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 that improve the mechanical properties of soils. In addition, the small-strain stiffness is an important parameter for various geotechnical design applications. Therefore, I aim from this research to study the availability of Free–Free Resonant frequency method (FFR) in measuring the Young’s modulus and Poisson ratio for epoxy treated sand (ETS). Moreover, detecting the effect of the additives on the strength of treated sand by applying compression test on both types of treated specimens: cement treated sand (CTS) and (ETS), and then comparing between the results.
Next, the results have been analyzed and then Young modulus and Poisson ratio have been calculated. There was reversal relations between the both parameters according to the additives percentages, where E increased, Poisson ratio decreased. Then, the compression tests were applied on cylindrical specimens, the more additive percentages was the higher maximum load. The treated sand with epoxy percentage from 2% up to 5% was stronger than the treated sand with 50% cement.
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.
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% [
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).
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 [
The components of the specimens in this research was sand, epoxy and cement. The specific gravity of sand was equal (G_{S}= 2.6399) and grain size distribution was analyzed as shown in Fig.
Grain Size Distribution of Sand
Properties of epoxy
Property | Component A | Component B | Component A+B (A:B is 2:1) |
---|---|---|---|
11.7kN/m^{3} | 10kN/m^{3} | 11.4 kN/m^{3} | |
ca. 600 mPa.s (milli Pascal. second) | ca. 400 mPa.s (milli Pascal. second) | ca. 550 mPa.s (milli Pascal. second) | |
100 MPa | |||
Max 50 °C | |||
300 MPa | |||
95 |
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.
The cylindrical specimens a) sand mixed with each of 10%, 20%, 30% of cement b) sand mixed with 50% of cement
The prism specimen (sand + epoxy) a) in the wooden mold b) after extrusion
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
Dimensions of specimens
Specimen No. | 1(small) | 2(medium) | 3(large) |
---|---|---|---|
Cylindrical | |||
Height of specimen (L) mm | 70 | 86 | 105 |
Diameter of specimen(D)mm | 42 | 42 | 42 |
Aspect ratio D/L | 0.6 | 0.488 | 0.4 |
Prism | 1 | 2 | |
Length of Specimen mm | 150.27 | 150.71 | |
Width of specimen mm | 101.39 | 113.12 | |
Thickness of specimen mm | 11.82 | 12.01 |
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.
c) cylindrical specimen connected to software d) flexural frequency for prism specimen with 3% epoxy
According to ASTM E1875 [
After measuring the frequencies for all specimens, the equations
Where:
Poisson ratio for cylindrical treated specimens
Additive’s Percentage | Aspect Ratio of Cylindrical Specimens | Poisson Ratio (proposal) | Poisson Ratio (calculated) |
---|---|---|---|
1% | 0.6 | 0.3 | 0.301343101 |
0.48 | 0.29 | 0.292045291 | |
0.4 | 0.29 | 0.291639096 | |
2% | 0.6 | 0.26 | 0.259105869 |
0.48 | 0.24 | 0.241980416 | |
0.4 | 0.24 | 0.241586634 | |
3% | 0.6 | 0.22 | 0.221253169 |
0.48 | 0.2 | 0.20559029 | |
0.4 | 0.18 | 0.181458296 | |
4% | 0.6 | 0.165 | 0.162515082 |
0.48 | 0.16 | 0.162010583 | |
0.4 | 0.17 | 0.170111179 | |
5% | 0.6 | 0.15 | 0.150715709 |
0.48 | 0.14 | 0.142043808 | |
0.4 | 0.14 | 0.140292754 |
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.
Young Modulus (E) vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%
Figure 5: Young Modulus (E) vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%
Fig.
Young Modulus (E) vs the additives percentage for all sizes of cylindrical specimens
Fig.
Poisson ratio vs the aspect ratio for treated cylindrical specimens with additives from 1% up to 5%
However, Fig.
Poisson ratio vs the additives percentage for all sizes of cylindrical specimens
For more clarification, Fig.
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
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 [
Upon analyzing the results, the maximum load values of ETS specimens versus the additives percentages are presented in Fig.
Strength (MPa) of cylindrical specimens versus the additives’ percentage
Maximum load (N) vs the aspect ratio for treated specimens with additives from 1% up to 5%
Strength (MPa) of cylindrical specimens vs the aspect ratio
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 [