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Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen
Journal Pre-proofs Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen Junjie Wang, Shiyuan Huang, Wanli Guo, Zhenfeng Qiu, Kai Kang PII: DOI: Reference:
S0013-7944(19)31129-4 https://doi.org/10.1016/j.engfracmech.2019.106814 EFM 106814
To appear in:
Engineering Fracture Mechanics
Received Date: Revised Date: Accepted Date:
16 September 2019 8 December 2019 9 December 2019
Please cite this article as: Wang, J., Huang, S., Guo, W., Qiu, Z., Kang, K., Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen, Engineering Fracture Mechanics (2019), doi: https://doi.org/10.1016/j.engfracmech.2019.106814
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Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen Junjie Wang a, b, Shiyuan Huang a, b *, Wanli Guo b, Zhenfeng Qiu a, Kai Kang c a
Engineering
Research
Center
of
Diagnosis
Technology
and
Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China b
Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dam of the Ministry of Water Resources, Nanjing 210029, China
c
School of Environment and Civil Engineering, Jiangnan University, Wuxi, 214122, China
* Corresponding Author. E-mail address: [email protected] (Shiyuan Huang) Address: 66 Xuefu Road, Nan’an District, Chongqing, 400074, China Phone number: (8623) 6289 6924 Fax number: (8623) 6265 2841
1
Abstract: Single-edge notched beam specimens have been used widely to determine the fracture toughness KIC of compacted clays under three-point bending loading. However, this specimen type is not very suitable for the material with low strength. In this study, notched semi-circular bending specimens were employed to determine the KIC of a compacted clay, the effects of initial notch length, specimen thickness, moisture content and dry density on KIC were investigated. Based on the testing results, the ratio of initial notch length to specimen radius a0/R = 0.3–0.5 was suggested. There was no remarkable thickness-dependent size effect for the compacted clay. To investigate the relationship between the KIC and tensile strength σt of the compacted clay, unnotched semi-circular bending specimens were employed for determining the σt. It is concluded that there is a good linear relationship between these two parameters. According to the discussion on the testing results of different compacted clays, an empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays. Additionally, the size of fracture process zone of the compacted clay was calculated by an estimation method. Keywords: Compacted clay; Fracture toughness; Semi-circular bend; Tensile strength
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1. Introduction Fracture mechanics has become an important field of study for solving safety problems related to the strength of geomaterials used in civil engineering. For instance, it can be used to predict and identify the failure of structures made of geomaterials, thereby providing instruction for improving the safety of such structures as well as for analyzing the hydraulic fracturing, slope stability, excavation process [1]. In fracture processes that are not associated with high strain rates, mode I fracture toughness (KIC) is the crucial property that reflects a material’s ability to resist crack initiation and propagation. It is determined from the stress intensity factor (KI) at which a thin crack begins to grow in the material. Due to the weakness of geomaterials under tension state, mode I fracture is most frequently encountered among the three basic fracture modes [2]. Therefore, it is important to develop convenient testing approaches for accurately measuring KIC of geomaterials. The International Society for Rock Mechanics and Rock Engineering (ISRM) has suggested several standard testing methods to determine KIC of rock materials [3]. However, clay soil, another geomaterial that is often used as the core of dams and the liner in landfills, has been investigated less frequently than rocks. Until now, none of generally acknowledged methods has been proposed for determining KIC of clay soil, the KIC of clay soils has been investigated by various test methods as summarized in Table 1 [4-19]. 3
In earlier studies, Lee et al. [5] and Lakshmikantha et al. [9] used the compact tension specimen to investigate the KIC of clay soils. Due to the complex specimen geometry and the complicated sample preparation, this method which is suggested by American Society of Testing Materials (ASTM) [20] for metallic materials, is quite inconvenient. Compared with direct tension method mentioned above, indirect method is more easily. Splitting test is a typical indirect tension method, the sample structure such as Brazilian disk is simple. However, the unpredictability of fracturing path may compromise the accuracy of the measurement, which is not suitable for clay soils. As shown in Table 1, three-point bending test on a single-edge notched beam (SENB) specimen, another suggested method by ASTM, has been used most widely because of its simple sample structure and convenient operation. However, Amarasiri et al. [13] noted that it is difficult to conduct tests on large-sized SENB clay soil specimens because they have low strength, and therefore, self-weight plays a major role. To solve this problem, Wang et al. [11] proposed an improved method in which the effect of self-weight was eliminated. Unlike in the case of rock, concrete, and asphalt specimens, clay soil fracture specimens cannot be prepared using a cutting machine or by a pouring action. Generally, a clay soil specimen is prepared by a compacting action and the artificial pre-crack is prepared by a cutting 4
sharp knife. Therefore, it can be easily influenced by different disturbances before tests such as crack prefabrication and specimen transfer due to its low strength. Thus, disturbances during test preparation cannot be ignored. As shown in Table 1, the length-width ratio of SENB specimens in references [4], [8], [10], [11], [13], [15], and [17] were 2.5, 3.0, 2.7, 4.0, 3.3, 3.0, and 4.0, respectively. If an SENB specimen’s length-width ratio is too large, it may break under a light load before test loading. For example, the peak load of a typical SENB specimen was about 13 N in [11], peak loads of SENB test specimens of three different dry densities were about 4, 8, and 15 N in [10], maximum and minimum peak loads of SENB test specimens with different moisture contents were respectively about 80 and 3 N in [13], and the maximum peak load of SENB test specimens was about 40 N in [17]. Overall, the peak loads of SENB clay soil specimens are usually low. Consequently, relatively light disturbance during test preparation may cause the specimen to break and thereby influence the test efficiency. If the specimen has small dimensions, the impact of the above-mentioned problems will reduce. Furthermore, less clay soil material will be required, thereby improving the efficiency of laboratory tests. Semi-circular bend specimen, usually used for rock fracture testing seems a good alternative for clay soil material because of its small size 5
and simple test procedure. For clarity, specimen with notch is called NSCB specimen, and specimen without notch is called SCB specimen. Initially, Chong et al. [21] proposed NSCB specimen for rock materials, then many researchers used the specimen for fracture testing of other materials. So far, researchers have not experimentally studied the KIC of clay soils using this specimen type. In the present study, mode I fracture toughness KIC of a compacted clay was obtained experimentally using NSCB specimen. The effects of specimen dimensions and clay characteristics on KIC were investigated and the reasonability of test results was discussed. On the other hand, tensile strength σt, also represents the ability of the material to resist failure under tension condition, has a correlation with KIC [11]. Thus as the second step of this study, three-point bending test on SCB specimen, which is an indirect tension method generally used in rock materials [22, 23], was used to determine the σt of the same clay. The relationship between KIC and σt of the tested clay was obtained. Finally, based on the testing results of different compacted clays from references, a discussion was made.
2. Testing Method 2.1. Mode I fracture toughness
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Fig. 1a shows the dimensions for NSCB specimens suggested by ISRM. In the Figure, R is the semicircular specimen radius, B is the semicircular specimen thickness, a0 is the initial notch length, S is the distance between support points, and F is the load on the specimen. With the conventional loading assembly shown in Fig. 1a, both the NSCB clay specimen’s self-weight and load F both act in the vertically downward direction. The clay’s self-weight may strongly affect the test results owing to its low tensile strength, and therefore, it cannot be neglected. To minimize or eliminate the influence of self-weight, the improved loading assembly shown in Fig. 1b was used, in which the direction of load F was perpendicular to that of the self-weight. The details of the test procedure were illustrated in the next section. According to linear elastic fracture mechanics, the fracture initiates from the crack tip as the load F reaches the peak Fmax, and the KIC value of the NSCB specimen can be determined using the following equations [24]:
K IC =Y
Fmax a0 2 BR
(1)
S S a0 S a ) (1.071 34.401 ) 0 Y = 1.297 9.516 (0.47 16.457 2R 2R R 2R R
2
(2)
where Y is the nondimensional stress intensity factor (SIF) corresponding 7
to specimen geometry. Table 2 shows the ISRM-suggested dimensions for NSCB specimen. Notably, Eq. (2) is only valid for a0/R ≥ 0.2 [24]. 2.2. Tensile strength In tension test, the SCB specimen geometry and loading configuration are the same to those of the NSCB specimen (Fig. 1) except for no notch. Aliha [22] suggested a formula that can be used to estimate the tensile strength by conducting this specimen. The σt value of the SCB specimen can be computed by the following formula.
B
S
F
t 0.146 0.8896 4.02 1.052 max 2R 2R BR
(3)
3. Specimen Preparation and Testing Scheme 3.1. Testing material The test specimens were prepared using clay obtained from a construction site in Chongqing, China. The basic physical properties of the clay are as follows: specific gravity GS = 2.72, plasticity index IP = 20.1, liquid limit WL = 50.1%, plastic limit WP = 30.0%, maximum dry density ρmax = 1.68 g/cm3, and optimum moisture content wop = 16.6%. It consists of the following different grain size fractions: 0.5–0.25 mm (0.5%), 0.25–0.1 mm (17.9%), 0.1–0.075 mm (41.6%), and <0.075 mm 8
(40.0%). 3.2. Testing Scheme In order to obtain a reasonable or valid KIC value by using NSCB specimen, the reasonable geometric size for NSCB specimen should be selected first. For the radius of specimen R, ISRM-suggested dimension is larger than 5 × grain size or 38 mm. Because the maximum grain size of the clay is 0.5mm, the suggested R value should be larger than 2.5mm or 38mm (the bigger value should be selected), thus R = 50mm was used in this study. The loading distance ratio of specimen S/2R was recommended as 0.5-0.8, a high ratio approaching to 0.8 was preferred unless the material is too weak to be tested [24, 25]. According to the attempts before the test, S/2R = 0.8 was proved to be suitable for the tested clay with different moisture contents around the optimum moisture content. The KIC testing scheme is shown in Table 3. In N-1, 24 NSCB specimens with six different a0/R values were tested first. By contrast, for the same tested clay, three-point bending tests on four SENB specimens with a0/W = 0.4 (where W is the specimen width) were conducted. The specimen dimensions were the same as those in the study by Wang et al. [17], their study results indicated that constant KIC value could be obtained with this initial length ratio. After the limit of notch length of 9
a0/R was suggested, the effects of thickness of specimen B, moisture content w and dry density ρ on KIC were investigated in N-2, N-3 and N-4. As shown in Table 4, 24 SCB specimens were employed for determining the σt of the compacted clay. 3.3. Specimen Preparation The SENB specimens were prepared by the method of Wang et al. [11]. The NSCB and SCB specimens were processed as follows: (1) The weight of clay to be prepared was calculated according to the desired moisture content and dry density of the specimen as shown in Table 3 and Table 4. A rectangular specimen with 440-mm length, 100-mm width, and 65-mm height (when B = 65 mm) was compacted in a custom-made rectangular compaction device (440 mm × 100 mm × 200 mm) according to Trade Standard of P. R. China [26]. The specimen was compacted in three layers with equal weight and equal thickness of the soil. To eliminate the influence of excess pore water pressure on testing, the specimen was stored in a sealed container for at least 24 h. Fig. 2 shows the compaction process. (2) A semicircular cutting ring (SCCR) with one sharp edge was designed to cut the rectangular specimen into small specimens. The inner diameter and thickness of SCCR are the same as the diameter and 10
thickness of NSCB and SCB specimens (Fig. 3). Eight SCCRs were placed on the compacted rectangular specimen and then completely embedded into them using a compaction hammer to obtain eight SCB specimens. In the process, vaseline should be applied to the SCCR surface to separate it easily from the SCB specimen. (3) For NSCB specimen, a notch with 1.8-mm width was created using a thin, sharp knife. Fig. 4 displays typical specimens employed in the tests. 3.4. Testing Procedure These tests were conducted in the Key Laboratory for Hydraulic and Waterway Engineering of the Ministry of Education of Chongqing Jiaotong University. A soil fracture mechanic testing system (Jiangsu Yongchang Science and Education Instrument Manufacturing Co. Ltd., Leiyang, Jiangsu Province, China) was utilized for loading with a loading rate of 0.8 mm/min. The loading assembly shown in Fig. 5, which was developed based on the loading assembly shown in Fig. 1, was used to conduct the experiments. It consists of a load sensor, a displacement sensor, an indenter, two support pins, a graduated scale, two slidable baseplates, and a data logger. Additionally, it has a horizontal loading direction, thereby 11
eliminating the influence of the specimen’s self-weight on the testing results.
4. Results and analysis 4.1. The effect of a0/R on KIC As shown in Fig. 6, three-point bending tests on 24 NSCB specimens with six different a0/R values were conducted. Fig. 7 shows typical load versus displacement curves of NSCB specimens with a0/R = 0.2 and 0.5. The plots clearly show that before the F value reaches its peak, the load versus displacement relationship is almost linear. The F value reaches its peak at a displacement of 1.65–2.33 mm for specimens with a0/R = 0.2, and the F value reaches its peak at a displacement of 0.54–1.52 mm for specimens with a0/R = 0.5, beyond which it decreases rapidly. The KI value can be calculated using Eq. (1) and Eq. (2). When the peak F value was used, the calculated KI value equaled the KIC value. Fig. 8 shows the failure mode of the NSCB specimens under mode I loading conditions, the crack clearly propagated along the initial fracture plane. Fig. 9 shows the experimental data for NSCB specimens with different a0/R values. Overall, the KIC value decreases as the a0/R value increases. When 0.3 ≤ a0/R ≤ 0.5, the mean KIC value is nearly constant. 12
As a mechanical parameter of material, the value of KIC should be a constant value, so that it could be regarded as a valid value [17, 24, 27, 28]. The limit of notch length may be due to the discreteness problem of clay soil or the size of fracture process zone (FPZ), it will be discussed later. The constant KIC value of this tested clay as obtained using NSCB specimens is about 18.3 kPa·m0.5. As shown in Table 5, the average KIC value of SENB specimens is 20.4 kPa·m0.5, indicating that the NSCB specimen gives somewhat conservative results for the KIC. The error of the NSCB specimen KIC value with respect to the SENB specimen KIC value is about 10%, which could be acceptable in geotechnical engineering. Therefore, it can be indicated that a reasonable KIC value of the compacted clay could be obtained using NSCB specimen. During the tests, two SENB specimens were reworked due to specimen damage. Table 5 shows that the average peak load of SENB specimens is around 10 N, this value is too low and therefore, specimens can easily break during test preparation. While the average peak loads of NSCB specimens (a0/R = 0.3, 0.4, and 0.5) are 114.5, 86.6, and 62.3 N, and these are around 11, 9, and 6 times larger than those of SENB specimens, respectively. It implies that the NSCB specimen is less susceptible to disturbance before test. It also indicates that KIC value of NSCB specimen 13
is more sensitive to notch length than that of SENB specimen because the peak value of loading is linear with KIC value. As a result, the limit of notch length of these NSCB clay specimens is suggested a0/R = 0.3–0.5, which is slightly different from the range suggested by ISRM. In the following tests, a0/R = 0.4 was used. 4.2. The effect of B on KIC The effect of specimen thickness B on KIC was examined by conducting a series of tests on the NSCB specimens with four specimen thicknesses (Fig. 10). Fig. 11 plots the KIC values changing with respect to the specimen thickness B, it appears that the KIC value decreases as B increases and tends to be stable when B ≥ 50. However, the difference of these data is small (the error between the maximum KIC and minimum KIC is less than 5%), the KIC values of four specimen thicknesses could be regarded as a constant. Thus, it is indicated that there exists no remarkable thickness-dependent size effect for the compacted clay specimens used in this study and the KIC values of specimens with B ≥ 20mm could represent the plane strain KIC. 4.3. The effects of w and ρ on KIC and σt For a compacted clay, the moisture content w and dry density ρ are two main influence factors on its strength. As shown in Fig. 12a, the 14
values of KIC are increasing with increasing the ρ from 1.62 to 1.70 for w of 16.6%. This result is consistent with the results of Wang et al. [11] and Hanson et al. [7]. As a greater compaction effort is required to compact a denser specimen, the value of KIC also increases with the compaction effort. Fig. 12b shows that the values of KIC are decreasing with increasing the w from 14.6% to 20.6% for ρ of 1.66 g/cm3. This is consistent with the results of Harison et al. [7] and Cao [18]. As shown in Fig. 13, the σt of compacted clay increases with increasing ρ and decreasing w. The effects of ρ on KIC and σt are similar, and the effects of w on KIC and σt are also similar. Fig. 14 shows a typical SCB specimen right before and after fracturing, the failure mode is similar to that of NSCB specimen. It is therefore reasonable to assume the parameters KIC and σt of the compacted clay are positively correlated. 4.4. The relationship between KIC and σt Generally, KIC = aσt has been used to described the relationship between KIC and σt [7, 11, 13, 18, 19], where a is proportionality coefficient. In Fig. 15a, the data points were plotted and the relationship between KIC and σt was fitted by a linear curve. The result of correlation is: KIC = 0.2800σt
R2 = 0.9357
(4)
which shows a reasonably high coefficient. Meanwhile, a power-law 15
function is used to fit their relationship shown in Fig. 15b, the result of correlation is: KIC = 0.2443σt1.0318
R2 = 0.9329
(5)
Above all, both of linear regression and power-law regression are fitted well. However, using fewer parameter to predict the relationship in practical engineering is more convenient, so the linear function (Eq. 4) is used generally. The empirical relationship could provide a helpful method for estimating the KIC from the σt of materials which can be measured more easily.
5. Discussion 5.1. Relationships between KIC and σt of different compacted clays Currently, only a few scholars have attempted to investigate the relationship between the KIC and σt of compacted clays (Table 6). All of them found that the KIC has a linear relationship with σt and these two properties coexist or vanish simultaneously. As shown in Table 6, the values of proportionality coefficient a are various according to different studies, the maximum value is 0.3546 and the minimum value is 0.0706. The reasons for the difference can be summarized [11, 18, 19, 29] as follows: (1) Different components of the tested compacted clay; (2) Different KIC test methods; (3) Different σt test methods. (4) Different 16
preparation methods of compacted clay. In order to investigate the reason, the data points of various compacted clays from the different studies were replotted in log-log scale in Fig. 16. Harison et al. [7] compacted the ring test specimens and then air dried them to designated moisture content. Amarasiri et al. [13] used the same method to prepare specimens, then the KIC was determined using SENB specimens and the σt was back-calculated by matching the numerically modelled load-load point displacement curves. In the study of Agaiby [19], the specimens were kept in a 40 degrees oven to maintain dry until the testing procedure started. Cao [18], Wang et al [11] and this study used directly compacted clay specimens without drying process, the weight of the soil and water used was calculated according to the moisture content and the dry density of each specimen to be prepared. As discussed above, it can be concluded that the linear fitting correlation is appropriate to all types of clays. As shown in Table 6 and Fig. 16, it can be indicated that the relationship between KIC and σt depends on the specimen preparation method. Compared with directly compacted clays, oven-dried compacted clays and air-dried compacted clays usually have larger values of KIC and σt due to the loss of water. Moreover, the proportionality coefficients are generally smaller. Though a same regularity was found that low moisture 17
contents contribute to high KIC or σt of compacted clays, but for the same clay, directly compacted specimen and air-dried or oven-dried compacted clay specimen with a same moisture content may have different soil structures due to the different moulding moisture contents. Using air-drying or oven-drying method to prepare specimens, it is easy to develop desiccation cracks in the specimens especially at a high temperature. In addition, the water distribution in the specimens is nonuniform that leads the specimens have obvious heterogeneity. The above reasons may make the proportionality coefficients of the fitting equations of air-dried and oven-dried compacted clays various. For directly compacted clays, the moisture contents selected in test are usually near the optimal moisture content because it is difficult to compact drier and wetter clay specimens. Thus, directly compacted clay generally have a smaller strength range and a larger proportionality coefficient a. The range of KIC in this study is about 8-25 kPa·m0.5, which is close to that of Wang et al. [11] (range is 5-35 kPa·m0.5) and Cao [18] (range is 2-30 kPa·m0.5). The range of σt in this paper is approximately 35-87 kPa, which is also close to that obtained by Wang et al. [11] (range is 20-90 kPa) and Cao [18] (range is 5-90 kPa). As shown in Fig. 17a, the data points of three directly compacted clays are close and the a values of the linear fitting functions are also close. If the data points of the three 18
directly compacted clays are fitted by a linear function, it can be also found that there is a good linear fitting relationship, as shown in Fig. 17b, whose proportionality coefficient a is 0.3283 and correlation coefficient R2 is about 0.80. Though the properties such as liquid limit, plastic limit, maximum density and optimum moisture content of these directly compacted clays are different, a similar linear relationship could be used for them. For the core of an earth-rock fill dam, the clay as its material is always compacted by compacting plants. Therefore, this empirical formula can be used to preliminarily predict the KIC of the core clay of an earth-rock fill dam during the construction period. 5.2. Fracture process zone According to the conventional linear elastic fracture mechanics (LEFM), the valid KIC can be obtained as long as the fracture process zone (FPZ) is reasonably small compared with the specimen dimensions such as initial notch length, specimen thickness and ligament length. Generally, a sufficiently large specimen size is required that the effect of FPZ could be neglected [13, 24, 28, 30, 31]. However, the dimension requirements of the standards for rock and metallic materials seem too restrictive for clay materials. According to ASTM E399-12 [20] for metallic materials, the initial notch length, the specimen thickness and the ligament length of SENB specimens must 19
each be larger than 2.5 (KIC/σys)2, where σys is the yield strength. Because the yield strength could not be defined on load displacement curves easily for geomaterials, the tensile strength σt is usually used instead. Thus the values of 2.5 (KIC/σt)2 can be calculated by the relationships between KIC and σt of different compacted clays as shown in Table 6. Investigated by Wang et al. [11], the values of 2.5 (KIC/σt)2 are around 300mm, which are 10 times larger than the dimensions of specimens they used. Investigated by Amarasiri et al. [13], the values are about 70mm, which are also larger than the dimensions of specimens they used. For rock materials, Chong et al. [32] suggested a dimension requirement for the NSCB specimen that the specimen diameter D should be greater than 2.0 (KIC/σt)2. Based on this requirement, the values of 2.0 (KIC/σt)2 of the tested clay in this study are around 150mm, which are 1.5 times larger than the value of D. From above analysis, it seems that the size of compacted clay specimens required according to these standards is impractical. Amarasiri et al. [13] thought the validity of results obtained by testing is uncertain because the lack of a standard for testing KIC of compacted clay materials. To assess this, the apparent lengths of FPZs at peak load were retrieved from numerical models in their study. Results showed that the sizes of FPZs are all smaller than the dimensions of specimens they used, moreover, they are much smaller than the values of 20
2.5 (KIC/σt)2. It is indicated that the FPZ size of compacted clay is overestimated by using the standards for rock and metallic materials. In rock fracture mechanics, the critical distance rc, usually considered as the size of FPZ in front of the crack tip, is generally assumed to be a constant parameter material property [30]. Schmidt [31] suggested that the size of FPZ in rock materials can be estimated from: 1 K IC rc = 2 t
2
(6)
It is obviously seen that the value of rc is related to KIC and σt. This equation is used widely in rock materials, but it is not clear whether it can be used in compacted clays. In order to verify the applicability of the formula in compacted clay materials, the rc values of different compacted clays mentioned in Section 5.1 were calculated by this equation. As shown in Table 7, it is seen that the rc of the SENB specimens used by Amarasiri et al. [13] is about 4.6mm, which is close to their calculated value. In their study, the FPZ size of a specimen with the highest moisture content w = 50.3% is about 4.2mm. Thus, it indicates that using Eq. (6) to estimate the size of FPZ of compacted clays approximately is possible. In this way, the rc value of the clay tested in this study is about 12.5mm, which is much smaller than the specimen diameter D = 50mm. According to the suggested notch length ratio of 21
NSCB clay specimens in this study, the ranges of notch length and the ligament length are 15-25mm and 25-35mm, respectively. When a0/R = 0.5, the initial notch length a0 = 25mm and the ligament length a0 = 25mm are twice larger than the value of rc. All the dimensions of the specimens used in this study are greater than the rc value estimated by Eq. (6). Above all, a reasonable and valid KIC could obtained by using NSCB specimens with a0/R = 0.3-0.5, D = 50mm and B = 20-65mm in this study. Compared with compacted clays, rock materials usually have smaller FPZ sizes. From [30], the rc values of Kimachi sandstone, Saudi Arabian limestone, Harsin marble, Johnstone-mudstone and Guiting limestone calculated by Eq. (6) are about 1.45, 5.1, 3.0, 3.6 and 2.3mm, respectively. It is indicated that the harder the material is, the greater rc value is, which is also an evidence that the FPZ size of the compacted clay tested in this study is reasonable. 5.3. Limitations The relationship between the KIC and σt is useful for predicting the the KIC from σt of compacted clays. In this study, an empirical formula KIC = 0.3283σt for directly compacted clays was obtained. However, the conclusion is based on the data from limited studies because few scholars tested the two parameters together. Therefore, more data of other directly 22
compacted clays are needed for full confirmation. The proportionality coefficient a of the linear fitting relationship could be used to predict the FPZ size of the tested compacted clay. Generally, the FPZ sizes of compacted clays are larger than those of rocks, thus it requires a larger size for compacted clay specimens than rock specimens. However, the suggested ratio of FPZ size to the minimum dimension of specimen is unclear. Investigated by the authors [17], the difference in values of KIC from the small size SENB specimens and the large size SENB specimens was very small, which showed there was no remarkable size-effect on the KIC of the compacted clay. In their study, the suggested ranges of initial notch length and the ligament length of the small size SENB specimens were 15-30mm and 20-35mm, it is indicated possibly that the minimum notch length or ligament length is not much larger than the FPZ size. Above all, the real FPZ sizes in compacted clay specimens are still unknown, this merits further research to experimentally characterize the FPZ size by studying the microcracking behavior of NSCB specimen in the KIC test. The specimen preparation method used in this study may is limited to clay with a small amount of gravel, if the content of gravel is large, it is difficult to prepare qualified specimens. Therefore, an improved method was proposed in Figure 18. Additionally, for the compacted clay 23
specimens in this paper, the crack plane is normal to the compacting plane, and the crack propagates in a direction parallel to the compacting plane. Similar to layered rocks [32], compacted clay could be treated as transversely isotropic, which leads the fracture toughness and tensile strength of compacted clay depend on direction of propagation of the crack in relation to the anisotropy. Further testing, however, is needed to study these issues.
6. Conclusions
(1) A sample preparation method for NSCB compacted clay specimen was established, NSCB specimen is easier to prepare and test than SENB specimen. NSCB specimen is cost-effective because it requires minimal soil material and effort to use, and it can provide mode I fracture parameters as reliably as that of SENB specimen. (2) A limit of initial notch length of a0/R = 0.3–0.5 was suggested for the compacted clay investigated in the present study. The KIC value decreases slightly as the B increases, there exists no remarkable thickness-dependent size effect over the range of conditions examined here. (3) The relationships between the KIC and σt of different compacted clays can be fitted by linear functions, but the proportionality coefficient 24
a depends on the compacted specimen preparation method. An empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays. (4) The FPZ size of the tested compacted clay can be calculated by an estimation method. In this way, the reasonability of the testing results was discussed and proved.
Acknowledgements The authors gratefully acknowledge the financial supports from the Open Research Fund of Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dam of the Ministry of Water Resources under Grant no. YK319001, the National Natural Science Foundation of China under Grant no. U1865103, and the National Key R&D Program of China under Grant no. 2018YFC1504903, respectively.
References [1] Wang JJ. Hydraulic fracturing in earth-rock fill dams. Singapore: John Wiley & Sons Singapore Pte. Ltd.; 2014. [2] Hoek E, Martin CD. Fracture initiation and propagation in intact rock – A review. Journal of Rock Mechanics and Geotechnical Engineering 2014; 6(4): 287-300. 25
Doi: http://dx.doi.org/10.1016/j.jrmge.2014.06.001 [3] Ulusay R. The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007-2014. Springer International Publishing 2014; 15(1): 47-48. Doi: https://doi.org/10.1007/978-3-319-07713-0 [4] Chandler HW. The use of non-linear fracture mechanics to study the fracture properties of soils. Journal of Agricultural Engineering Research 1984; 29(4): 321-327. Doi: https://doi.org/10.1016/0021-8634(84)90087-8 [5] Lee FH, Lo KW, Lee SL. Tension Crack Development in Soils. Journal of Geotechnical Engineering 1988; 114(8):915-929. Doi: https://doi.org/10.1061/(ASCE)0733-9410(1988)114:8(915) [6] Zhang ZG, Ding JS. Studies on the Fracture Toughness KIC of Cohesive Soil. Rock and Soil Mechanics 1993; 14(3): 47-52. (In Chinese) [7] Hanson JA, Hardin BO, Mahboub K. Fracture Toughness of Compacted Cohesive Soils Using Ring Test. Journal of Geotechnical Engineering 1994; 120(5): 872-891. Doi: https://doi.org/10.1061/(ASCE)0733-9410(1994)120:5(872) [8] Li HS, Yang HT. Experimental investigation of fracture toughness of 26
frozen soil. J Cold Region Eng 2000; 14(1): 43–9. Doi: https://doi.org/10.1061/(ASCE)0887-381X(2000)14:1(43) [9] Nishimura SI, Shimizu H. A study of the measurement of fracture toughness in cohesive soil – relationship between the size of initial crack and diameter of specimen. Paddy and Water Environment 2004; 2(1): 27-32. Doi: https://doi.org/10.1007/s10333-004-0036-5 [10] Aluko OB, Chandler HW. A Fracture strength parameter for brittle agricultural soils. Biosystems Engineering 2006; 93(2): 245-252. Doi: https://doi.org/10.1016/j.biosystemseng.2005.11.007 [11] Wang JJ, Zhu JG, Chiu CF, Zhang H. Experimental study on fracture toughness and tensile strength of a clay. Engineering Geology 2007; 94(1): 65-75. Doi: https://doi.org/10.1016/j.enggeo.2007.06.005 [12] Hallett PD, Dexter AR, Seville JPK. The application of fracture mechanics to crack propagation in dry soil. European Journal of Soil Science1995; 46(4): 591-599. Doi: https://doi.org/10.1111/j.1365-2389.1995.tb01355.x [13] Amarasiri AL, Costa S, Kodikara JK. Determination of cohesive 27
properties for mode I fracture from compacted clay beams. Canadian Geotechnical Journal 2011; 48(8): 1163-1173. Doi: https://doi.org/10.1139/T11-031 [14] Costa S, Kodikara J. Evaluation of J Integral for Clay Soils Using a New Ring Test. Geotechnical Testing Journal 2012; 35(6): 981-989. Doi: https://doi.org/10.1520/GTJ104271 [15] Lenci S, Clementi F, Sadowski T. Experimental determination of the fracture properties of unfired dry earth. Engineering Fracture Mechanics 2012; 87: 62-72. Doi: https://doi.org/10.1016/j.engfracmech.2012.03.005 [16] Lakshmikantha MR, Prat PC, Ledesma A. Experimental evidence of size effect in soil cracking. Canadian Geotechnical Journal 2012; 49(3): 264-284. Doi: https://doi.org/10.1139/t11-102 [17] Wang JJ, Huang SY, Hu JF. Limit of crack depth in KIC testing for a clay. Engineering Fracture Mechanics 2016; 164: 19-23. Doi: https://doi.org/10.1016/j.engfracmech.2016.08.006 [18] Cao KD. Determination of Mode I Fracture Toughness, Tensile Strength and Adhesion of Compacted Clays. Master’s thesis, University 28
of Calgary, Alberta, Canada. 2018. [19] Agaiby W. Fracture Characterization of Clays and Clay-Like Materials Using Flattened Brazilian Test. Master’s thesis, Massachusetts Institute of Technology, Massachusetts, United States. 2013. [20] ASTM Standard E399-12. Standard test method for linear-elastic plane-strain fracture toughness KIC of metallic materials. Annual book of ASTM standards. West Conshohocken, PA: ASTM International, 2013. [21] Chong KP, Kuruppu MD. New specimen for fracture toughness determination of rock and other materials. International Journal of Fracture 1984, 26(2): R59-R62. Doi: https://doi.org/10.1007/BF01157555 [22] Aliha MRM. Indirect tensile test assessments for rock materials using 3-D disc-type specimens. Arabian Journal of Geoscience 2014; 7, 4757–4766. Doi: https://doi.org/10.1007/s12517-013-1037-8 [23] Choi BH, Lee YK, Park C, et al. Measurement of tensile strength of brittle rocks using a half ring shaped specimen. Geosciences Journal 2018; 23(4), 649–660. [24] Kuruppu MD, Chong KP. Fracture toughness testing of brittle materials using semi-circular bend (SCB) specimen. Engineering Fracture 29
Mechanics, 2012; 91: 133–50. Doi: https://doi.org/10.1016/j.engfracmech.2012.01.013 [25] Kuruppu MD, Obara Y, Ayatollahi MR. ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen. Rock Mechanics and Rock Engineering 2014; 47(1): 267-274. Doi: https://doi.org/10.1007/s00603-013-0422-7 [26] Trade Standard of P.R. China, SL237-011, 1999. Standard method for moisture-density test of soils. Specification of Soil Test. The Ministry of Water Resources of P.R. China, Beijing, P.R. China (in Chinese) [27] Sorem WA, Dodds RH, Rolfe ST. Effects of crack depth on elastic-plastic fracture toughness. International Journal of Fracture 1991; 47(2): 105-126. Doi: https://doi.org/10.1007/BF00032572 [28] Lim IL, Johnston I W, Choi SK, Boland J. Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 1—Mode 1. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts 1994; 31(3): 185-197. Doi: https://doi.org/10.1016/0148-9062(94)90463-4 30
[29] Xu X, Wu S, Jin A, Gao Y. Review of the Relationships between Crack Initiation Stress, Mode I Fracture Toughness and Tensile Strength of Geo-Materials; International Journal of Geomechanics 2018; 18(10): 4018136. Doi: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001227 [30] Aliha M R M, Ayatollahi M R. Two-parameter fracture analysis of SCB rock specimen under mixed mode loading. Engineering Fracture Mechanics, 2013, 103: 115-123. Doi: https://doi.org/10.1016/j.engfracmech.2012.09.021 [31] Schmidt RA. A Microcrack model and its significance to hydraulic fracturing and fracture toughness testing. In: Proceedings of 21st US symposium rock mechanics; 1980. p. 581–590. [32] Chong KP , Kuruppu MD , Kuszmaul JS . Fracture toughness determination of layered materials. Engineering Fracture Mechanics, 1987, 28(1):43-54. Doi: https://doi.org/10.1016/0013-7944(87)90118-4
31
Fig. 1. Specimen geometry and loading configuration of NSCB specimen.
A F
B
Notch
R
R a0
a0
S
A
A
男女交谈为何如此困难 A
(a) Conventional method F
a0 R B Notch
(b) Improved method
32
Fig. 2. Compaction processes of tested soil.
33
Fig. 3. Semicircular cutting ring used to cut the large block into small specimens.
34
Fig. 4. Typical specimens employed in the tests.
35
Fig. 5. Testing system for loading.
36
Fig. 6. NSCB specimens with different a0/R employed in the tests.
37
Fig. 7. Typical load-displacement curves.
200 1
2
3
4
Load/N
160
120
80
40
0 0
1
2
3
Displacement/mm
(a) a0/R = 0.2 80 1
2
3
4
Load/N
60
40
20
0 0
1
2
Displacement/mm
(b) a0/R = 0.5
38
3
Fig. 8. Failure process of a typical NSCB specimen.
39
Fig. 9. Variation of KIC with a0/R.
25
KIC/kPa·m0.5
20
15
10 Experimental data Average 5 0
0.2
0.4 a0 /R
40
0.6
0.8
Fig. 10. Typical NSCB specimens with different thicknesses.
41
Fig. 11. Variation of KIC with B.
25
KIC/kPa·m0.5
20
15
10 Experimental data Average 5 5
20
35
42
50 B/mm
65
80
Fig. 12. Variation of KIC with w and ρ.
25
KIC/kPa·m0.5
20
15
10
Fitting curve 5 1.6
1.62
1.64
1.66 1.68 ρ / g·cm3
1.7
1.72
(a) KIC ~ ρ
25
KIC/kPa·m0.5
20
15
10
Fitting curve 5 14
16
18 w/%
(b) KIC ~ w 43
20
22
Fig. 13. Variation of σt with w and ρ.
100
σt / kPa
80
60
40
Fitting curve 20 1.6
1.62
1.64
1.66 1.68 ρ / g·cm3
1.7
1.72
(a) σt ~ ρ
100
σt / kPa
80
60
40
Fitting curve 20 14
16
18 w/%
(b) σt ~ w
44
20
22
Fig. 14. Failure process of a typical SCB specimen.
45
Fig. 15. Relationship between KIC and σt of the tested compacted clay.
35 This study 30
Fitting curve KIC = 0.28σt ; R² = 0.9357
KIC/kPa·m0.5
25 20 15 10 5 0 0
20
40
60
80
100
σt / kPa
(a) Linear relationship
35 This study
30
Fitting curve KIC = 0.2443σt 1.0318 ; R² = 0.9329
KIC/kPa·m0.5
25 20 15 10 5 0 0
20
40
60
80
σt / kPa
(b) Power-law relationship
46
100
Fig. 16. Relationships between KIC and σt of different compacted clays from references.
1000 Oven-dried compacted clay This study Hanson et al. [7] Wang et al. [11] Amarasiri et al. [13] Cao [18] Agaiby [19]
KIC/kPa·m0.5
100
Directly compacted clay 10
Air-dried compacted clay 1 1
10
100
σt / kPa
47
1000
10000
Fig. 17. Relationships between KIC and σt of directly compacted clays.
35 This study 30
Wang et al. [11]
KIC = 0.3546σt R² = 0.8814
Cao [18] 25
This study
KIC/kPa·m0.5
Wang et al. [11] 20
Cao [18]
15 KIC = 0.2800σt R² = 0.9357
10 5
KIC = 0.3179σt R² = 0.8261
0 0
20
40
60
80
100
σt / kPa
(a) Fitting relationship from respective test result 35 Directly compacted clays 30
Fitting curve
KIC/kPa·m0.5
25 20 15 10 5
KIC = 0.3283σt R² = 0.7800
0 0
20
40
60
80
100
σt / kPa
(b) Fitting relationship of all the data points
48
Fig. 18. A proposed NSCB specimen preparation method for clay mixed with gravel.
Empty assembled mould
Compacting clay soils in the mould
49
Prepared NSCB specimen
Table 1. Summary of experimental studies on mode I fracture parameters of various soil materials from references.
References
Materials
Specimen type
Specimen dimensions (mm)
Chandler [4]
Clay mixed with 5% ordinary Portland cement
Single-edge notched beam
S × W × B: 250 × 100 × 100
w: 26-42% ρ: 1.47-1.57 g/cm3
Four-point bending test
Jc
Lee et al. [5]
Overconsolidated cohesive soil
Compact tension specimen
S × W × B: 150 × 150 × 25
w: 40% ρ: unspecified
Compact tension test
GIC
Zhang and Ding [6]
Silty clay
Single-edge notched beam
S × W × B: 160 × 140 × 70
w: 15-19% ρ: 1.60-1.80 g/cm3
Uniaxial tension test
KIC
Hanson et al. [7]
Two residual soils from Kentucky
Circular ring
Rin × Rout × B: 6.25 × 50 × 12.5
w: 2-23% ρ: 1.64 g/cm3 and 1.89 g/cm3
Ring test
Jc
Single-edge notched beam
S × W × B: 210 × 70 × 70, 300 × 100 × 100, 420 × 140 × 140
w: 19.0-29.5% ρ: unspecified
Three-point bending test
KIC
Li and Yang [8]
Frozen Lanzhou loess
50
Specimen Condition
Test method
Parameter measured
Nishimura and Shimizu [9]
Soft pyroclastic ash loam
Centre crack cylinder
D × H: 70 × 100, 80 × 100, 90 × 100
w: 61-66% ρ: 0.95-0.97 g/cm3
Tri-axial compression test
GIC
Three-point bending test
KIC
Aluko and Chandler [10]
Sandy loam, clay loam, and cemented sand soil
Single-edge notched beam
S × W × B: 76 × 28 × 40
Sandy loam w: 176.0% ρ: 1.26-1.52 g/cm3 Clay loam w: 234.7% ρ: 1.16~1.40 g/cm3 Cemented sand soil w: 64.1% ρ: 1.49 g/cm3
Wang et al. [11]
Clay with a small amount of gravel
Single-edge notched beam
S × W × B: 185 × 46 × 23
w: 16.3- 9.3% ρ: 1.60-1.76 g/cm3
Three-point bending test
KIC
Hallett et al. [12]
Three mixtures of fine silica sand and kaolinite
Centre crack cylinder
D: 27.6, 52.0, 77.5, 102.3 H: unspecified
Dry soil
Splitting tension test
KIC
Amarasiri et al. [13]
Werribee clay
Single-edge notched beam
S × W × B: 100 × 30 × 30
w: 17.6-50.3% ρ: 1.01-1.87 g/cm3
Three-point bending test
KIC
Costa and Kodikara [14]
Werribee clay
Double circular ring
Rin × Rout × B: 33 × 104 × 12.5
wi: 252% ρ: unspecified
Ring test
Jc
51
Unfired dry earth
Single-edge notched beam
S × W × B: 355 × 112 × 85
Dry soil
Three-point bending test
KIC, CTODC
Barcelona silty clay
Compact tension specimen
S × W × B: 60 × 45 × 25, 120 × 90 × 50
w: 11-30% ρ: 1.40-1.60 g/cm3
Compact tension test
KIC
Wang et al. [17]
Red clay
Single-edge notched beam
S × W × B: 200 × 50 × 25, 320 × 80 × 40
Three-point bending test
KIC
Cao [18]
Calgary till and Regina clay
Straight notched disk bending
Unspecified
Three-point bending test
KIC
Agaiby [19]
Bangladesh Clay, Boston Blue Clay and Presumpscot Maine Clay
Flattened Brazilian disk
D × B: 60 × 20
Splitting tension test
KIC
Lenci et al. [15] Lakshmikantha et al. [16]
w: 16.6% ρ: 1.63 g/cm3 and 1.70 g/cm3 Calgary till w: 11-19.5% ρ: 1.75-1.85 g/cm3 Regina clay w: 19.5-31% ρ: 1.45-1.85 g/cm3 Dry soil
Note. KIC: Mode-I fracture toughness; GIC: Critical energy release rate; Jc: J integral; S: Effective length of specimen; W: Width of specimen; B: Thickness of specimen; D: Diameter of specimen; H: Height of specimen; Rin: Inner radius of specimen; Rout: outer radius of specimen; ρ: dry density; w: moisture content. 52
Table 2. ISRM-suggested dimensions for NSCB specimen.
Parameter
Suggested range or value
Radius of specimen (R)
Larger of 5 × grain size or 38 mm
Thickness of specimen (B)
Larger of 0.8R or 30 mm
Initial notch length ratio of specimen (a0/R)
0.4 ≤ a0/R ≤ 0.6
Loading distance ratio of specimen (S/2R)
0.5 ≤ S/2R ≤ 0.8
53
Table 3. Testing scheme of NSCB specimens. Testing scheme name
a0/R
w (%)
N-1
0.2, 0.3, 0.4, 0.5, 0.6, 0.7
16.6 14.6, 18.6, 20.6
N-2 N-3 N-4
A suggested value from N-1
ρ
B (mm)
Number of specimens
1.66
65
24
1.66
65
9
65
12
20, 35, 50
9
(g·cm3)
1.62, 1.64, 1.68, 1.70 1.66
16.6 16.6
Note. In N-1, four specimens were subjected to each test group; In N-2, N-3 and N-4, three parallel test groups were selected.
54
Table 4. Testing scheme of SCB specimens. Testing scheme name
w (%)
ρ (g·cm3)
B (mm)
Number of specimens
S-1
14.6, 16.6, 18.6, 20.6
1.66
65
12
S-2
16.6
1.62, 1.64, 1.68, 1.70
65
12
Note. In S-1 and S-2, three specimens were subjected to each test group.
55
Table 5. Testing results of SENB specimens.
No.
Peak load (N)
Values of KIC (kPa·m0.5)
1
10.3
19.6
2
12.1
23.0
3
9.5
18.0
4
11.1
21.1
Average value of KIC (kPa·m0.5)
20.4
56
Table 6. Relationships between KIC and σt of different compacted clays.
Researches
Specimen preparation method
a = KIC/σt
R2
Hanson et al. [7]
Air-dried compacted
0.0706
0.93
Wang et al. [11]
Directly compacted
0.3546
0.88
Amarasiri et al. [13]
Air-dried compacted
0.1700
0.99
Cao [18]
Directly compacted
0.3179
0.83
Agaiby [19]
Oven-dried compacted
0.1434
0.92
This study
Directly compacted
0.2800
0.94
57
Table 7. Estimation of the value of rc based on the relationship between KIC and σt of different compacted clays.
Researches
a = KIC/σt
rc (mm)
Hanson et al. [7]
0.0706
0.8
Wang et al. [11]
0.3546
20.0
Amarasiri et al. [13]
0.1700
4.6
Cao [18]
0.3179
16.1
Agaiby [19]
0.1434
3.3
This study
0.2800
12.5
58
Highlights (1) Notched semi-circular bending specimens were employed to determine the KIC of a compacted clay.
(2) The ratio of initial notch length to specimen radius a0/R = 0.3–0.5 was suggested.
(3) An empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays.
Conflict of Interest The authors declare that they have no conflict of interest.
59
S0013-7944(19)31129-4 https://doi.org/10.1016/j.engfracmech.2019.106814 EFM 106814
To appear in:
Engineering Fracture Mechanics
Received Date: Revised Date: Accepted Date:
16 September 2019 8 December 2019 9 December 2019
Please cite this article as: Wang, J., Huang, S., Guo, W., Qiu, Z., Kang, K., Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen, Engineering Fracture Mechanics (2019), doi: https://doi.org/10.1016/j.engfracmech.2019.106814
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© 2019 Published by Elsevier Ltd.
Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen Junjie Wang a, b, Shiyuan Huang a, b *, Wanli Guo b, Zhenfeng Qiu a, Kai Kang c a
Engineering
Research
Center
of
Diagnosis
Technology
and
Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China b
Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dam of the Ministry of Water Resources, Nanjing 210029, China
c
School of Environment and Civil Engineering, Jiangnan University, Wuxi, 214122, China
* Corresponding Author. E-mail address: [email protected] (Shiyuan Huang) Address: 66 Xuefu Road, Nan’an District, Chongqing, 400074, China Phone number: (8623) 6289 6924 Fax number: (8623) 6265 2841
1
Abstract: Single-edge notched beam specimens have been used widely to determine the fracture toughness KIC of compacted clays under three-point bending loading. However, this specimen type is not very suitable for the material with low strength. In this study, notched semi-circular bending specimens were employed to determine the KIC of a compacted clay, the effects of initial notch length, specimen thickness, moisture content and dry density on KIC were investigated. Based on the testing results, the ratio of initial notch length to specimen radius a0/R = 0.3–0.5 was suggested. There was no remarkable thickness-dependent size effect for the compacted clay. To investigate the relationship between the KIC and tensile strength σt of the compacted clay, unnotched semi-circular bending specimens were employed for determining the σt. It is concluded that there is a good linear relationship between these two parameters. According to the discussion on the testing results of different compacted clays, an empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays. Additionally, the size of fracture process zone of the compacted clay was calculated by an estimation method. Keywords: Compacted clay; Fracture toughness; Semi-circular bend; Tensile strength
2
1. Introduction Fracture mechanics has become an important field of study for solving safety problems related to the strength of geomaterials used in civil engineering. For instance, it can be used to predict and identify the failure of structures made of geomaterials, thereby providing instruction for improving the safety of such structures as well as for analyzing the hydraulic fracturing, slope stability, excavation process [1]. In fracture processes that are not associated with high strain rates, mode I fracture toughness (KIC) is the crucial property that reflects a material’s ability to resist crack initiation and propagation. It is determined from the stress intensity factor (KI) at which a thin crack begins to grow in the material. Due to the weakness of geomaterials under tension state, mode I fracture is most frequently encountered among the three basic fracture modes [2]. Therefore, it is important to develop convenient testing approaches for accurately measuring KIC of geomaterials. The International Society for Rock Mechanics and Rock Engineering (ISRM) has suggested several standard testing methods to determine KIC of rock materials [3]. However, clay soil, another geomaterial that is often used as the core of dams and the liner in landfills, has been investigated less frequently than rocks. Until now, none of generally acknowledged methods has been proposed for determining KIC of clay soil, the KIC of clay soils has been investigated by various test methods as summarized in Table 1 [4-19]. 3
In earlier studies, Lee et al. [5] and Lakshmikantha et al. [9] used the compact tension specimen to investigate the KIC of clay soils. Due to the complex specimen geometry and the complicated sample preparation, this method which is suggested by American Society of Testing Materials (ASTM) [20] for metallic materials, is quite inconvenient. Compared with direct tension method mentioned above, indirect method is more easily. Splitting test is a typical indirect tension method, the sample structure such as Brazilian disk is simple. However, the unpredictability of fracturing path may compromise the accuracy of the measurement, which is not suitable for clay soils. As shown in Table 1, three-point bending test on a single-edge notched beam (SENB) specimen, another suggested method by ASTM, has been used most widely because of its simple sample structure and convenient operation. However, Amarasiri et al. [13] noted that it is difficult to conduct tests on large-sized SENB clay soil specimens because they have low strength, and therefore, self-weight plays a major role. To solve this problem, Wang et al. [11] proposed an improved method in which the effect of self-weight was eliminated. Unlike in the case of rock, concrete, and asphalt specimens, clay soil fracture specimens cannot be prepared using a cutting machine or by a pouring action. Generally, a clay soil specimen is prepared by a compacting action and the artificial pre-crack is prepared by a cutting 4
sharp knife. Therefore, it can be easily influenced by different disturbances before tests such as crack prefabrication and specimen transfer due to its low strength. Thus, disturbances during test preparation cannot be ignored. As shown in Table 1, the length-width ratio of SENB specimens in references [4], [8], [10], [11], [13], [15], and [17] were 2.5, 3.0, 2.7, 4.0, 3.3, 3.0, and 4.0, respectively. If an SENB specimen’s length-width ratio is too large, it may break under a light load before test loading. For example, the peak load of a typical SENB specimen was about 13 N in [11], peak loads of SENB test specimens of three different dry densities were about 4, 8, and 15 N in [10], maximum and minimum peak loads of SENB test specimens with different moisture contents were respectively about 80 and 3 N in [13], and the maximum peak load of SENB test specimens was about 40 N in [17]. Overall, the peak loads of SENB clay soil specimens are usually low. Consequently, relatively light disturbance during test preparation may cause the specimen to break and thereby influence the test efficiency. If the specimen has small dimensions, the impact of the above-mentioned problems will reduce. Furthermore, less clay soil material will be required, thereby improving the efficiency of laboratory tests. Semi-circular bend specimen, usually used for rock fracture testing seems a good alternative for clay soil material because of its small size 5
and simple test procedure. For clarity, specimen with notch is called NSCB specimen, and specimen without notch is called SCB specimen. Initially, Chong et al. [21] proposed NSCB specimen for rock materials, then many researchers used the specimen for fracture testing of other materials. So far, researchers have not experimentally studied the KIC of clay soils using this specimen type. In the present study, mode I fracture toughness KIC of a compacted clay was obtained experimentally using NSCB specimen. The effects of specimen dimensions and clay characteristics on KIC were investigated and the reasonability of test results was discussed. On the other hand, tensile strength σt, also represents the ability of the material to resist failure under tension condition, has a correlation with KIC [11]. Thus as the second step of this study, three-point bending test on SCB specimen, which is an indirect tension method generally used in rock materials [22, 23], was used to determine the σt of the same clay. The relationship between KIC and σt of the tested clay was obtained. Finally, based on the testing results of different compacted clays from references, a discussion was made.
2. Testing Method 2.1. Mode I fracture toughness
6
Fig. 1a shows the dimensions for NSCB specimens suggested by ISRM. In the Figure, R is the semicircular specimen radius, B is the semicircular specimen thickness, a0 is the initial notch length, S is the distance between support points, and F is the load on the specimen. With the conventional loading assembly shown in Fig. 1a, both the NSCB clay specimen’s self-weight and load F both act in the vertically downward direction. The clay’s self-weight may strongly affect the test results owing to its low tensile strength, and therefore, it cannot be neglected. To minimize or eliminate the influence of self-weight, the improved loading assembly shown in Fig. 1b was used, in which the direction of load F was perpendicular to that of the self-weight. The details of the test procedure were illustrated in the next section. According to linear elastic fracture mechanics, the fracture initiates from the crack tip as the load F reaches the peak Fmax, and the KIC value of the NSCB specimen can be determined using the following equations [24]:
K IC =Y
Fmax a0 2 BR
(1)
S S a0 S a ) (1.071 34.401 ) 0 Y = 1.297 9.516 (0.47 16.457 2R 2R R 2R R
2
(2)
where Y is the nondimensional stress intensity factor (SIF) corresponding 7
to specimen geometry. Table 2 shows the ISRM-suggested dimensions for NSCB specimen. Notably, Eq. (2) is only valid for a0/R ≥ 0.2 [24]. 2.2. Tensile strength In tension test, the SCB specimen geometry and loading configuration are the same to those of the NSCB specimen (Fig. 1) except for no notch. Aliha [22] suggested a formula that can be used to estimate the tensile strength by conducting this specimen. The σt value of the SCB specimen can be computed by the following formula.
B
S
F
t 0.146 0.8896 4.02 1.052 max 2R 2R BR
(3)
3. Specimen Preparation and Testing Scheme 3.1. Testing material The test specimens were prepared using clay obtained from a construction site in Chongqing, China. The basic physical properties of the clay are as follows: specific gravity GS = 2.72, plasticity index IP = 20.1, liquid limit WL = 50.1%, plastic limit WP = 30.0%, maximum dry density ρmax = 1.68 g/cm3, and optimum moisture content wop = 16.6%. It consists of the following different grain size fractions: 0.5–0.25 mm (0.5%), 0.25–0.1 mm (17.9%), 0.1–0.075 mm (41.6%), and <0.075 mm 8
(40.0%). 3.2. Testing Scheme In order to obtain a reasonable or valid KIC value by using NSCB specimen, the reasonable geometric size for NSCB specimen should be selected first. For the radius of specimen R, ISRM-suggested dimension is larger than 5 × grain size or 38 mm. Because the maximum grain size of the clay is 0.5mm, the suggested R value should be larger than 2.5mm or 38mm (the bigger value should be selected), thus R = 50mm was used in this study. The loading distance ratio of specimen S/2R was recommended as 0.5-0.8, a high ratio approaching to 0.8 was preferred unless the material is too weak to be tested [24, 25]. According to the attempts before the test, S/2R = 0.8 was proved to be suitable for the tested clay with different moisture contents around the optimum moisture content. The KIC testing scheme is shown in Table 3. In N-1, 24 NSCB specimens with six different a0/R values were tested first. By contrast, for the same tested clay, three-point bending tests on four SENB specimens with a0/W = 0.4 (where W is the specimen width) were conducted. The specimen dimensions were the same as those in the study by Wang et al. [17], their study results indicated that constant KIC value could be obtained with this initial length ratio. After the limit of notch length of 9
a0/R was suggested, the effects of thickness of specimen B, moisture content w and dry density ρ on KIC were investigated in N-2, N-3 and N-4. As shown in Table 4, 24 SCB specimens were employed for determining the σt of the compacted clay. 3.3. Specimen Preparation The SENB specimens were prepared by the method of Wang et al. [11]. The NSCB and SCB specimens were processed as follows: (1) The weight of clay to be prepared was calculated according to the desired moisture content and dry density of the specimen as shown in Table 3 and Table 4. A rectangular specimen with 440-mm length, 100-mm width, and 65-mm height (when B = 65 mm) was compacted in a custom-made rectangular compaction device (440 mm × 100 mm × 200 mm) according to Trade Standard of P. R. China [26]. The specimen was compacted in three layers with equal weight and equal thickness of the soil. To eliminate the influence of excess pore water pressure on testing, the specimen was stored in a sealed container for at least 24 h. Fig. 2 shows the compaction process. (2) A semicircular cutting ring (SCCR) with one sharp edge was designed to cut the rectangular specimen into small specimens. The inner diameter and thickness of SCCR are the same as the diameter and 10
thickness of NSCB and SCB specimens (Fig. 3). Eight SCCRs were placed on the compacted rectangular specimen and then completely embedded into them using a compaction hammer to obtain eight SCB specimens. In the process, vaseline should be applied to the SCCR surface to separate it easily from the SCB specimen. (3) For NSCB specimen, a notch with 1.8-mm width was created using a thin, sharp knife. Fig. 4 displays typical specimens employed in the tests. 3.4. Testing Procedure These tests were conducted in the Key Laboratory for Hydraulic and Waterway Engineering of the Ministry of Education of Chongqing Jiaotong University. A soil fracture mechanic testing system (Jiangsu Yongchang Science and Education Instrument Manufacturing Co. Ltd., Leiyang, Jiangsu Province, China) was utilized for loading with a loading rate of 0.8 mm/min. The loading assembly shown in Fig. 5, which was developed based on the loading assembly shown in Fig. 1, was used to conduct the experiments. It consists of a load sensor, a displacement sensor, an indenter, two support pins, a graduated scale, two slidable baseplates, and a data logger. Additionally, it has a horizontal loading direction, thereby 11
eliminating the influence of the specimen’s self-weight on the testing results.
4. Results and analysis 4.1. The effect of a0/R on KIC As shown in Fig. 6, three-point bending tests on 24 NSCB specimens with six different a0/R values were conducted. Fig. 7 shows typical load versus displacement curves of NSCB specimens with a0/R = 0.2 and 0.5. The plots clearly show that before the F value reaches its peak, the load versus displacement relationship is almost linear. The F value reaches its peak at a displacement of 1.65–2.33 mm for specimens with a0/R = 0.2, and the F value reaches its peak at a displacement of 0.54–1.52 mm for specimens with a0/R = 0.5, beyond which it decreases rapidly. The KI value can be calculated using Eq. (1) and Eq. (2). When the peak F value was used, the calculated KI value equaled the KIC value. Fig. 8 shows the failure mode of the NSCB specimens under mode I loading conditions, the crack clearly propagated along the initial fracture plane. Fig. 9 shows the experimental data for NSCB specimens with different a0/R values. Overall, the KIC value decreases as the a0/R value increases. When 0.3 ≤ a0/R ≤ 0.5, the mean KIC value is nearly constant. 12
As a mechanical parameter of material, the value of KIC should be a constant value, so that it could be regarded as a valid value [17, 24, 27, 28]. The limit of notch length may be due to the discreteness problem of clay soil or the size of fracture process zone (FPZ), it will be discussed later. The constant KIC value of this tested clay as obtained using NSCB specimens is about 18.3 kPa·m0.5. As shown in Table 5, the average KIC value of SENB specimens is 20.4 kPa·m0.5, indicating that the NSCB specimen gives somewhat conservative results for the KIC. The error of the NSCB specimen KIC value with respect to the SENB specimen KIC value is about 10%, which could be acceptable in geotechnical engineering. Therefore, it can be indicated that a reasonable KIC value of the compacted clay could be obtained using NSCB specimen. During the tests, two SENB specimens were reworked due to specimen damage. Table 5 shows that the average peak load of SENB specimens is around 10 N, this value is too low and therefore, specimens can easily break during test preparation. While the average peak loads of NSCB specimens (a0/R = 0.3, 0.4, and 0.5) are 114.5, 86.6, and 62.3 N, and these are around 11, 9, and 6 times larger than those of SENB specimens, respectively. It implies that the NSCB specimen is less susceptible to disturbance before test. It also indicates that KIC value of NSCB specimen 13
is more sensitive to notch length than that of SENB specimen because the peak value of loading is linear with KIC value. As a result, the limit of notch length of these NSCB clay specimens is suggested a0/R = 0.3–0.5, which is slightly different from the range suggested by ISRM. In the following tests, a0/R = 0.4 was used. 4.2. The effect of B on KIC The effect of specimen thickness B on KIC was examined by conducting a series of tests on the NSCB specimens with four specimen thicknesses (Fig. 10). Fig. 11 plots the KIC values changing with respect to the specimen thickness B, it appears that the KIC value decreases as B increases and tends to be stable when B ≥ 50. However, the difference of these data is small (the error between the maximum KIC and minimum KIC is less than 5%), the KIC values of four specimen thicknesses could be regarded as a constant. Thus, it is indicated that there exists no remarkable thickness-dependent size effect for the compacted clay specimens used in this study and the KIC values of specimens with B ≥ 20mm could represent the plane strain KIC. 4.3. The effects of w and ρ on KIC and σt For a compacted clay, the moisture content w and dry density ρ are two main influence factors on its strength. As shown in Fig. 12a, the 14
values of KIC are increasing with increasing the ρ from 1.62 to 1.70 for w of 16.6%. This result is consistent with the results of Wang et al. [11] and Hanson et al. [7]. As a greater compaction effort is required to compact a denser specimen, the value of KIC also increases with the compaction effort. Fig. 12b shows that the values of KIC are decreasing with increasing the w from 14.6% to 20.6% for ρ of 1.66 g/cm3. This is consistent with the results of Harison et al. [7] and Cao [18]. As shown in Fig. 13, the σt of compacted clay increases with increasing ρ and decreasing w. The effects of ρ on KIC and σt are similar, and the effects of w on KIC and σt are also similar. Fig. 14 shows a typical SCB specimen right before and after fracturing, the failure mode is similar to that of NSCB specimen. It is therefore reasonable to assume the parameters KIC and σt of the compacted clay are positively correlated. 4.4. The relationship between KIC and σt Generally, KIC = aσt has been used to described the relationship between KIC and σt [7, 11, 13, 18, 19], where a is proportionality coefficient. In Fig. 15a, the data points were plotted and the relationship between KIC and σt was fitted by a linear curve. The result of correlation is: KIC = 0.2800σt
R2 = 0.9357
(4)
which shows a reasonably high coefficient. Meanwhile, a power-law 15
function is used to fit their relationship shown in Fig. 15b, the result of correlation is: KIC = 0.2443σt1.0318
R2 = 0.9329
(5)
Above all, both of linear regression and power-law regression are fitted well. However, using fewer parameter to predict the relationship in practical engineering is more convenient, so the linear function (Eq. 4) is used generally. The empirical relationship could provide a helpful method for estimating the KIC from the σt of materials which can be measured more easily.
5. Discussion 5.1. Relationships between KIC and σt of different compacted clays Currently, only a few scholars have attempted to investigate the relationship between the KIC and σt of compacted clays (Table 6). All of them found that the KIC has a linear relationship with σt and these two properties coexist or vanish simultaneously. As shown in Table 6, the values of proportionality coefficient a are various according to different studies, the maximum value is 0.3546 and the minimum value is 0.0706. The reasons for the difference can be summarized [11, 18, 19, 29] as follows: (1) Different components of the tested compacted clay; (2) Different KIC test methods; (3) Different σt test methods. (4) Different 16
preparation methods of compacted clay. In order to investigate the reason, the data points of various compacted clays from the different studies were replotted in log-log scale in Fig. 16. Harison et al. [7] compacted the ring test specimens and then air dried them to designated moisture content. Amarasiri et al. [13] used the same method to prepare specimens, then the KIC was determined using SENB specimens and the σt was back-calculated by matching the numerically modelled load-load point displacement curves. In the study of Agaiby [19], the specimens were kept in a 40 degrees oven to maintain dry until the testing procedure started. Cao [18], Wang et al [11] and this study used directly compacted clay specimens without drying process, the weight of the soil and water used was calculated according to the moisture content and the dry density of each specimen to be prepared. As discussed above, it can be concluded that the linear fitting correlation is appropriate to all types of clays. As shown in Table 6 and Fig. 16, it can be indicated that the relationship between KIC and σt depends on the specimen preparation method. Compared with directly compacted clays, oven-dried compacted clays and air-dried compacted clays usually have larger values of KIC and σt due to the loss of water. Moreover, the proportionality coefficients are generally smaller. Though a same regularity was found that low moisture 17
contents contribute to high KIC or σt of compacted clays, but for the same clay, directly compacted specimen and air-dried or oven-dried compacted clay specimen with a same moisture content may have different soil structures due to the different moulding moisture contents. Using air-drying or oven-drying method to prepare specimens, it is easy to develop desiccation cracks in the specimens especially at a high temperature. In addition, the water distribution in the specimens is nonuniform that leads the specimens have obvious heterogeneity. The above reasons may make the proportionality coefficients of the fitting equations of air-dried and oven-dried compacted clays various. For directly compacted clays, the moisture contents selected in test are usually near the optimal moisture content because it is difficult to compact drier and wetter clay specimens. Thus, directly compacted clay generally have a smaller strength range and a larger proportionality coefficient a. The range of KIC in this study is about 8-25 kPa·m0.5, which is close to that of Wang et al. [11] (range is 5-35 kPa·m0.5) and Cao [18] (range is 2-30 kPa·m0.5). The range of σt in this paper is approximately 35-87 kPa, which is also close to that obtained by Wang et al. [11] (range is 20-90 kPa) and Cao [18] (range is 5-90 kPa). As shown in Fig. 17a, the data points of three directly compacted clays are close and the a values of the linear fitting functions are also close. If the data points of the three 18
directly compacted clays are fitted by a linear function, it can be also found that there is a good linear fitting relationship, as shown in Fig. 17b, whose proportionality coefficient a is 0.3283 and correlation coefficient R2 is about 0.80. Though the properties such as liquid limit, plastic limit, maximum density and optimum moisture content of these directly compacted clays are different, a similar linear relationship could be used for them. For the core of an earth-rock fill dam, the clay as its material is always compacted by compacting plants. Therefore, this empirical formula can be used to preliminarily predict the KIC of the core clay of an earth-rock fill dam during the construction period. 5.2. Fracture process zone According to the conventional linear elastic fracture mechanics (LEFM), the valid KIC can be obtained as long as the fracture process zone (FPZ) is reasonably small compared with the specimen dimensions such as initial notch length, specimen thickness and ligament length. Generally, a sufficiently large specimen size is required that the effect of FPZ could be neglected [13, 24, 28, 30, 31]. However, the dimension requirements of the standards for rock and metallic materials seem too restrictive for clay materials. According to ASTM E399-12 [20] for metallic materials, the initial notch length, the specimen thickness and the ligament length of SENB specimens must 19
each be larger than 2.5 (KIC/σys)2, where σys is the yield strength. Because the yield strength could not be defined on load displacement curves easily for geomaterials, the tensile strength σt is usually used instead. Thus the values of 2.5 (KIC/σt)2 can be calculated by the relationships between KIC and σt of different compacted clays as shown in Table 6. Investigated by Wang et al. [11], the values of 2.5 (KIC/σt)2 are around 300mm, which are 10 times larger than the dimensions of specimens they used. Investigated by Amarasiri et al. [13], the values are about 70mm, which are also larger than the dimensions of specimens they used. For rock materials, Chong et al. [32] suggested a dimension requirement for the NSCB specimen that the specimen diameter D should be greater than 2.0 (KIC/σt)2. Based on this requirement, the values of 2.0 (KIC/σt)2 of the tested clay in this study are around 150mm, which are 1.5 times larger than the value of D. From above analysis, it seems that the size of compacted clay specimens required according to these standards is impractical. Amarasiri et al. [13] thought the validity of results obtained by testing is uncertain because the lack of a standard for testing KIC of compacted clay materials. To assess this, the apparent lengths of FPZs at peak load were retrieved from numerical models in their study. Results showed that the sizes of FPZs are all smaller than the dimensions of specimens they used, moreover, they are much smaller than the values of 20
2.5 (KIC/σt)2. It is indicated that the FPZ size of compacted clay is overestimated by using the standards for rock and metallic materials. In rock fracture mechanics, the critical distance rc, usually considered as the size of FPZ in front of the crack tip, is generally assumed to be a constant parameter material property [30]. Schmidt [31] suggested that the size of FPZ in rock materials can be estimated from: 1 K IC rc = 2 t
2
(6)
It is obviously seen that the value of rc is related to KIC and σt. This equation is used widely in rock materials, but it is not clear whether it can be used in compacted clays. In order to verify the applicability of the formula in compacted clay materials, the rc values of different compacted clays mentioned in Section 5.1 were calculated by this equation. As shown in Table 7, it is seen that the rc of the SENB specimens used by Amarasiri et al. [13] is about 4.6mm, which is close to their calculated value. In their study, the FPZ size of a specimen with the highest moisture content w = 50.3% is about 4.2mm. Thus, it indicates that using Eq. (6) to estimate the size of FPZ of compacted clays approximately is possible. In this way, the rc value of the clay tested in this study is about 12.5mm, which is much smaller than the specimen diameter D = 50mm. According to the suggested notch length ratio of 21
NSCB clay specimens in this study, the ranges of notch length and the ligament length are 15-25mm and 25-35mm, respectively. When a0/R = 0.5, the initial notch length a0 = 25mm and the ligament length a0 = 25mm are twice larger than the value of rc. All the dimensions of the specimens used in this study are greater than the rc value estimated by Eq. (6). Above all, a reasonable and valid KIC could obtained by using NSCB specimens with a0/R = 0.3-0.5, D = 50mm and B = 20-65mm in this study. Compared with compacted clays, rock materials usually have smaller FPZ sizes. From [30], the rc values of Kimachi sandstone, Saudi Arabian limestone, Harsin marble, Johnstone-mudstone and Guiting limestone calculated by Eq. (6) are about 1.45, 5.1, 3.0, 3.6 and 2.3mm, respectively. It is indicated that the harder the material is, the greater rc value is, which is also an evidence that the FPZ size of the compacted clay tested in this study is reasonable. 5.3. Limitations The relationship between the KIC and σt is useful for predicting the the KIC from σt of compacted clays. In this study, an empirical formula KIC = 0.3283σt for directly compacted clays was obtained. However, the conclusion is based on the data from limited studies because few scholars tested the two parameters together. Therefore, more data of other directly 22
compacted clays are needed for full confirmation. The proportionality coefficient a of the linear fitting relationship could be used to predict the FPZ size of the tested compacted clay. Generally, the FPZ sizes of compacted clays are larger than those of rocks, thus it requires a larger size for compacted clay specimens than rock specimens. However, the suggested ratio of FPZ size to the minimum dimension of specimen is unclear. Investigated by the authors [17], the difference in values of KIC from the small size SENB specimens and the large size SENB specimens was very small, which showed there was no remarkable size-effect on the KIC of the compacted clay. In their study, the suggested ranges of initial notch length and the ligament length of the small size SENB specimens were 15-30mm and 20-35mm, it is indicated possibly that the minimum notch length or ligament length is not much larger than the FPZ size. Above all, the real FPZ sizes in compacted clay specimens are still unknown, this merits further research to experimentally characterize the FPZ size by studying the microcracking behavior of NSCB specimen in the KIC test. The specimen preparation method used in this study may is limited to clay with a small amount of gravel, if the content of gravel is large, it is difficult to prepare qualified specimens. Therefore, an improved method was proposed in Figure 18. Additionally, for the compacted clay 23
specimens in this paper, the crack plane is normal to the compacting plane, and the crack propagates in a direction parallel to the compacting plane. Similar to layered rocks [32], compacted clay could be treated as transversely isotropic, which leads the fracture toughness and tensile strength of compacted clay depend on direction of propagation of the crack in relation to the anisotropy. Further testing, however, is needed to study these issues.
6. Conclusions
(1) A sample preparation method for NSCB compacted clay specimen was established, NSCB specimen is easier to prepare and test than SENB specimen. NSCB specimen is cost-effective because it requires minimal soil material and effort to use, and it can provide mode I fracture parameters as reliably as that of SENB specimen. (2) A limit of initial notch length of a0/R = 0.3–0.5 was suggested for the compacted clay investigated in the present study. The KIC value decreases slightly as the B increases, there exists no remarkable thickness-dependent size effect over the range of conditions examined here. (3) The relationships between the KIC and σt of different compacted clays can be fitted by linear functions, but the proportionality coefficient 24
a depends on the compacted specimen preparation method. An empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays. (4) The FPZ size of the tested compacted clay can be calculated by an estimation method. In this way, the reasonability of the testing results was discussed and proved.
Acknowledgements The authors gratefully acknowledge the financial supports from the Open Research Fund of Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dam of the Ministry of Water Resources under Grant no. YK319001, the National Natural Science Foundation of China under Grant no. U1865103, and the National Key R&D Program of China under Grant no. 2018YFC1504903, respectively.
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Fig. 1. Specimen geometry and loading configuration of NSCB specimen.
A F
B
Notch
R
R a0
a0
S
A
A
男女交谈为何如此困难 A
(a) Conventional method F
a0 R B Notch
(b) Improved method
32
Fig. 2. Compaction processes of tested soil.
33
Fig. 3. Semicircular cutting ring used to cut the large block into small specimens.
34
Fig. 4. Typical specimens employed in the tests.
35
Fig. 5. Testing system for loading.
36
Fig. 6. NSCB specimens with different a0/R employed in the tests.
37
Fig. 7. Typical load-displacement curves.
200 1
2
3
4
Load/N
160
120
80
40
0 0
1
2
3
Displacement/mm
(a) a0/R = 0.2 80 1
2
3
4
Load/N
60
40
20
0 0
1
2
Displacement/mm
(b) a0/R = 0.5
38
3
Fig. 8. Failure process of a typical NSCB specimen.
39
Fig. 9. Variation of KIC with a0/R.
25
KIC/kPa·m0.5
20
15
10 Experimental data Average 5 0
0.2
0.4 a0 /R
40
0.6
0.8
Fig. 10. Typical NSCB specimens with different thicknesses.
41
Fig. 11. Variation of KIC with B.
25
KIC/kPa·m0.5
20
15
10 Experimental data Average 5 5
20
35
42
50 B/mm
65
80
Fig. 12. Variation of KIC with w and ρ.
25
KIC/kPa·m0.5
20
15
10
Fitting curve 5 1.6
1.62
1.64
1.66 1.68 ρ / g·cm3
1.7
1.72
(a) KIC ~ ρ
25
KIC/kPa·m0.5
20
15
10
Fitting curve 5 14
16
18 w/%
(b) KIC ~ w 43
20
22
Fig. 13. Variation of σt with w and ρ.
100
σt / kPa
80
60
40
Fitting curve 20 1.6
1.62
1.64
1.66 1.68 ρ / g·cm3
1.7
1.72
(a) σt ~ ρ
100
σt / kPa
80
60
40
Fitting curve 20 14
16
18 w/%
(b) σt ~ w
44
20
22
Fig. 14. Failure process of a typical SCB specimen.
45
Fig. 15. Relationship between KIC and σt of the tested compacted clay.
35 This study 30
Fitting curve KIC = 0.28σt ; R² = 0.9357
KIC/kPa·m0.5
25 20 15 10 5 0 0
20
40
60
80
100
σt / kPa
(a) Linear relationship
35 This study
30
Fitting curve KIC = 0.2443σt 1.0318 ; R² = 0.9329
KIC/kPa·m0.5
25 20 15 10 5 0 0
20
40
60
80
σt / kPa
(b) Power-law relationship
46
100
Fig. 16. Relationships between KIC and σt of different compacted clays from references.
1000 Oven-dried compacted clay This study Hanson et al. [7] Wang et al. [11] Amarasiri et al. [13] Cao [18] Agaiby [19]
KIC/kPa·m0.5
100
Directly compacted clay 10
Air-dried compacted clay 1 1
10
100
σt / kPa
47
1000
10000
Fig. 17. Relationships between KIC and σt of directly compacted clays.
35 This study 30
Wang et al. [11]
KIC = 0.3546σt R² = 0.8814
Cao [18] 25
This study
KIC/kPa·m0.5
Wang et al. [11] 20
Cao [18]
15 KIC = 0.2800σt R² = 0.9357
10 5
KIC = 0.3179σt R² = 0.8261
0 0
20
40
60
80
100
σt / kPa
(a) Fitting relationship from respective test result 35 Directly compacted clays 30
Fitting curve
KIC/kPa·m0.5
25 20 15 10 5
KIC = 0.3283σt R² = 0.7800
0 0
20
40
60
80
100
σt / kPa
(b) Fitting relationship of all the data points
48
Fig. 18. A proposed NSCB specimen preparation method for clay mixed with gravel.
Empty assembled mould
Compacting clay soils in the mould
49
Prepared NSCB specimen
Table 1. Summary of experimental studies on mode I fracture parameters of various soil materials from references.
References
Materials
Specimen type
Specimen dimensions (mm)
Chandler [4]
Clay mixed with 5% ordinary Portland cement
Single-edge notched beam
S × W × B: 250 × 100 × 100
w: 26-42% ρ: 1.47-1.57 g/cm3
Four-point bending test
Jc
Lee et al. [5]
Overconsolidated cohesive soil
Compact tension specimen
S × W × B: 150 × 150 × 25
w: 40% ρ: unspecified
Compact tension test
GIC
Zhang and Ding [6]
Silty clay
Single-edge notched beam
S × W × B: 160 × 140 × 70
w: 15-19% ρ: 1.60-1.80 g/cm3
Uniaxial tension test
KIC
Hanson et al. [7]
Two residual soils from Kentucky
Circular ring
Rin × Rout × B: 6.25 × 50 × 12.5
w: 2-23% ρ: 1.64 g/cm3 and 1.89 g/cm3
Ring test
Jc
Single-edge notched beam
S × W × B: 210 × 70 × 70, 300 × 100 × 100, 420 × 140 × 140
w: 19.0-29.5% ρ: unspecified
Three-point bending test
KIC
Li and Yang [8]
Frozen Lanzhou loess
50
Specimen Condition
Test method
Parameter measured
Nishimura and Shimizu [9]
Soft pyroclastic ash loam
Centre crack cylinder
D × H: 70 × 100, 80 × 100, 90 × 100
w: 61-66% ρ: 0.95-0.97 g/cm3
Tri-axial compression test
GIC
Three-point bending test
KIC
Aluko and Chandler [10]
Sandy loam, clay loam, and cemented sand soil
Single-edge notched beam
S × W × B: 76 × 28 × 40
Sandy loam w: 176.0% ρ: 1.26-1.52 g/cm3 Clay loam w: 234.7% ρ: 1.16~1.40 g/cm3 Cemented sand soil w: 64.1% ρ: 1.49 g/cm3
Wang et al. [11]
Clay with a small amount of gravel
Single-edge notched beam
S × W × B: 185 × 46 × 23
w: 16.3- 9.3% ρ: 1.60-1.76 g/cm3
Three-point bending test
KIC
Hallett et al. [12]
Three mixtures of fine silica sand and kaolinite
Centre crack cylinder
D: 27.6, 52.0, 77.5, 102.3 H: unspecified
Dry soil
Splitting tension test
KIC
Amarasiri et al. [13]
Werribee clay
Single-edge notched beam
S × W × B: 100 × 30 × 30
w: 17.6-50.3% ρ: 1.01-1.87 g/cm3
Three-point bending test
KIC
Costa and Kodikara [14]
Werribee clay
Double circular ring
Rin × Rout × B: 33 × 104 × 12.5
wi: 252% ρ: unspecified
Ring test
Jc
51
Unfired dry earth
Single-edge notched beam
S × W × B: 355 × 112 × 85
Dry soil
Three-point bending test
KIC, CTODC
Barcelona silty clay
Compact tension specimen
S × W × B: 60 × 45 × 25, 120 × 90 × 50
w: 11-30% ρ: 1.40-1.60 g/cm3
Compact tension test
KIC
Wang et al. [17]
Red clay
Single-edge notched beam
S × W × B: 200 × 50 × 25, 320 × 80 × 40
Three-point bending test
KIC
Cao [18]
Calgary till and Regina clay
Straight notched disk bending
Unspecified
Three-point bending test
KIC
Agaiby [19]
Bangladesh Clay, Boston Blue Clay and Presumpscot Maine Clay
Flattened Brazilian disk
D × B: 60 × 20
Splitting tension test
KIC
Lenci et al. [15] Lakshmikantha et al. [16]
w: 16.6% ρ: 1.63 g/cm3 and 1.70 g/cm3 Calgary till w: 11-19.5% ρ: 1.75-1.85 g/cm3 Regina clay w: 19.5-31% ρ: 1.45-1.85 g/cm3 Dry soil
Note. KIC: Mode-I fracture toughness; GIC: Critical energy release rate; Jc: J integral; S: Effective length of specimen; W: Width of specimen; B: Thickness of specimen; D: Diameter of specimen; H: Height of specimen; Rin: Inner radius of specimen; Rout: outer radius of specimen; ρ: dry density; w: moisture content. 52
Table 2. ISRM-suggested dimensions for NSCB specimen.
Parameter
Suggested range or value
Radius of specimen (R)
Larger of 5 × grain size or 38 mm
Thickness of specimen (B)
Larger of 0.8R or 30 mm
Initial notch length ratio of specimen (a0/R)
0.4 ≤ a0/R ≤ 0.6
Loading distance ratio of specimen (S/2R)
0.5 ≤ S/2R ≤ 0.8
53
Table 3. Testing scheme of NSCB specimens. Testing scheme name
a0/R
w (%)
N-1
0.2, 0.3, 0.4, 0.5, 0.6, 0.7
16.6 14.6, 18.6, 20.6
N-2 N-3 N-4
A suggested value from N-1
ρ
B (mm)
Number of specimens
1.66
65
24
1.66
65
9
65
12
20, 35, 50
9
(g·cm3)
1.62, 1.64, 1.68, 1.70 1.66
16.6 16.6
Note. In N-1, four specimens were subjected to each test group; In N-2, N-3 and N-4, three parallel test groups were selected.
54
Table 4. Testing scheme of SCB specimens. Testing scheme name
w (%)
ρ (g·cm3)
B (mm)
Number of specimens
S-1
14.6, 16.6, 18.6, 20.6
1.66
65
12
S-2
16.6
1.62, 1.64, 1.68, 1.70
65
12
Note. In S-1 and S-2, three specimens were subjected to each test group.
55
Table 5. Testing results of SENB specimens.
No.
Peak load (N)
Values of KIC (kPa·m0.5)
1
10.3
19.6
2
12.1
23.0
3
9.5
18.0
4
11.1
21.1
Average value of KIC (kPa·m0.5)
20.4
56
Table 6. Relationships between KIC and σt of different compacted clays.
Researches
Specimen preparation method
a = KIC/σt
R2
Hanson et al. [7]
Air-dried compacted
0.0706
0.93
Wang et al. [11]
Directly compacted
0.3546
0.88
Amarasiri et al. [13]
Air-dried compacted
0.1700
0.99
Cao [18]
Directly compacted
0.3179
0.83
Agaiby [19]
Oven-dried compacted
0.1434
0.92
This study
Directly compacted
0.2800
0.94
57
Table 7. Estimation of the value of rc based on the relationship between KIC and σt of different compacted clays.
Researches
a = KIC/σt
rc (mm)
Hanson et al. [7]
0.0706
0.8
Wang et al. [11]
0.3546
20.0
Amarasiri et al. [13]
0.1700
4.6
Cao [18]
0.3179
16.1
Agaiby [19]
0.1434
3.3
This study
0.2800
12.5
58
Highlights (1) Notched semi-circular bending specimens were employed to determine the KIC of a compacted clay.
(2) The ratio of initial notch length to specimen radius a0/R = 0.3–0.5 was suggested.
(3) An empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays.
Conflict of Interest The authors declare that they have no conflict of interest.
59