# Deformation Behavior of Recycled Concrete Aggregate during Cyclic and Dynamic Loading Laboratory Tests

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−3}%. In the accommodation response, also known as “plastic shakedown”, the plastic strains also dissipate, but the steady state is observed as a closed hysteresis loop. In the ratcheting state, the soil accumulates plastic strains in each cycle. This leads to exceeding the soil’s serviceability limit and, eventually, causing its collapse.

## 2. Materials and Methods

#### 2.1. Material and Sample Preparation

_{b}, R

_{g}, X) ≤ 1% m/m), in accordance with European Union standards (EN 933-11:2009, 33).

#### 2.2. Physical Properties Analysis

^{3}mold. This procedure creates constant energy of compaction, whose level is equal to 0.59 J/cm

^{3}.

#### 2.3. The Static Tests

^{−3}compaction energy. This was done in order to prevent grain crushing and, therefore, changes in particle size distribution. Standard stress values were loaded on top of the shear box. The tests were conducted subsequently after vertical displacements reached a constant value. On top of the sample, a linear variable differential transformer (LVDT, GDS, Hampshire, UK) was installed. When the LVDT records showed no further changes in the sample height, the DSTs were performed. The experiments were terminated once the horizontal shear strains reached 9% or a visible peak and residual values in shear strength were recorded.

#### 2.4. Torsional Shear Test

#### 2.5. Static and Long-Term Cyclic Triaxial Tests

_{m}superimposed to a forward-moving pulsating sine wave with constant stress amplitude q

_{a}. The parameters of the S-N curves (S stands for stress—repetitive load and N stands for number of cycles to failure) are presented in Figure 1. Details of the applied loading are shown in Table 1. Repeated loading triaxial tests were conducted in the consolidated-undrained (CU) conditions. The frequency used during the test was 1.0 Hz. The cyclic stresses and initial confining pressure levels shown were used to define the effects of cyclic loading on soil behavior.

## 3. Results and Discussion

#### 3.1. Results of Physical Tests

^{3}. The optimal moisture content and energy of compaction were rescaled at each test stage to obtain uniform boundary conditions for the material properties.

#### 3.2. Results of Static Tests

_{U}= 6.6 and a grain size distribution similar to the RCAs studied here were previously found to be around ϕ = 39.6° and c = 0 (see [36,37]). Studies on sandy gravel subjected to triaxial compression led to the estimation of the friction angles in the range 39° < ϕ < 48° to NAs, depending on the relative density changes during the consolidation step [38].

_{max}/p’ where p’ = 1/3(σ’

_{1}+ 2σ3’) and q

_{max}= (σ’

_{1max}− σ3’)). Such a slope relates to the effective friction angle ϕ’ according to $M=(6\mathrm{sin}\varphi \prime )/(3-\mathrm{sin}\varphi \prime )$. The slope of the critical state lines in Figure 4b amount to 2.17, which corresponds to a friction angle of 53°.

#### 3.3. Results of Torsional Shear Tests

_{max}) and normalized damping ratio (D/D

_{min}) at different frequencies f are shown as a function of γ in Figure 5 and Figure 6. The results show the low dependence of G/G

_{max}and D/D

_{min}on the frequency value. The values of the low-amplitude shear modulus (G

_{max}) and damping ratio (D

_{min}) are lower than the shear modulus and damping ratio at higher frequencies (see Table 3). With increasing f, G

_{max}values rise between 9% (for f = 1 Hz) and 2% (for f = 10 Hz) with respect to the G

_{max}value for f = 0.1 Hz. The G

_{max}and D

_{min}values characterize the low dispersion of points, and that suggests that their increase is linear in f.

#### 3.4. Cyclic Triaxial Test Results

_{max}= 38.8 kPa. DST results showed a friction angle $\varphi $ = 39.5°. Maximal deviator stresses q

_{max}were calculated from:

_{0}= 45 kPa) and q = 314.6 kPa (for p’

_{0}= 90 kPa). The applied deviator stresses during cyclic loading tests were, therefore, a fraction of q

_{max}.

_{0}= 45 kPa, the maximal deviator stresses q

_{max}were equal to 38.8 kPa, 142.9 kPa and 193.61 kPa. These values correspond to 15%, 55% and 75% of q (p’

_{0}= 45 kPa), respectively. In the second loading stage, p’

_{0}= 90 kPa, the maximal deviator stress q

_{max}was equal to 28.84 kPa, 64.70 kPa and 178.79 kPa, corresponding to 10%, 20% and 57% of q (p’

_{0}= 90 kPa), respectively.

_{max}and the stress amplitude q

_{a}are greatly affected by changes in p’

_{0}.

_{0}= 45 kPa and q

_{max}= 38.8 kPa, the excess pore pressure rose slowly and stabilized after the 10th cycle. The same was observed for Test 2.1 (see Table 1 and Figure 8). During Tests 1.2 and 2.2, the pore pressure rose in two stages, as it did during Tests 1.1 and 2.1 (the former after the 10th cycle and the latter after the 100th cycle). However, after the 100th cycle, the velocity of pore pressure decreased slower in these tests. This can be caused by the existence of a threshold deviator stress, under which the pore pressure stabilizes itself. Nevertheless, indirect conclusions can be drawn from the analysis of the accumulation of plastic strains, which are presented in Figure 9.

_{a}. The first 100 cycles, which correspond to a process of compaction and grain movement, present a different pattern of plastic strain generation. A possible explanation for this fact lies in how the consolidation process was conducted. Although anisotropic consolidation, which represents a natural sedimentation environment, represents conditions found in nature, the artificial grains in RCAs may be acting differently when compared to natural aggregates.

^{5}cycles, the plastic strains during cycling vanished. In the absence of plastic strains, the excess pore pressure generation also stops. This suggests that, in undrained conditions, the development of plastic axial strain is greatly influenced by the excess pore water pressure. The strain stress plots show that axial strain curves have similar shapes for the tests presented in Figure 10c–f.

_{a}during Test 1.1 resulted in lower residual values of axial strain in comparison with Tests 1.2 and 1.3. For example, the values of permanent axial strain during the 1000th cycle (Figure 10e) were, approximately, 2.0- and 1.4-times smaller in Test 1.1 when compared to Tests 1.3 and 1.2, respectively. The effect of confining pressures is also clear from the results, with confining pressures conditioning the RCA sample to a much stiffer response to cyclical loading.

_{max}. Deviator stress amplitude q

_{a}also has an impact on the RCA sample behavior, with lower q

_{a}values accounting for lower total axial strains. However, the impact of q

_{a}on plastic strain development seems to be insensitive to effective stress p’

_{0}and maximal axial stress q

_{max}. This can be clearly observed in Figure 9 and when comparing Figure 10b with Figure 10d and Figure 10c with Figure 10f.

_{max}− q

_{min}) and ${\epsilon}_{r}$ for the resilient strain.

_{r}after plastic hardening (approximately 10

^{2}to 10

^{3}cycles) happens due the degradation of the RCA stiffness. This was observed in all tests, except for 2.1. In the latter case (Figure 11, green dashed line), hardening still occurs after 3 × 10

^{4}cycles. This process leads to RCA compaction, resulting in the increase of Mr. It is expected that, for a large enough number of cycles, maximal compaction will occur akin to the remaining curves shown here. At this point, Mr is expected to reach its highest value, after which the degradation phenomena should take place.

_{f max}(see Table 2). The coefficients A and b can be calculated from q

_{f max}(obtained from the static triaxial tests), stress characteristic parameters and confining pressures.

_{f max}is governed by the A

_{f}parameter, which is given by:

^{2}value for Equation (5) equals 0.999. A plot of Equation (5) with its corresponding experimental data is shown in Figure 12a.

_{f}relates to ${q}_{fmax}$, ${q}_{a}$ and ${q}_{m}$ according to:

_{f}given by:

^{2}value for Equation (5) equals 0.747. A plot of Equation (7) with its corresponding experimental data is shown in Figure 12b.

^{2}higher than 0.98 for all corresponding experiments (see Table 5). The calculations of plastic strain were later employed to calculate the number of cycles until the failure (N

_{f}), which represents the largest strain predicted to occur in a designed structure. These results formed the basis of the stress-life method in the Wohler S-N diagram. The S-N diagram shows the stress amplitude S

_{a}as a function of the number of cycles, until the occurrence of the failure at N

_{f}. Results are presented in Figure 13.

## 4. Conclusions

- CBR test results ranged between 71.7% and 101.5% for a 2.5-mm plunger depth and between 91.3% and 100.4% for 5.00 mm. These results fulfill the standards necessary to classify RCAs as a subbase layer application.
- DSTs allowed an estimation of the friction angle ϕ = 39.5°, while not allowing a proper observation of the cohesion c. Static triaxial test results provided effective friction angle ϕ’ = 42° and apparent cohesion c = 45 kPa. The differences are caused by the RCA structure, which involves high roughness of the grain surface.
- Torsional shear tests allowed establishing the value of the shear modulus G
_{max}and damping ratio D_{min}for f = 1 Hz at approximately G_{max}= 60 MPa and D_{min}= 1.83%. - During the tests, excessive pore water pressures were observed. They started to stabilize after ca. 100 cycles, reaching steady low levels after approximately 1000 cycles.
- During the experiments, a change of the area of the hysteresis loops qx$\epsilon $ was observed. This was clearly observed during Test 1.1. The resilient modulus Mr also presented a decrease during the test. The decrease of Mr after the plastic hardening process (approximately 10
^{2}to 10^{3}cycles) is interpreted as a consequence of the degradation of RCA stiffness. This phenomena was observed in all tests, except Test 2.1. In the latter, the RCA showed hardening even after 3 × 10^{4}. The overall maximal obtained Mr was equal to 1715 kPa. - An empirical formulas (Equations (4)–(7)) for permanent strain development as a function of N, σ'
_{3}, q_{max}and q_{f max}has been established. Predicted permanent strains based on these formulas agree well with the test results. - Results were interpreted based on the stress-life method in the Wohler S-N diagram. The S-N diagram plots the stress amplitude q
_{a}versus cycles until the occurrence of the failure N_{f}. The RCA exhibits behavior in accordance to the Basquin law. The characteristic “knee”, which can be observed in the case of other materials, was not observed during the tests for the RCA. - Results suggest that the pore pressure development at early stages of cyclic loading is impacted by internal porosity and high water adsorption, which is characteristic for RCAs.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Stress parameters for a constant amplitude of loading for the tested recycled concrete aggregate (RCA). q

_{a}, stress amplitude; q

_{m}, average stress; Δq, stress difference; q

_{max}, maximal stress; q

_{min}, minimal stress.

**Figure 3.**Results of static tests on RCA: (

**a**) the California Bearing Ratio (CBR) test results and (

**b**) the direct shear test (DST) results.

**Figure 4.**Results of static triaxial tests on RCA: (

**a**) stress-strain curves; (

**b**) effective stress paths and (

**c**) Mohr–Coulomb effective failure envelope.

**Figure 5.**Normalized shear modulus G/G

_{max}versus shear strain amplitude for isotropically-consolidated RCA (σ3’ = 45 kPa) for various test frequencies.

**Figure 6.**Normalized damping ratio D/D

_{min}versus shear strain amplitude for isotropically-consolidated RCA (σ3’ = 45 kPa) for various test frequencies.

**Figure 7.**Stress paths for different test conditions: (

**a**) 1.1; (

**b**) 1.2; (

**c**) 1.3; (

**d**) 2.1; (

**e**) 2.2 and (

**f**) 2.3; as defined in Table 1.

**Figure 10.**Stress-strain plot during three test levels on an RCA sample under different effective stresses p’

_{0}, as indicated in the figures (different lines correspond to different loading cycles). The panels correspond to: (

**a**) Test 1.1; (

**b**) Test 2.1; (

**c**) 1.2; (

**d**) Test 2.2; (

**e**) Test 1.3; (

**f**) Test 2.3.

**Figure 12.**3D view of (

**a**) A

_{f}and (

**b**) b

_{f}parameter change in various confining pressure σ'

_{3}and maximal deviator stress during cyclic loading for q

_{max}values (black points stand for test results).

**Figure 13.**S-N plots for the RCA in various strain to failure conditions at effective stresses of (

**a**) p’

_{0}= 45 kPa and (

**b**) p’

_{0}= 90 kPa.

Caption | Δq (kPa) | q_{m} (kPa) | q_{min} (kPa) | q_{max} (kPa) | q_{a} (kPa) |
---|---|---|---|---|---|

Test 1.1 | 25.85 | 25.87 | 12.95 | 38.8 | 12.93 |

Test 1.2 | 129.39 | 78.21 | 13.51 | 142.9 | 64.7 |

Test 1.3 | 178.54 | 104.34 | 15.07 | 193.61 | 89.27 |

Test 2.1 | 5.46 | 26.11 | 23.38 | 28.84 | 2.73 |

Test 2.2 | 25.72 | 51.94 | 38.98 | 64.7 | 12.96 |

Test 2.3 | 99.78 | 128.91 | 79.01 | 178.79 | 49.9 |

Test No. | σ3’ Effective Minor Axial Stress Value (kPa) | Deviator Stress at Failure (kPa) |
---|---|---|

S.1 | 45.0 | 251.0 |

S.2 | 90.0 | 661.0 |

S.3 | 225.0 | 1346.0 |

Freq. (Hz) | D_{min} (%) | G_{max} (MPa) |
---|---|---|

0.1 | 1.61 | 55 |

1 | 1.83 | 60 |

10 | 3.1 | 56 |

No. of Test/No. of Cycle | 10^{1} | 10^{2} | 10^{3} | 10^{4} | 10^{5} |
---|---|---|---|---|---|

1.1 | 790 | 812 | 744 | 670 | 633 |

1.2 | 808 | 823 | 758 | - | - |

1.3 | 618 | 652 | 621 | - | - |

2.1 | 450 | 483 | 562 | 730 | - |

2.2 | 1436 | 1387 | 1410 | 1422 | - |

2.3 | 1654 | 1689 | 1715 | 1710 | - |

Test No. | A | b | R^{2} |
---|---|---|---|

1.1 | 0.0170 | −0.7890 | 0.992 |

1.2 | 0.0686 | −0.3231 | 0.997 |

1.3 | 0.1425 | −0.6649 | 0.997 |

2.1 | 0.0120 | −0.0489 | 0.982 |

2.2 | 0.0119 | −0.0586 | 0.997 |

2.3 | 0.0854 | −0.3923 | 0.987 |

**Table 6.**Coefficients C and d of the Basquin proposition of the strain line in the S-N relationship.

Caption | 45 kPa | 90 kPa | ||
---|---|---|---|---|

C | d | C | d | |

ε = 0.5% | 1.917 | −0.012 | 2.0537 | −0.008 |

ε = 0.75% | 1.8849 | −0.008 | 2.051 | −0.007 |

ε = 1.0% | 1.864 | −0.006 | 2.0518 | −0.006 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Sas, W.; Głuchowski, A.; Gabryś, K.; Soból, E.; Szymański, A.
Deformation Behavior of Recycled Concrete Aggregate during Cyclic and Dynamic Loading Laboratory Tests. *Materials* **2016**, *9*, 780.
https://doi.org/10.3390/ma9090780

**AMA Style**

Sas W, Głuchowski A, Gabryś K, Soból E, Szymański A.
Deformation Behavior of Recycled Concrete Aggregate during Cyclic and Dynamic Loading Laboratory Tests. *Materials*. 2016; 9(9):780.
https://doi.org/10.3390/ma9090780

**Chicago/Turabian Style**

Sas, Wojciech, Andrzej Głuchowski, Katarzyna Gabryś, Emil Soból, and Alojzy Szymański.
2016. "Deformation Behavior of Recycled Concrete Aggregate during Cyclic and Dynamic Loading Laboratory Tests" *Materials* 9, no. 9: 780.
https://doi.org/10.3390/ma9090780