Identifying the Impact Factors of the Dynamic Strength of Mudded Intercalations during Cyclic Loading

Despite reports on previous research associated with the dynamic strength of mudded intercalations during cyclic loading, a systematic investigation of the impact factors of this strength is still valuable. +is work aimed at experimentally revealing the impact factors of the strength along with their impacts. +e potential impact factors considered in this work include (i) water content, (ii) clay mineral composition, (iii) clay content, (iv) confining pressure, and (v) cyclic failure time. Specimens of mudded intercalations were collected from China and were remolded and prepared for a dynamic triaxial test under cyclic loads. +e test results showed that the dynamic strength is impacted by water content (strongly), clay mineral composition (moderately), confining pressure (moderately), and cyclic failure time (weakly); no significant impact of clay content was detected. Moreover, the dynamic cohesion is correlated with clay mineral composition (strongly), water content (moderately), and cyclic failure time (weakly); no significant correlation with clay content or confining pressure was detected. Finally, the dynamic friction angle is correlated with water content (strongly), clay content (moderately), and cyclic failure time (weakly); no significant correlation with clay mineral composition or confining pressure was detected.


Introduction
e presence of mudded intercalations is known to deteriorate rock engineering.ere exists a limited body of research on the dynamic strength associated with mudded intercalations during cyclic loading.Significant advances in this field include the report by Xue and Wang [1], who determined the dynamic strength indexes of mudded intercalations collected from the Xiaolangdi hydroproject using a cyclic simple shear test and a dynamic triaxial test.However, the potential impact of various factors (e.g., clay mineral composition, water content, grain gradation, and confining pressure) has not yet been reported.Despite numerous previous works investigating the impact factors of the dynamic strength of common fine-grain soils [2][3][4][5][6][7][8][9][10][11], little is known as to whether the same impacts occur in mudded intercalations, which are a special soil type whose main mineral composition is clay with breccia and rock fragments.
is work aims at experimentally identifying the impact factors of the dynamic strength of this special soil type and specifying their impacts.
e potential impact factors considered in this work include (i) water content, ω, (ii) clay mineral composition, M, (iii) clay content, C, (iv) confining pressure, σ 3 , and (v) cyclic failure time, N f .Test specimens were collected from geological audits that service the large hydroproject near the Hukou waterfall of the Yellow River.Eighty-one groups of specimens with different values of the considered potential impact factors were remolded and prepared for dynamic triaxial testing under cyclic loads.
e potential impacts of the factors were investigated and compared with those of related soils.e allowable frequency range is between 0 Hz and 10 Hz.

Materials and Methods
e specimens were sampled from a geological audit of a large hydroproject (location shown in Figure 2) and remolded into a standard size (shown in Figure 3).To investigate the potential impacts of (i) water content (ω), (ii) clay mineral composition (M), and (iii) clay content (C) on the dynamic strength and its indexes, specimens with various physical properties, as listed in   e grading results of the particle sizes are shown in Figure 4.

Test Procedure.
e test was conducted a total of 81 times.As listed in Table 1, there are 9 groups of remolded specimens for each type of main clay mineral composition.For each group of remolded specimens, 3 levels of con ning pressure (σ 3 ) are applied: 100 kPa, 200 kPa, and 300 kPa.For each level of con ning pressure, it is necessary to apply di erent axial dynamic loads (σ de ) to the 3 specimens.e loading process is shown in Figure 5.An equivalent sinusoidal wave with a frequency (f ) of 1 Hz is used as the axial dynamic load, and the consolidation stress ratio (K c ) is set at 1. e test procedure is shown in Figure 6.
In general, under isobaric pressure consolidation, typical soils can be expected to fail once the strain reaches 2 Advances in Civil Engineering 5% [3,4].However, the strength of the mudded intercalations tends to be smaller in comparison with common soils.As a result, under cyclic loading, the initial strain values are larger and the development of damage is slower.is 5% strain failure criterion is therefore not quite suitable for mudded intercalations.Instead, the 10% strain failure criterion [12] is more reasonable and was therefore adopted in the test.

Properties of Dynamic Strength, τ df .
e cyclic time corresponding to the time point at which the cumulative strain (ε d ) meets the prescriptive strain failure criterion is de ned as the cyclic failure time (N f ).e dynamic shear stress occurring when the cycle number (N) meets N f is de ned as the dynamic strength (τ df ).   Figure 7 shows the relationship between ε d and N. ε d initially increases slowly with N, followed by a more rapid increase.is trend is not a ected by the con ning pressure, σ 3 .Moreover, the increase of σ 3 and the cyclic stress ratio (r d ; r d σ de /σ 3 ) contribute to an increased initial cumulative strain value (ε 0 ), an increased rate of ε d , and a decreased N f .e relationship between τ df and N f is shown in Figure 8.As shown in Figure 8, τ df decreases with N f .eir relationship is tted as where A and B are tted coe cients.
e obtained values of A and B are listed in Table 2.More than 63% of the R 2 values are greater than 0.7, indicating a good t.

Impact Factors of Dynamic Strength, τ df .
e orthogonal test results show that τ df is correlated with ω (strongly), M, σ 3 (moderately), and N f (weakly).Figure 9 shows τ df ∼N f under di erent conditions, while Figure 10 shows the impact of factors on τ df , where the ordinate is k jm /k jmmax and the abscissa is the impact of the factors.Advances in Civil Engineering τ df initially increases slightly with ω but then decreases (Figure 10(a)).is phenomenon may be attributed to the critical water content, ω 0 .at is, for an ω value smaller than ω 0 , τ df increases with ω, whereas it decreases for an ω value greater than ω 0 .is behavior agrees with ndings for common soil reported in [13,14].

Impact
Factor II: Con ning Pressure, σ 3 .Figure 9(b) shows that τ df increases with σ 3 , where ω is 15.1% and the main clay mineral composition is mixed montmorillonite/ illite.A similar result is exhibited in Figure 10(c).ese results are consistent with those of ordinary soils, as demonstrated in [4,15,16].

Impact Factor III: Clay Mineral Composition, M.
Figure 9(c) shows τ df when the main clay mineral composition is primarily illite.A similar result is exhibited in Figure 10(b).is result di ers from that revealed in [17][18][19].

Impact
Factor IV: Cyclic Failure Time, N f .Figure 8 shows that τ df decreases with N f .A di erent result is presented in Figure 10(d), which shows that τ df does not always decrease with N f .e di erence is likely caused by Table 3: Orthogonal test results.K jm is the sum of the parameters for the row level m repeated tests for the j line factor.k jm is the average value of the parameters.R j is the range (i.e., the di erence between the maximum and minimum) of k jm .η j (R j / R j ) × 100%, such that η j represents the contribution of factor j to A or B.  Advances in Civil Engineering a variation in the compactness.at is, the compactness rises with N f , resulting in an increase in τ df [5].

Impact Factors of the Dynamic Strength Indexes, C d and φ d .
e dynamic strength indexes, C d and φ d , are determined as follows: rst, τ df is evaluated based on Seed's [20] equivalent cyclic failure time.en, using τ df , Mohr's stress circle can be obtained, and C d and φ d are consequently determined (see results in Table 4).As shown in Table 4, C d is closely related to the clay mineral composition, which has a contribution rate of 67.23%.φ d is closely related to ω. Figures 11 and 12 show the impacts of various factors on C d and φ d .

Impact Factor I: Water Content, ω. As shown in
Figure 11(a), C d increases with ω when ω is less than ω 0 , and vice versa for ω greater than ω 0 .φ d decreases with ω (Figure 12(a)).

Impact
Factor III: Cyclic Failure Time, N f .Figure 11(c) shows that C d initially increases slightly with N f and then decreases.A similar variation in φ d is observed (Figure 12(c)).

Comparison with Other Soils.
e dynamic strength indexes of the mudded intercalations are compared to those of soils from other sites, as documented in [1,[21][22][23].e test results are shown in Figure 13.
Figure 13 compares the upper and lower limit values of the dynamic strength for samples from various sites.e comparison shows that the dynamic strength of mudded intercalations is generally smaller than that of loess, silt, clay, and other common soils.Possible reasons for this phenomenon are as follows: (a) a structural disturbance due to remolding leads to a signi cant decrease in the dynamic strength; (b) the mudded intercalations tested in this work are partially composed of mixed montmorillonite/illite, which have relatively low strengths; and (c) the clay content varies depending upon the site, resulting in di erences in the dynamic strength.

Discussion
Previous literature has concluded that the τ df of mudded intercalations with kaolinite is higher than that for illite [17][18][19].However, a di erent result was observed here; namely, the former is lower than the latter (Figure 9(c)).As a factor that accounts for the disparity between the two results, the clay content of the mudded intercalations in this study corresponding to illite is only 21.0%. is is much lower than the clay content of kaolinite, which reaches 48.8%.e greater the clay content, the smaller the dynamic strength [24][25][26].A similar relationship is observed for the dynamic strength indexes of the mudded intercalations, as shown in Figure 11(b).As the mechanical properties of the main mineral composition improve, C d of the mudded

Lower limit of test results
Upper limit of test results Xue and Wang [1], the undisturbed siltized intercalation Jiang et al. [22], lower limit of saturated fine sand Jiang et al. [22], upper limit of saturated fine sand Tang and Chi [21], clay of dam foundation Tang and Chi [21], loam of dam foundation Tang and Chi [21], sandy loam of dam foundation Tang and Chi [21], silt of dam foundation Tang et al. [23], original silt soil Advances in Civil Engineering intercalations increases.Moreover, the impact of the clay content on φ d is more significant, as shown in Figure 12(b), where φ d decreases with clay content.e clay mineral composition and clay content constitute two primary impact factors for the dynamic strength indexes of mudded intercalations, which are different from common soils.

Conclusion
e impacts of various factors on the mudded intercalation dynamic strength, including (i) clay mineral composition, (ii) water content, (iii) clay content, (iv) confining pressure, and (v) cyclic failure time, were investigated.e following conclusions were drawn: (1) A greater confining pressure and cyclic stress ratio contribute to lower cyclic failure times.(2) e dynamic strength is strongly impacted by the water content.When the water content exceeds a critical value, the dynamic strength decreases with increasing water content.An opposite variation in dynamic strength with increasing water content is observed when the water content is less than the critical value.(3) e dynamic strength is impacted by the clay content and clay mineral composition.e strength is correlated with the main clay mineral composition and decreases with the clay content.(4) e dynamic cohesion is impacted by the clay mineral composition, water content, and cyclic failure time.Specifically, the dynamic cohesion of the mudded intercalations with illite is greater than that for mixed montmorillonite/illite but lower than that for kaolinite.Such cohesions initially increase slightly with water content and cyclic failure time but then decrease.(5) e dynamic friction angle is strongly impacted by the water content.Specifically, as the water content rises, the dynamic friction angle decreases.(6) e dynamic strength, cohesion, and friction angle of the mudded intercalations are smaller than those of loess, silt, clay, and common soils.

2. 1 .
Testing Instrument and Specimens.Dynamic triaxial tests were performed on a DDS-70 electromagnetic vibration triaxial apparatus, as shown in Figure 1. e maximum allowable axial displacement and maximum allowable axial force are 20 mm and 1370 N, respectively.

Figure 4 :
Figure 4: Grading of the particle sizes.
time, N f Dynamic strength, lg τ df (kPa) Test results Fitted lines

Figure 8 :
Figure 8: Relationship between τ df and N f .

Figure 11
(b)  shows that C d is a ected by the clay mineral composition.Speci cally, the C d values for illite as the main clay mineral composition are greater than those with mixed montmorillonite/illite but lower than those with kaolinite.Moreover, φ d decreases with C (Figure12(b)).

Table 1 :
Physical properties of remolded specimens.
Group numberSampling site Main clay mineral composition, M Clay content, C (%) Dry density (g/cm 3 )

Table 2 :
Obtained values of A and B.

Table 4 :
Values of C d and φ d determined for the case of N f 20.