А assessing the Distribution of Statistical Heterogeneity of the soil deformation modulus based on static soil sensing

. Cone penetration testing (CPT) has become one of the most commonly adopted in situ tests for site investigations, due to its reliability and repeatability of the measurements and the potential for direct use in design. CPT data we performed to a depth 5m in sandy soils within an area of 50x50m² of 232 datasets, the significant of cone resistance force were analysis used statistical methods. The heterogeneity of soil deformation modulus was vertical and horizontally in three-dimensional plane analyzed. Data was shows vertically heterogeneity soil deformation but horizontally not heterogeneity.


Introduction
A Building rests on a foundation designed to transfer structural loads and other payloads to the foundation soils.The base, perceiving these loads, experiences predominantly uneven deformations, which causes the appearance of additional displacements and forces in the structures.Improper preparation of foundations and erection of foundations can lead to the fact that the structure no longer meets the operational requirements [7].
With the gradual construction of a structure, an increase in load causes a gradual increase in the subsidence of the foundation.To determine the deformation characteristics of soils, static sounding data are used.For most industrial and civil structures, it provides accurate predictive settlement values.
In order to move on to more aggregated forecasts of foundation settlement, it is necessary to know how soil characteristics change.To do this, tests are carried out with a large number of sounding points and with a smaller step, thus it is possible to simulate changes in the heel or settlement of foundations depending on a random process, just a random spread of soil characteristics, for example, the modulus of deformation [6].
Due to the design of the structure, even if the strength of the soil is ensuring the deformations of the base occur.Usually they are uneven in nature and cause a redistribution of efforts in the structures of the Structure.Under certain conditions, this can make the structure work normally, and in some cases even lead to its failure [3].
Of interest in this work is the study of the factor of statistical heterogeneity of soil properties, namely, the modulus of soil deformation in x, y, and z planes.This question is very important when considering the settlement of foundations.The fact is that when calculating the characteristics of the soil, they are distinguished very discretely.
Namely, the measurements will be at five points at 100-200 meters.In addition, due to averaging, some averaging of these characteristics also occurs, these characteristics become the same.In order to move on to more accurate basement predictions, it is necessary to know how soil characteristics change.To do this, the test is carried out at a larger number of points with a smaller step, thus it is possible to model the change in the heel or settlement of the foundations depending on the random spread of soil characteristics, for example, the deformation modulus.In this paper, we will develop a method for estimating the distribution of statistical inhomogeneity of the soil deformation modulus in depth based on static sounding data by methods of correlation and spectral analysis using the Mat lab software and computing system.
For less cohesive soils, it is possible to obtain correlations with some geotechnical parameters and field tests and use the results in a quantitative assessment for foundation design, if the friction along the bars is negligible or properly corrected.
Cone penetration or cone penetrometer (CPT) is a technique used to determine the geotechnical properties of soils and delineate soil stratigraphy.It was originally developed in the 1950s at the Dutch Soil Mechanics Laboratory in Delft to study soft soils.Based on this story, it was also called "Dutch carob dough".Today, CPT is one of the most commonly used and recognized soil testing methods worldwide [1].

Theoretical part 2.1 Static sound
CPT is currently one of the main methods for studying soil conditions.Methods for determining the modulus of deformation of unbounded pavement materials vary considerably.The static response of a sensor refers to the ratio between the output and input of a sensor relative to a static input.Since the input and output are independent of time, the relationship between them is that the static response of the sensor is an algebraic equation without time variables, with the input is used as the abscissa and the corresponding output is used as the plotted characteristic curve along the Y-axis.Described which simply means the relationship between the output and input of the system when the input of the detection system is a constant signal that does not change with time.

Cone penetration test (cpt)
In a cone penetration test, a cone penetrometer connected to the end of a row of rods is hydraulically pressed into the ground at a constant speed (2 cm/s) and continuous cone penetrometer resistance measurements are recorded.The reference tester consists of a cone with 60 °an apex angle and a diameter of 35.7 mm ( mc 2 cross-sectional area 10) and 150mc 2 .
The friction sleeve is located above the cone.Resistance values are measured as the combined penetration resistance of the cone as tip resistance ( q c ) and friction bushing resistance as friction resistance (fs).Connecting additional sensors to the CPT system to measure water pore pressure, verticality, shear wave velocity, etc. can also provide relevant data in addition to tip resistance and friction.Both the cone and the sleeve must be made of steel of the type and hardness to resist wear due to abrasion.The cone must have and supported in use with a roughness μ ≤ 1 µm and the friction bushing must have a roughness of 0.5 µm ± 50%.
Coefficient of Friction: As mentioned above, the coefficient of friction FR often used in conjunction with q c in empirically derived charts to aid in soil classification.The coefficient of friction defined as the ratio between f s and q c and usually expressed as a percentage: In static sounding, the most commonly measured: The specific resistance of the soil under the cone, (MPa or KPa) in the form of the resistance force of this soil to the penetration of the cone into it, referred to the area of the base of the cone.
Ground resistance on the side surface of the probe, (KN), which is the soil resistance on the side surface of the entire buried part of the rod [2].
Static sounding determines indicators: Separation of a geological section and selection of an engineering-geological element (basic soil complex): Physical characteristics of soils, Deformation properties of soils, Strength properties of soils.
Soil resistance of pile foundations and Possibilities of driving piles into soils and bearing capacity of piles.For sandy soils, there is a linear dependence of the soil deformation modulus and the resistance of the probe cone, namely: Where E 0 the modulus of soil deformation is, q c is the resistance of the probe cone.

Objectives
In this paper, we assessing a method for estimating the distribution of statistical heterogeneity of the soil deformation modulus based on static sounding of soils, the influence of spatial variability of soil parameters on geotechnical and structural estimates of reference CPT data.Soil sounding taking into account several modes of destruction.For most industrial and civil structures, it allows you to get accurate values of the predicted settlement.

Literature review
Important fields of use in geotechnical engineering were the correlations between the cone tip resistance and other soil mechanical properties.These correlations mainly based on regression analysis of CPT and laboratory or in-situ tests, and include an uncertainty, which expressed by the coefficient of determination R 2 of the regression.If used with proper caution (verifying the similar geological conditions and soil types of the site in question and of the ones used for setting up the correlations), as in-situ measurements, they can support and improve the selection of representative values in a geotechnical model [10].

Development of the methodology 4.1 Research data
In this work, the data of statistical sounding of the area were investigated.
Entrance: The work based on the resistance data of the probe cone under the lower end of the penetrometer cone at a depth of 5000 mm in the plane every 5 mm.
Output: Descriptive statistics of soil deformation modulus by Correlation function of soil deformation modulus in plan, Correlation radius of soil deformation modulus in plane, Spectral density of soil deformation modulus in plane.
The essence of the problem is to use the methods of mathematical statistics to assess the inhomogeneity of the modulus of soil deformation in plan according to statistical sounding data.Before starting evaluation and simulation, it is necessary to convert the original probe cone resistance data into deformation modulus data, check the data for homogeneity, and determine the amount of correlation between the values.Based on these data, an appropriate spectrum selected for modeling statistical inhomogeneity.

Equal Means Hypothesis Test
Checking the homogeneity of two samples was carried according to Student's criterion (or t-criterion).Consider the statement of the problem of checking the homogeneity of samples.It is necessary to test the hypothesis that the total means of the two samples are equal.Using the data analysis package built into Excel, we will find the basic data of descriptive statistics.Fig. 3. Descriptive statistics of data on the modulus of deformation along the "y" axis.
Using the "Data Analysis" package built into Excel, we will use the analysis of variance method (ANOVA, Analysis Of Variance), which analyzes the influence of the strain modulus values depending on the location of the test along the OX and OY axes every meter.With the help of analysis of variance, you can test the hypothesis that the mean values of the samples are equal.Therefore, we conclude that the value of the t-statistic is greater than the p-critical value, which implies that we accept the hypothesis of equality of means, i.e., the means do not depend on points along the y-axis.
To verify the absolute homogeneity of the data, we will test the hypothesis about the equality of the averages along the x-axis.
Conclusion: The data is homogeneous, since the hypothesis about the equality of the average values along the two axes X and Y, that is, in the plan, we will model a stationary process.Fig. 5. Model of linear regression of the modulus of deformation of a horizontal line in plan.

Determination of the modulus of deformation by resistivity
Since the task is to estimate the distribution of the statistical inhomogeneity of the soil deformation modulus, and initially there are only on the resistance of the probe cone, we will find the soil deformation modulus.
A table of the dependence of the modulus of deformation on the resistivity of sands (soil), adopted in the Russian regulatory document SP 11-105-97, is given.

Conclusions
Establishment of correlations: An important element of statistical analysis is the grouping of soils according to the nature of the relationship between the target parameter and the CPT parameters.At this stage, group elements are selected, which are measured or calculated in GST (ground sounding data), whose values best highlight groups of soils with similar behavior of correlations and soil deformation occurs only in the direction of load application.
The data on the resistance of the probe cone q c relative to the depth of immersion, it is possible to obtain the dependences of the change in the deformation modulus with depth, taking into account random processes based on the methods of correlation and spectral analysis using the Mat lab software and computer complex.
According to my result, the deformation modulus of the horizontal plane of the soil strongly correlated, while the vertical one is weakly correlated, which implies that the fields are uneven with depth, it shows uniformity in the plane.
The simulated models of random processes are statistically identical (because they have the same distribution and spectral density) to the initial dependences of the soil deformation modulus on the depth of penetration of the probe into the soil, which confirms the correctness of the simulation.To expand the model, it is necessary significantly increase the number of processing of sounding points.

Fig. 4 .E3S
Fig. 4. Descriptive statistics of data on the modulus of deformation along the "x" axis.

E3S 5 . 4 .Fig. 6 .
Fig. 6.The surface of the modulus of deformation in the area of 50 by 50 mm in increments of 0.08 with the results of testing values.