the deformation modulus based on the results of in-situ tests and numerical experiments showed that the deviation of the numerical experiments results is not more than 33 % to the lesser side. Values of the transition factor Re by the results of numerical experiments are less than values of this factor by the results of in-situ tests. This indicates sufficient accuracy of the proposed dependencies (1) and (2) for express assessment of the soil deformation modulus based on the wave analysis by MASW at a preliminary geotechnical site assessment.
5. Correctness of numerical modeling depends on the adequacy of adopted soil model, which requires calibration of input parameters and, accordingly, of the model deformation curve on the experimental deformation curve based on standard triaxial tests.
5. Acknowledgements
The authors thank the research support services of Perm National Research Polytechnic University for providing the equipment for field and laboratory testing. This research did not receive any specific grant funding from agencies in the public, commercial, or not-for-profit sectors.
R.D., Xia, J. Multichannel analysis of surface waves. Geophysics. 1999. 64(3). Pp. 800-808. DOI:
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Contacts:
Vadim Antipov, seekerva@mail.ru Vadim Ofrikhter, ofrikhter@mail.ru
© Antipov, V.V.,Ofrikhter, V.G., 2020
