# Analysis of the Stressed State of Sand-Soil Using Ultrasound

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## Abstract

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## 1. Introduction

## 2. Laboratory Measurements

^{3}and the friction angle 32°. The material was considered in the dry state.

## 3. Analysis and Interpretation

#### 3.1. Local Pressure

_{1}= 0.2 m) the horizontal tensions acted as inversely proportional to the test load. This effect can be highlighted by calculating the mean vertical and horizontal tensions and plotting them over the test load, like in Figure 8. Figure 9 visualizes the tension distribution in 3D, which helps understand local dynamic variations of tension. On the bottom, the highest tension was measured in the vertical direction in the center. At this position, the highest values without loading appeared, but the increase due to the load was the smallest among the vertical tensions. At the front and the rear position on the bottom, the vertical and the horizontal tensions remained low. On the first level, the opposite situation arose. The highest tensions were measured on the rear and the front.

- The energy from the stamp was converted into a vertical, elastically movement of sand soil, as shown in Figure 11.
- On the sidewalls, the movement energy was mainly consumed by friction with the wooden walls since high vertical dynamic in combination with pronounced horizontal tensions appeared in these spots. In the center, the movement energy caused a high material pressure which can be concluded from the reduction of the dynamic and the rising static share in tension from top to bottom.
- The distribution of tension was inhomogeneous.

#### 3.2. P-Wave Propagation Velocity

## 4. Discussion

## 5. Conclusions

- Internal pressure in the land layer influences the pressure wave propagation velocity. Increase of the pressure from 2 to 23 kPa at the bottom of the box results in an increase in the vertical wave velocity from 180 to 360 m/s. The relation between ballast pressure and wave propagation velocity is nonlinear.
- The vertical stress distribution over the ballast box is subjected to high local inhomogeneity with up to two times the stress concentration in the central part of the box bottom.
- The residual pressure appears at the bottom of the ballast box and accumulates after the loading cycles. The residual stresses amount to up to 60% of the maximal ones.
- The residual pressure has an influence on the wave propagation velocity.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Schema of the ultrasound measuring system, (

**b**) Drawing of the test box with ultrasonic transmitter and receivers.

**Figure 2.**(

**a**) Receiving unit with LCARD E-502 system, (

**b**) Transmitting unit with microcontroller and booster unit.

**Figure 3.**(

**a**) Pressure measurement cell, (

**b**) 3D model of the test box with sensor locations, (

**c**) QuantumX DAQ system.

**Figure 4.**(

**a**) Measuring station at the ZWICK HB 160 testing machine, (

**b**) Interior view of the test box.

**Figure 9.**3D presentation of the pressure in the sand for all loading levels (red: vertical, blue: horizontal, black dots: center points of the spheres).

**Figure 10.**Two dimensional representation of the stresses in sand during the first load cycle: (

**a**) vertical stresses, (

**b**) horizontal stresses.

**Figure 12.**Distribution of residual pressure in the sand for the zero load steps of the test program.

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**MDPI and ACS Style**

Schumacher, L.B.; Sysyn, M.; Gerber, U.; Fischer, S.
Analysis of the Stressed State of Sand-Soil Using Ultrasound. *Infrastructures* **2023**, *8*, 4.
https://doi.org/10.3390/infrastructures8010004

**AMA Style**

Schumacher LB, Sysyn M, Gerber U, Fischer S.
Analysis of the Stressed State of Sand-Soil Using Ultrasound. *Infrastructures*. 2023; 8(1):4.
https://doi.org/10.3390/infrastructures8010004

**Chicago/Turabian Style**

Schumacher, Lukas Benedikt, Mykola Sysyn, Ulf Gerber, and Szabolcs Fischer.
2023. "Analysis of the Stressed State of Sand-Soil Using Ultrasound" *Infrastructures* 8, no. 1: 4.
https://doi.org/10.3390/infrastructures8010004