STIFFNESS MODULE AND COMPRESSION STRENGTH OF POLYMER-TREATED SAND

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Silesian University of Technology

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VOLUME 11 , ISSUE 1 (March 2018) > List of articles

STIFFNESS MODULE AND COMPRESSION STRENGTH OF POLYMER-TREATED SAND

Maiasa MLHEM *

Citation Information : Architecture, Civil Engineering, Environment. Volume 11, Issue 1, Pages 97-104, DOI: https://doi.org/10.21307/ACEE-2018-010

License : (CC-BY-NC-ND 4.0)

Received Date : 15-June-2017 / Accepted: 19-February-2018 / Published Online: 01-April-2019

ARTICLE

ABSTRACT

Streszczenie

Zgodnie z rosnącym zapotrzebowaniem na przygotowanie odpowiednich gruntów pod różne typy fundamentów w projektach geotechnicznych, wielu badaczy próbuje znaleźć najlepszy rodzaj dodatków, które poprawiają właściwości mechaniczne gruntów. Ponadto zmienność sztywności w zakresie małych odkształceń jest ważnym aspektem dla różnych zastosowań w projektowaniu geotechnicznym. Stąd, celem wykonanych badań jest ocena przydatności metody FFR (Free-Free Resonant frequency) do pomiaru modułu Younga i współczynnika Poissona dla piasku poddanego obróbce epoksydowej (ETS). Dodatkowym celem badań jest ocena wpływu dodatków na wytrzymałość poddanego obróbce piasku w próbie ściskania na obu rodzajach poddanych obróbce próbek: piasku stabilizowanego cementem (CTS) i (ETS), a następnie porównanie wyników.

Po przeprowadzaniu analizy wyników badań, wyznaczono moduł Younga i współczynnik Poissona. Między obydwoma parametrami występowały relacje odwrotne w zależności od procentów dodatków, tzn. przy wzroście modułu E, współczynnik Poissona zmniejszał się. Następnie poddano ściskaniu próbki cylindryczne; przy większej zawartości dodatków, uzyskiwano większe nośności. Modyfikowany piasek z zawartością epoksydu od 2% do 5% okazał się być mocniejszy od piasku z dodatkiem 50% cementu.

1. INTRODUCTION

According to the increasing demand of suitable soils under different types of foundation in the geotechnical engineering projects, many researchers try to find the best type of additives to enhance the strength of soils and to improve its mechanical properties. It is a big challenge to define the stress–strain behavior of the soil because it is complex and nonlinear. Young’s modulus (E) and the shear modulus (G) of the soil are not constant; it may significantly change with the strain level.

Moreover, the small-strain stiffness is an important parameter for various geotechnical design applications, including small-strain dynamic analysis such as those used to predict the soil behavior or soil–structure interaction during earthquakes, explosions, machine vibrations or traffic vibrations. Small-strain stiffness may also be used as an indirect indication of other soil parameters, as it (in many cases) correlates well to other soil properties. For example, when studying the hardening process of polymer treated soil, an increase in stiffness and compressive strength can be expected with increasing inter-particle cementation. At small strains, the stiffness is relatively high, while at strains close to the failure the stiffness is low. However, the behavior was sufficiently constant and linear below an approximate strain level of 0.001% [1].

The objective of this research is to study the availability of Free–Free Resonant frequency method (FFR) in measuring the Young’s modulus and Poisson ratio for (ETS). Moreover, detecting the effect of additives on the strength of treated sand by applying compression test on both types of treated specimens: (CTS) and (ETS).

2. METHODS FOR MEASURING SMALL-STRAIN STIFFNESS

The small-strain stiffness is usually determined in the laboratories by direct methods such as the bender/extender elements, or by indirect methods, such as the resonant column test. The free–free resonant frequency method (FFR) is a simplified testing procedure (based on the resonant column-testing concept) that has recently been used for the characterization of cement-treated soils [2, 3, 4, 5, 6, 7]. FFR testing was applied by allowing a cylindrical specimen to vibrate at its fundamental frequency and then, the stiffness was evaluated from the measured fundamental frequency, density and length of the specimen through a straightforward formula based on theories of one-dimensional wave propagation in an elastic rod. However, the interpretation of stiffness from the FFR results might be affected by the uncertainties that related to the boundary conditions (uncertainties of which the laboratory is not perfectly free) or to the diameter-to-length ratio (aspect ratio) of the specimen [4, 6] and to the nature of material whether it is isotropic or not.

3. MATERIALS

The components of the specimens in this research was sand, epoxy and cement. The specific gravity of sand was equal (GS= 2.6399) and grain size distribution was analyzed as shown in Fig. 1 according to ISO/DIS 17892-3. One type of epoxy was used, but it consists of two components A&B and the table 1 summarize the available properties for that type of Epoxy. In addition, a blast-furnace slag cement was used consisting of approximately 70% ground granulated blast furnace slag, 26% portland clinker and 4% gypsum and its minimal normalized mortar strength at 28 days was 42.5 N/mm2 [8].

Figure 1.

Grain Size Distribution of Sand

10.21307_ACEE-2018-010-f001.jpg
Table 1.

Properties of epoxy

10.21307_ACEE-2018-010-tbl1.jpg

4. SPECIMEN PREPARATION

15 cylindrical specimens were prepared and divided according to the epoxy additives percentage from 1% up to 5% with 1% step into five groups as shown in Fig. 2. Each group contains 3 specimens. In addition, nine cylindrical specimens have been prepared and divided into 3 groups according to the cement additive percentage 10%, 20%, 30% (Fig. 2a). Each group contains three specimens. Unfortunately, upon extrusion, the cemented specimens has failed. Therefore, another group of three specimens was reprepared containing 50% of cement + 50% of sand (Fig. 2b). Lastly, two groups of prism specimens were prepared (in order to apply the tests as explained in ASTM standards for the both shapes of specimens) more than shape of material, each group contains 2 specimens, at two epoxy additives percentages 3% and 4%, as shown in Fig. 3, just for comparison.

Figure 2.

The cylindrical specimens a) sand mixed with each of 10%, 20%, 30% of cement b) sand mixed with 50% of cement

10.21307_ACEE-2018-010-f002.jpg
Figure 3.

The prism specimen (sand + epoxy) a) in the wooden mold b) after extrusion

10.21307_ACEE-2018-010-f003.jpg

The process of preparing the specimens was as follows: the sand and the additives were mixed dry in a dough mixer for about 5 minutes until reaching a homogeneous paste form. The consistency of the paste after mixing remained plastic. Following, the mixture was poured into steel cylindrical molds of different aspect ratios and into wood molds for prism specimens. Then, the cylindrical molds were vibrated lightly in order to remove any trapped air bubbles. Then, the cylindrical specimens were cured for maximum one week, in a conditioned room at about 20°C, and for two weeks for the prism specimens (during this period, no FFR testing could be done on the specimens). Following the period of curing, the specimens were strong enough to be extruded from the molds and table 2 displays the final dimensions of the specimens after extrusion. Next, the FFR testing has been applied on cylindrical specimens and prism specimens, however, the compression test was applied on the cylindrical specimens only.

Table 2.

Dimensions of specimens

10.21307_ACEE-2018-010-tbl2.jpg

5. PRACTICAL TESTS

5.1. Free–Free Resonant Frequency Method

The free–free resonant frequency (FFR) method is an attractive alternative (due to its simplicity) for measuring the small-strain Young’s modulus and Shear modulus of (unconfined) cemented or cohesive soil in the laboratory. However, it was not applied on polymer treated soil, which maybe add some complexity to the interpretation.

Fig. 4 illustrates the FFR testing set-up used in this study. Here, the cylindrical soil specimen is laid horizontally on top of 30-mm-thick soft polyurethane foam to approach fully free boundary conditions. The selected foam in this research has a unit weight of 21 kN/m3 and an approximate Young’s modulus of E=20kPa.

Figure 4.

c) cylindrical specimen connected to software d) flexural frequency for prism specimen with 3% epoxy

10.21307_ACEE-2018-010-f004.jpg

According to ASTM E1875 [9], the FFR test was applied on cylindrical and prism specimens. A small hammer is used to excite the specimens. The hammer should have most of its mass concentrated at the point of impact and should have enough mass to induce a measurable mechanical vibration, but not so much as to displace or damage the specimen. The used hammer in this research consists of a high-purity soda-lime glass bead, about 4 mm in diameter, glued (with Loctite Super Glue) to one end of a flexible 100-mm-long and 3.5-mm-wide nylon strip (ordinary cable tie). The vibratory response of the specimen was captured with a compact-size accelerometer type PCB A353B68 with a frequency range up to 10 kHz, which was sufficient for the measured frequencies of the tested specimens in this research. The accelerometer was put in contact with a specimen at its anti-nodes (points of maximum deformation amplitude) with the help of a laboratory stand provided with a hinged add-on rod that allowed for rotation so that the accelerometer could be aligned axially or transversally with respect to the soil specimen. Fig.4c shows the method and tools for measuring the frequency for cylindrical specimen and Fig. 4d shows measuring the frequencies for prism specimens.

5.2. FFR test results

After measuring the frequencies for all specimens, the equations 1 and 2 were used in order to calculate Young module (E), Shear module (G) and then Poisson ratio for these specimens [10] [11] [12]:

(1)
Vs=2Lft,G=ρ(Vs)210.21307_ACEE-2018-010-eqn1.jpg
(2)
Vl=2Lfl,E=ρ(VL)2,v=(E2G)110.21307_ACEE-2018-010-eqn2.jpg

Where: E (Pascal), G (Pascal), L length of specimen (mm), ρ the density of specimen (g/mm3), fl the fundamental longitudinal frequency (Hz), ft the fundamental transverse frequency (Hz). The exact Poisson ratio for the specimens was not known, in this research, so many trials were done until reaching to the matching Poisson ratio according the above equations as illustrated in Table 3.

Table 3.

Poisson ratio for cylindrical treated specimens

10.21307_ACEE-2018-010-tbl3.jpg

Upon analyzing the results and after calculating E, G values and Poisson ratios for all specimens, the prism specimens do not give reasonable values so, I kept it away from this research and I concentrated on discussing the values of E and Poisson ratio for cylindrical specimens only.

Fig. 5 shows a reversal relation between the aspect ratio and (E) values at all percentages of additives. Where the smallest sample has the lowest value of (E), the biggest sample has the highest value of E.

Figure 5.

Young Modulus (E) vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%

10.21307_ACEE-2018-010-f005.jpg

Figure 5: Young Modulus (E) vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%

Fig. 6 illustrates the direct relation between (E) and additives’ percentages. (E) increases slightly from 1% up to 4% and then it increases sharply after the 4% percentage for all sizes of specimens especially for the smallest size.

Figure 6.

Young Modulus (E) vs the additives percentage for all sizes of cylindrical specimens

10.21307_ACEE-2018-010-f006.jpg

Fig. 7 presents the Poisson ratio versus the aspect ratio of cylindrical specimens. There is no evident relation between the both parameters; and it occurs a slight changing of the values for different aspect ratios at most of additives percentages.

Figure 7.

Poisson ratio vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%

10.21307_ACEE-2018-010-f007.jpg

However, Fig. 8 clarify that there is reversal relation between additives percentage and Poisson ratio, for all sizes of specimens. This is logic, it is noted that as much additives percentage in the composition of the specimens increases as much the strength of the specimens increases and its deformation upon applying compression load decrease, which cause consequently a decrease of Poisson ratio.

Figure 8.

Poisson ratio vs the additives percentage for all sizes of cylindrical specimens

10.21307_ACEE-2018-010-f008.jpg

For more clarification, Fig. 9 shows the different trends of (E) and Poisson ratio. Whenever (E) increases, Poisson decreases, and this is repeated at all aspect ratio values.

Figure 9.

Young modulus (E) & Poisson ratio vs the additives percentage for cylindrical specimens a) aspect ratio 0.4, b) aspect ratio 0.48, c) aspect ratio 0.6

10.21307_ACEE-2018-010-f009.jpg

5.3. Compressive Strength Test

Increasing the strength for any type of material is very important issue for all engineers. Therefore, the compression strength test was applied on the both treated specimens: w/epoxy and w/cement in order to define the effect of epoxy comparing with the effect of cement in changing the strength of sand. The compression test was according to the ASTM C 39 [13] by hydraulic press.

Upon analyzing the results, the maximum load values of ETS specimens versus the additives percentages are presented in Fig. 10. Apparently, the more additives percentages the higher strength. Moreover, fig.11 illustrates the relation between the maximum load values and the aspect ratios (D/L) which is somehow steady when D/L < 0.5, but it changes after that i.e. the less aspect ratio the higher maximum load. Fig. 12 shows the remarkable difference between the effect of the cement and the effect of the epoxy on the strength of the specimens. It is clear that there is a sharp increase of compression strength after 2% epoxy additives which exceeds the strength of specimens with 50% cement additives, e.g. the strength of specimens (at 5% epoxy) exceed 4 times the strength of specimen at 50% cement additives.

Figure 10.

Strength (MPa) of cylindrical specimens versus the additives’ percentage

10.21307_ACEE-2018-010-f010.jpg
Figure 11.

Maximum load (N) vs the aspect ratio for treated specimens with additives from 1% up to 5%

10.21307_ACEE-2018-010-f011.jpg
Figure 12.

Strength (MPa) of cylindrical specimens vs the aspect ratio

10.21307_ACEE-2018-010-f012.jpg

6. CONCLUSION

The objective of this research was firstly, to validate the free–free resonant frequency method and its interpretation to determine the small-strain stiffness moduli of polymer-treated soil. Secondly, to check the effect of epoxy additives on the strength of sand and comparing with the effect of cement on the same type of sand. The reliability of the measured fundamental frequencies obtained from the FFR testing were evaluated through calculating Young modules and Poisson ratio. According to previous studies [14] [15] [16] Young modulus (E) for sand is ranging (10–30) MPa but, upon adding the epoxy to the sand, its (E) modulus increased. For instance, E for the smallest specimens (highest aspect ratio) increased from 45 MPa up to 104 MPa at 1%, 5% respectively. This is a positive indication about the effect of the epoxy on the sand. E modulus increase when aspect ratio decreases i.e. the length of specimen increases. For our specimens, we keep the same diameter for all specimens but change the length so, the value of stress is still the same whereas the strain value changes. According to Hook law, the smallest specimens (highest aspect ratio) show the lowest value of Young modulus. Furthermore, Poisson ratio decreased as much as additives percentages increased, for example, it dropped from 0.3 to 0.15 at 1%, 5% respectively for aspect ratio 0.6, and this is logic trend between Young (E) and Poisson. At compression test on both types of treated soils: epoxy treated specimens and cemented treated one, the maximum load boomed! The maximum load, that specimen could bear, increased from 490 N up to 13300 N at 1%, 5% respectively. The maximum load of ETS at 3% epoxy additives (6670N) is a twice of the strength of the CTS at 50% cement additives (3264N). In addition, the smaller the sample, the greater its strength was observed. Finally, the above results have encouraged me to complete in researching and looking for another type of polymer additives and trying new scenario on cylindrical and prism specimens. It is recommended to use another tests method because we have used only FFR method in this research.

References


  1. Clayton, C.R.I., (2011). Stiffness at small strain: research and practice. Géotechnique 61(1), 5–37.
    [CROSSREF]
  2. Nazarian, S., Yuan, D., Tandon, V., Arellano, M., (2005). Quality management of flexible pavement layers by seismic methods, Research Report 0-1735-3, The Center for Transportation Infrastructure Systems, The University of Texas at El Paso, El Paso, Texas.
  3. Rydén, N., (2009). Determining the asphalt mastercurve from free–free resonant testing on cylindrical samples. In: Proceedings of the 7th International Symposium on Non-Destructive Testing in Civil Engineering (NDTCE09). Nantes, France.
  4. Åhnberg, H., Holmen, M., (2011). Assessment of stabilized soil strength with geophysical methods. Ground Improv. 164(3), 109–116.
    [CROSSREF]
  5. Toohey, N.M., Mooney, M.A., (2012). Seismic modulus growth of lime stabilized soil during curing. Géotechnique 62(2), 161–170.
    [CROSSREF]
  6. Schaeffer, K., Bearce, R., Wang, J., (2013). Dynamic modulus and damping ratio measurements from free–free resonance and fixed-free resonant column procedures. J. Geotech. Geoenviron. Eng. 139, 2145–2155.
    [CROSSREF]
  7. Guimond-Barrett, A., Nauleau, E., Le Kouby, A., Pantet, A., Reiffsteck, P., (2013). Free–free resonance testing of in situ deep mixed soils. Geotechn. Test. J. 36(2), 283–291.
  8. UCL, (2015). Civil engineering faculty, soil mechanics laboratory, Belgium.
  9. ASTM E 1875 Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance.
  10. Verástegui, R.D., Di Emidio, G., Bezuijen, A., Vanwalleghem, J., Kersemans, M., (2015). Evaluation of the free–free resonant frequency method to determine stiffness moduli of cement-treated soil, Soils and Foundations 55, 943–950.
    [CROSSREF]
  11. Wayen, E., Sam, S., (1962). Cross-Sectional Correction for Computing Young’s Modulus for Longitudinal Resonance Vibrations of Square and Cylindrical Rods, Journal of Research of the National Bureau of Standards-A. Physics and Chemistry 66A(2), March-April.
  12. Pierce, Allan D., (1989). Acoustics: An Introduction to Its Physical Principles and Applications. Acoustical Society of America, Woodbury, NY.
  13. ASTM C39 Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens.
  14. Obrzud, R. & Truty, A., (2012). The Hardening Soil Model – A Practical Guidbook Z Soil PC 100701 report, revised 31.01.
  15. Kezdi, A., (1974). Handbook of Soil Mechanics. Elsevier, Amsterdam.
  16. Prat, M., Bisch, E., Millard, A., Mestat, P., and Cabot, G., (1995). La modelisation des ouvrages (Modeling works). Hermes, Paris.
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FIGURES & TABLES

Figure 1.

Grain Size Distribution of Sand

Full Size   |   Slide (.pptx)

Figure 2.

The cylindrical specimens a) sand mixed with each of 10%, 20%, 30% of cement b) sand mixed with 50% of cement

Full Size   |   Slide (.pptx)

Figure 3.

The prism specimen (sand + epoxy) a) in the wooden mold b) after extrusion

Full Size   |   Slide (.pptx)

Figure 4.

c) cylindrical specimen connected to software d) flexural frequency for prism specimen with 3% epoxy

Full Size   |   Slide (.pptx)

Figure 5.

Young Modulus (E) vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%

Full Size   |   Slide (.pptx)

Figure 6.

Young Modulus (E) vs the additives percentage for all sizes of cylindrical specimens

Full Size   |   Slide (.pptx)

Figure 7.

Poisson ratio vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%

Full Size   |   Slide (.pptx)

Figure 8.

Poisson ratio vs the additives percentage for all sizes of cylindrical specimens

Full Size   |   Slide (.pptx)

Figure 9.

Young modulus (E) & Poisson ratio vs the additives percentage for cylindrical specimens a) aspect ratio 0.4, b) aspect ratio 0.48, c) aspect ratio 0.6

Full Size   |   Slide (.pptx)

Figure 10.

Strength (MPa) of cylindrical specimens versus the additives’ percentage

Full Size   |   Slide (.pptx)

Figure 11.

Maximum load (N) vs the aspect ratio for treated specimens with additives from 1% up to 5%

Full Size   |   Slide (.pptx)

Figure 12.

Strength (MPa) of cylindrical specimens vs the aspect ratio

Full Size   |   Slide (.pptx)

REFERENCES

  1. Clayton, C.R.I., (2011). Stiffness at small strain: research and practice. Géotechnique 61(1), 5–37.
    [CROSSREF]
  2. Nazarian, S., Yuan, D., Tandon, V., Arellano, M., (2005). Quality management of flexible pavement layers by seismic methods, Research Report 0-1735-3, The Center for Transportation Infrastructure Systems, The University of Texas at El Paso, El Paso, Texas.
  3. Rydén, N., (2009). Determining the asphalt mastercurve from free–free resonant testing on cylindrical samples. In: Proceedings of the 7th International Symposium on Non-Destructive Testing in Civil Engineering (NDTCE09). Nantes, France.
  4. Åhnberg, H., Holmen, M., (2011). Assessment of stabilized soil strength with geophysical methods. Ground Improv. 164(3), 109–116.
    [CROSSREF]
  5. Toohey, N.M., Mooney, M.A., (2012). Seismic modulus growth of lime stabilized soil during curing. Géotechnique 62(2), 161–170.
    [CROSSREF]
  6. Schaeffer, K., Bearce, R., Wang, J., (2013). Dynamic modulus and damping ratio measurements from free–free resonance and fixed-free resonant column procedures. J. Geotech. Geoenviron. Eng. 139, 2145–2155.
    [CROSSREF]
  7. Guimond-Barrett, A., Nauleau, E., Le Kouby, A., Pantet, A., Reiffsteck, P., (2013). Free–free resonance testing of in situ deep mixed soils. Geotechn. Test. J. 36(2), 283–291.
  8. UCL, (2015). Civil engineering faculty, soil mechanics laboratory, Belgium.
  9. ASTM E 1875 Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance.
  10. Verástegui, R.D., Di Emidio, G., Bezuijen, A., Vanwalleghem, J., Kersemans, M., (2015). Evaluation of the free–free resonant frequency method to determine stiffness moduli of cement-treated soil, Soils and Foundations 55, 943–950.
    [CROSSREF]
  11. Wayen, E., Sam, S., (1962). Cross-Sectional Correction for Computing Young’s Modulus for Longitudinal Resonance Vibrations of Square and Cylindrical Rods, Journal of Research of the National Bureau of Standards-A. Physics and Chemistry 66A(2), March-April.
  12. Pierce, Allan D., (1989). Acoustics: An Introduction to Its Physical Principles and Applications. Acoustical Society of America, Woodbury, NY.
  13. ASTM C39 Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens.
  14. Obrzud, R. & Truty, A., (2012). The Hardening Soil Model – A Practical Guidbook Z Soil PC 100701 report, revised 31.01.
  15. Kezdi, A., (1974). Handbook of Soil Mechanics. Elsevier, Amsterdam.
  16. Prat, M., Bisch, E., Millard, A., Mestat, P., and Cabot, G., (1995). La modelisation des ouvrages (Modeling works). Hermes, Paris.

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