**6.1 Uncemented sand**

*Sandy Materials in Civil Engineering - Usage and Management*

*Shear wave velocity changes during curing of bio-cemented specimens.*

the setting of gypsum involves a hydration reaction that can be affected by changes in temperature and humidity. The samples were effectively sealed with limited supply of oxygen during the curing reaction, and with low gypsum contents, temperature rises associated with the exothermic reaction would be limited, hence limiting the reaction rate. After the hardening phase, the samples were left unattended overnight, and during this time no significant change in shear wave velocity was captured. The variations of shear wave velocity during the calcite precipitation and hardening of the bio-cemented samples are shown in **Figure 6**. Small step changes in the shear wave velocity shown in **Figure 6** are a consequence of manual intervention in the semiautomated interpretation procedure and do not reflect the material response. For the range of final calcite values shown, the reaction time is very similar. In all cases there is a lag of about 1 hour before the cementation process begins, and the process is complete in about 12 hours after which the shear wave velocity remains constant. Samples were left for 24 hours before commencing the triaxial tests, and during this time the stiffness remained essentially constant. **Figure 6** also shows that the initial 100 m/s value increases over time, which is proportional to the

stiffness and tends to increase with the calcite content as expected.

The comparative study on shear wave signal responses during curing for selected gypsum-cemented and bio-cemented sand samples is projected in **Figure 7**. The trend in the responses are similar for 5% gypsum and 1.88% calcite, whereas UCS tests have shown that the strength associated with 1.88% calcite is equivalent to about 10% gypsum. However, the rates of the cementation reactions depend on the chemistry of the hydration and MICP processes and are not expected to influence strength and stiffness. Nevertheless, it may be noted that the ratio between strength and stiffness varies with the cement type. The calcite-cemented samples have lower stiffness (shear wave velocity) than gypsum samples with the same strength. A likewise pattern was seen in the UCS tests and was inferred to be a simple consequence

No triaxial tests were performed with calcite contents lower than 1.88%, and thus it is unclear whether with lower calcite contents the reaction time will increase, which occurred for low gypsum contents. In other tests [19, 29], when the cementation occurred underwater, the time required for curing was greater than 24 hours, and it is expected that the curing time will depend on the chemical and

**116**

**Figure 6.**

of the low amount of calcite cement.

To enable the influence of the cement to be appreciated, triaxial tests have been performed on loose Sydney sand. Samples with various relative densities have been subjected to standard drained (CID) and undrained (CIU) tests with different confining pressures. Test results as in **Figure 8** are presented in terms of stress ratio (q/p′) against the axial strain. The results indicate that in all tests the stress ratio rises to a peak before gradually reducing toward a critical state value at large strain. Where the stress ratio dropped rapidly post peak, the samples had formed pronounced shear planes. The dotted line in **Figure 8** shows the estimated critical state stress ratio, M = 1.35, which corresponds to a friction angle of 32°.

**Figure 8.** *Response of uncemented Sydney sand.*

**Figure 9.** *Volumetric strains for CID tests on uncemented sand.*

The volumetric responses from the drained tests reported in **Figure 8** are displayed in **Figure 9**. In all cases the samples expanded on shearing, which is consistent with their mobilizing peak stress ratios greater than the critical state value [30].

The bender element technique was used to obtain the shear wave velocity (Vs) for the uncemented sand. This has also allowed comparison with data on uncemented sand obtained from other studies and hence to demonstrate the reliability of the estimated soil stiffnesses. Knowing the shear wave velocity and bulk density (ρ) of the sand, the small strain shear modulus (Gmax) can be determined from Eq. (1):

$$\mathbf{G\_{max}} = \mathbf{p} \,\,\mathsf{V\_s}^2 \tag{1}$$

The parameter functions of Gmax and the mean effective stress (p′) for two typical uncemented sand samples, P1 and P2, are shown in **Figure 10(a)**. During isotropic compression an identical response is obtained, which may be described by Eq. (2):

$$\mathbf{G}\_{\text{max}} = \mathbf{11.27} \,\mathrm{p}^{\prime 0.475} \tag{2}$$

where G is in MPa and p′ is in kPa.

Data on which Eq. (2) is based covers a range of p′ from 10 to 3000 kPa, which is greater than incorporated in most published relations. For comparison, the data obtained in this study are plotted in **Figure 10(b)** with another published empirical relation for Gmax which is given by Eq. (3). This incorporates a function of void ratio f (e) = (2.17-e)2 /(1 + e) and constants A and n which are coefficients that depend on the type of material (**Table 3**).

$$\mathbf{G}\_{\text{max}} = \mathbf{A}f(\mathbf{e}) \text{ p}^{\prime \text{n}} \tag{3}$$

**119**

**Figure 10.**

**Table 3.**

*Constants proposed for empirical equation Gmax.*

*published data.*

*Geomechanical Behavior of Bio-Cemented Sand for Foundation Works*

drained test results. Comparison with **Figure 8** for the uncemented sand shows the cemented samples developed high peak stress ratios and these are mobilized at lower axial strains than for the uncemented sand. For the drained tests, samples with confining stress of 50 kPa, the peak stress ratio and deviator stress increase with cement content as expected. For the undrained tests, a similar trend with cement content is apparent; however, for the more cemented samples, the stress ratio reaches the limiting value in the triaxial apparatus, which is 3. Once this occurs further loading is equivalent to performing a UCS test and the failure strengths of these samples are between 650 and 1300 kPa, in the range of the UCS strengths of the gypsum-cemented samples shown in **Figure 4**. After the peak the stress ratio reduces

*Variation of Gmax with p' for uncemented sand (a) dry and saturated Sydney sand (b) validation with* 

*A n* **Reference** 0.5 Shibuya and Tanaka [31] 0.5 Kokusho [32] 0.5 Hardin and Richart [33]

*DOI: http://dx.doi.org/10.5772/intechopen.88159*

The predicted Gmax values from [31, 32] are similar to the Sydney sand data, and the linear relationship between Gmax and p′ in this study is closest to the equation proposed for Toyoura sand [32] which is to be expected given the similarity of mineralogy, particle size, and shape of the two granular materials.

#### **6.2 Gypsum-cemented sand results**

Results from triaxial tests on gypsum-cemented samples are presented in **Figures 11**–**13**. **Figure 11** shows the stress ratio and axial strain responses of cemented samples with gypsum contents between 5% and 20% and includes undrained and

**Figure 10.**

*Sandy Materials in Civil Engineering - Usage and Management*

The volumetric responses from the drained tests reported in **Figure 8** are displayed in **Figure 9**. In all cases the samples expanded on shearing, which is consistent with their mobilizing peak stress ratios greater than the critical state value [30]. The bender element technique was used to obtain the shear wave velocity (Vs) for the uncemented sand. This has also allowed comparison with data on uncemented sand obtained from other studies and hence to demonstrate the reliability of the estimated soil stiffnesses. Knowing the shear wave velocity and bulk density (ρ) of the sand, the small strain shear modulus (Gmax) can be determined from Eq. (1):

Gmax = ρ

Gmax = 11.27 p′

Data on which Eq. (2) is based covers a range of p′ from 10 to 3000 kPa, which is greater than incorporated in most published relations. For comparison, the data obtained in this study are plotted in **Figure 10(b)** with another published empirical relation for Gmax which is given by Eq. (3). This incorporates a function of void ratio

Gmax = A *f*(e) p′

Results from triaxial tests on gypsum-cemented samples are presented in **Figures 11**–**13**. **Figure 11** shows the stress ratio and axial strain responses of cemented samples with gypsum contents between 5% and 20% and includes undrained and

mineralogy, particle size, and shape of the two granular materials.

The predicted Gmax values from [31, 32] are similar to the Sydney sand data, and the linear relationship between Gmax and p′ in this study is closest to the equation proposed for Toyoura sand [32] which is to be expected given the similarity of

/(1 + e) and constants A and n which are coefficients that depend on

where G is in MPa and p′ is in kPa.

*Volumetric strains for CID tests on uncemented sand.*

The parameter functions of Gmax and the mean effective stress (p′) for two typical uncemented sand samples, P1 and P2, are shown in **Figure 10(a)**. During isotropic compression an identical response is obtained, which may be described by Eq. (2):

<sup>2</sup> (1)

0.475 (2)

<sup>n</sup> (3)

**118**

f (e) = (2.17-e)2

**Figure 9.**

the type of material (**Table 3**).

**6.2 Gypsum-cemented sand results**

*Variation of Gmax with p' for uncemented sand (a) dry and saturated Sydney sand (b) validation with published data.*


**Table 3.**

*Constants proposed for empirical equation Gmax.*

drained test results. Comparison with **Figure 8** for the uncemented sand shows the cemented samples developed high peak stress ratios and these are mobilized at lower axial strains than for the uncemented sand. For the drained tests, samples with confining stress of 50 kPa, the peak stress ratio and deviator stress increase with cement content as expected. For the undrained tests, a similar trend with cement content is apparent; however, for the more cemented samples, the stress ratio reaches the limiting value in the triaxial apparatus, which is 3. Once this occurs further loading is equivalent to performing a UCS test and the failure strengths of these samples are between 650 and 1300 kPa, in the range of the UCS strengths of the gypsum-cemented samples shown in **Figure 4**. After the peak the stress ratio reduces

**Figure 11.**

*Stress ratio, axial strain responses for all gypsum-cemented specimens.*

**Figure 12.** *Deviator stress, axial strain responses from drained tests (p*′*c = 50 kPa).*

approaching a constant value at large strain, however unlike the uncemented samples, the stress ratio does not appear to approach a unique value. It is believed that this is a consequence of nonhomogeneous deformation and if the samples could be sheared uniformly, they would approach the value of the ultimate critical state, M = 1.35 similar to the uncemented sand. Other studies (e.g., see [14, 34]) in which gypsumcemented sands were tested showed that the presence of gypsum, up to 20%, did not influence the ultimate frictional resistance.

**Figures 12** and **13** show the reactions of gypsum-cemented samples in drained triaxial tests. The gypsum cement leads to significant increases in strength compared with the uncemented sand, and even small amounts of gypsum increase the strength considerably. Further, the comparison with the UCS test responses shown in **Figure 1** indicates that there is a remarkable contribution with even a slight amount of gypsum, which is much greater in the triaxial tests. This is believed to be due to the applied confining stress which prevents the tensile failure mode that occurs in UCS tests. Samples cemented with gypsum reached their maximum strength at axial

**121**

mented response.

*Geomechanical Behavior of Bio-Cemented Sand for Foundation Works*

*Volume strain, axial strain responses from drained tests (p′c = 50 kPa).*

strains <1.5%, while for the uncemented sand, the maximum strength occurred at axial strains of between 2 and 5%. **Figure 13** shows the cementation initially prevents the expansion that occurs almost from the beginning of shear for the uncemented samples. The uncemented samples expand steadily during shear eventually reaching a maximum volume strain of about −0.04 for axial deformations greater than 10%. Even though their densities are similar, the gypsum cemented shows different behavior. The specimens initially compress due to increasing mean stress, but as they approach the peak, they begin to expand at a rapid rate, much more rapidly than the uncemented sand. The rate of expansion then drops as pronounced shear bands develop. In general, these results are typical of the behavior of artificially cemented

**Figure 14** shows the response and changes of Gmax with p′ for typical gypsum-

cemented samples and comparison with the response for uncemented sand. The responses include an initial isotropic compression stage to 50 kPa followed by drained shearing to large deformations. The figure shows the cement has a remarkable contribution on the small strain stiffness, with Gmax nearly constant until reaching the peak strength. However, looking in detail, it is found that Gmax increases slightly with p′ and then decreases as the cementation begins to break. After the peak, the shear modulus falls significantly and approaches the unce-

specimens prepared with a range of cement types [18–37].

*Variation of Gmax during compression and shear for gypsum-cemented specimens.*

*DOI: http://dx.doi.org/10.5772/intechopen.88159*

**Figure 13.**

**Figure 14.**

#### *Geomechanical Behavior of Bio-Cemented Sand for Foundation Works DOI: http://dx.doi.org/10.5772/intechopen.88159*

**Figure 13.**

*Sandy Materials in Civil Engineering - Usage and Management*

approaching a constant value at large strain, however unlike the uncemented samples, the stress ratio does not appear to approach a unique value. It is believed that this is a consequence of nonhomogeneous deformation and if the samples could be sheared uniformly, they would approach the value of the ultimate critical state, M = 1.35 similar to the uncemented sand. Other studies (e.g., see [14, 34]) in which gypsumcemented sands were tested showed that the presence of gypsum, up to 20%, did not

**Figures 12** and **13** show the reactions of gypsum-cemented samples in drained triaxial tests. The gypsum cement leads to significant increases in strength compared with the uncemented sand, and even small amounts of gypsum increase the strength

considerably. Further, the comparison with the UCS test responses shown in **Figure 1** indicates that there is a remarkable contribution with even a slight amount of gypsum, which is much greater in the triaxial tests. This is believed to be due to the applied confining stress which prevents the tensile failure mode that occurs in UCS tests. Samples cemented with gypsum reached their maximum strength at axial

influence the ultimate frictional resistance.

*Deviator stress, axial strain responses from drained tests (p*′*c = 50 kPa).*

*Stress ratio, axial strain responses for all gypsum-cemented specimens.*

**120**

**Figure 12.**

**Figure 11.**

*Volume strain, axial strain responses from drained tests (p′c = 50 kPa).*

**Figure 14.** *Variation of Gmax during compression and shear for gypsum-cemented specimens.*

strains <1.5%, while for the uncemented sand, the maximum strength occurred at axial strains of between 2 and 5%. **Figure 13** shows the cementation initially prevents the expansion that occurs almost from the beginning of shear for the uncemented samples. The uncemented samples expand steadily during shear eventually reaching a maximum volume strain of about −0.04 for axial deformations greater than 10%. Even though their densities are similar, the gypsum cemented shows different behavior. The specimens initially compress due to increasing mean stress, but as they approach the peak, they begin to expand at a rapid rate, much more rapidly than the uncemented sand. The rate of expansion then drops as pronounced shear bands develop. In general, these results are typical of the behavior of artificially cemented specimens prepared with a range of cement types [18–37].

**Figure 14** shows the response and changes of Gmax with p′ for typical gypsumcemented samples and comparison with the response for uncemented sand. The responses include an initial isotropic compression stage to 50 kPa followed by drained shearing to large deformations. The figure shows the cement has a remarkable contribution on the small strain stiffness, with Gmax nearly constant until reaching the peak strength. However, looking in detail, it is found that Gmax increases slightly with p′ and then decreases as the cementation begins to break. After the peak, the shear modulus falls significantly and approaches the uncemented response.
