Figure 1

Figure 2
![Stiffness parameters of standard drained triaxial test results: (1) for the MC model, (2) for the HS model, (3) for the HSS model [66]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLACURJPQ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T061906Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMX%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIC2MP3CUMB0E7pCy2drvQhvbO4S%2Fi0ISuvQRa7g6PL7oAiEA3zjebGZBwyFr7eeKbfzLpFASP81JpPUY%2FSvseKJaVZIqxgUIjv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJH%2BpGFDU7yH4gA7GCqaBWqcm0q6xQoCaAO3lmWLZx0yqvLuQlHtWpAPMYaDhez0XDRF58bxcGFE0tPZ6y5EjYput0QgO%2BJs9n0VQx907DMMZNrUJmWQ36%2BUhnlAUjz9xoAUgmu4jRk7Py7mGdMSHnFci9Da89pzdLEkDDrn1n5DvPBp7d1a3E2HPXDy5ocb7u41ajWq6jRFPpws0j5QfKPD%2Fg1qFflXroW7eq2itSygCNtJI0NkFeaBxIxBLoGze7YY9rfHVj2sVcNX573UVEbotFpr%2FuQSNCt%2BZjOi%2B6bteuSAuncmdKjUVNSukzgwAByrtXB9mDQ0ZPf5S26J18axe2kvgzHdDJKHRhqGCZFOCvB64do6MgszmRI1ym07WAveSwbR0R0YILRtJFuopWeKCHHgH7HhRlVOVmOO4XhRvxonSHWYAZXRtM2ARW%2FhZmfqigZrbr9%2FJ8BOVAKyt5KO03VH4yGKvCXBuRUhQ4xYL6N8L7KbpTd2%2BSsJvqOU6YNrIW59nJLUg2jz5Fzo9Fdk3V8XYdCMhX6iau%2BchDVijgpbPvkMtb6DtFL4hinHbtaV5Pyz0koK9TtxQWVJpyGv8mtG9%2BkE7i6TRwq1HtL9MqmsZn9eJ59rjZ9wnV%2FLQp9V93IdntSZR6qCSIRcfFOUwnHQPu8vRXjQDF0TmILhTHtRCXvJj6Nj5U2A3%2BeCD7lICWn1WHF%2BAwPxr7gebgaAxbyz3Uvpt8auDSOhb9lphd8Org1K3nuadhWJnRPm3%2Fa3cu3hPf2offNZMd1NGywZxgE6jaW%2B1nsqd0IwpzV6kiHictmCLprAJGTl2Zl1tzfR2yl62a8uU5uqM%2Fvxp%2Fi1MCq13Z32RIkI0r46KNnU8mvl0UGKB0oYVsIYWpXDHJu6OwzOilKpojCC19%2FMBjqxAaZVCxlixycq0GTqMOiifq0w7eA3iBU4MmlzowiM2ZCd6PGs97u62rjwTX6wdVjOpONgrfQt79tuTCEAhimUV5PP35pQAdwxumEQDVU5COT5UEeutqwwcchGQkllqdudmdTCDpMI5gJAu5V4za1eCS%2Fnb7QWk77pxs7aiJF3BkdadbJ20LqvdBdcH155JZ6O0IHlxh%2FJKhaqCla2HRdLxAqwHdZqKjJFtv634fIBmIXxtQ%3D%3D&X-Amz-Signature=f2f270d25651f833f56e4c44a798573184d6ebe06020460036e4c0ca35ef68fa&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3
![Characteristic stiffness-strain behavior in logarithmic scale (after Atkinson and Sallfors [36] and Mair[76]) (Atkinson, 2000)[77].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLACURJPQ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T061906Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMX%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIC2MP3CUMB0E7pCy2drvQhvbO4S%2Fi0ISuvQRa7g6PL7oAiEA3zjebGZBwyFr7eeKbfzLpFASP81JpPUY%2FSvseKJaVZIqxgUIjv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJH%2BpGFDU7yH4gA7GCqaBWqcm0q6xQoCaAO3lmWLZx0yqvLuQlHtWpAPMYaDhez0XDRF58bxcGFE0tPZ6y5EjYput0QgO%2BJs9n0VQx907DMMZNrUJmWQ36%2BUhnlAUjz9xoAUgmu4jRk7Py7mGdMSHnFci9Da89pzdLEkDDrn1n5DvPBp7d1a3E2HPXDy5ocb7u41ajWq6jRFPpws0j5QfKPD%2Fg1qFflXroW7eq2itSygCNtJI0NkFeaBxIxBLoGze7YY9rfHVj2sVcNX573UVEbotFpr%2FuQSNCt%2BZjOi%2B6bteuSAuncmdKjUVNSukzgwAByrtXB9mDQ0ZPf5S26J18axe2kvgzHdDJKHRhqGCZFOCvB64do6MgszmRI1ym07WAveSwbR0R0YILRtJFuopWeKCHHgH7HhRlVOVmOO4XhRvxonSHWYAZXRtM2ARW%2FhZmfqigZrbr9%2FJ8BOVAKyt5KO03VH4yGKvCXBuRUhQ4xYL6N8L7KbpTd2%2BSsJvqOU6YNrIW59nJLUg2jz5Fzo9Fdk3V8XYdCMhX6iau%2BchDVijgpbPvkMtb6DtFL4hinHbtaV5Pyz0koK9TtxQWVJpyGv8mtG9%2BkE7i6TRwq1HtL9MqmsZn9eJ59rjZ9wnV%2FLQp9V93IdntSZR6qCSIRcfFOUwnHQPu8vRXjQDF0TmILhTHtRCXvJj6Nj5U2A3%2BeCD7lICWn1WHF%2BAwPxr7gebgaAxbyz3Uvpt8auDSOhb9lphd8Org1K3nuadhWJnRPm3%2Fa3cu3hPf2offNZMd1NGywZxgE6jaW%2B1nsqd0IwpzV6kiHictmCLprAJGTl2Zl1tzfR2yl62a8uU5uqM%2Fvxp%2Fi1MCq13Z32RIkI0r46KNnU8mvl0UGKB0oYVsIYWpXDHJu6OwzOilKpojCC19%2FMBjqxAaZVCxlixycq0GTqMOiifq0w7eA3iBU4MmlzowiM2ZCd6PGs97u62rjwTX6wdVjOpONgrfQt79tuTCEAhimUV5PP35pQAdwxumEQDVU5COT5UEeutqwwcchGQkllqdudmdTCDpMI5gJAu5V4za1eCS%2Fnb7QWk77pxs7aiJF3BkdadbJ20LqvdBdcH155JZ6O0IHlxh%2FJKhaqCla2HRdLxAqwHdZqKjJFtv634fIBmIXxtQ%3D%3D&X-Amz-Signature=18c5bad0989d5cbce9f1130891d3cf5bff2937955b2b9c632efc31f41b78d2d2&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9
![Nodal displacement vectors for the wharf supported piles (m)[28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_009.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLACURJPQ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T061906Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMX%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIC2MP3CUMB0E7pCy2drvQhvbO4S%2Fi0ISuvQRa7g6PL7oAiEA3zjebGZBwyFr7eeKbfzLpFASP81JpPUY%2FSvseKJaVZIqxgUIjv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJH%2BpGFDU7yH4gA7GCqaBWqcm0q6xQoCaAO3lmWLZx0yqvLuQlHtWpAPMYaDhez0XDRF58bxcGFE0tPZ6y5EjYput0QgO%2BJs9n0VQx907DMMZNrUJmWQ36%2BUhnlAUjz9xoAUgmu4jRk7Py7mGdMSHnFci9Da89pzdLEkDDrn1n5DvPBp7d1a3E2HPXDy5ocb7u41ajWq6jRFPpws0j5QfKPD%2Fg1qFflXroW7eq2itSygCNtJI0NkFeaBxIxBLoGze7YY9rfHVj2sVcNX573UVEbotFpr%2FuQSNCt%2BZjOi%2B6bteuSAuncmdKjUVNSukzgwAByrtXB9mDQ0ZPf5S26J18axe2kvgzHdDJKHRhqGCZFOCvB64do6MgszmRI1ym07WAveSwbR0R0YILRtJFuopWeKCHHgH7HhRlVOVmOO4XhRvxonSHWYAZXRtM2ARW%2FhZmfqigZrbr9%2FJ8BOVAKyt5KO03VH4yGKvCXBuRUhQ4xYL6N8L7KbpTd2%2BSsJvqOU6YNrIW59nJLUg2jz5Fzo9Fdk3V8XYdCMhX6iau%2BchDVijgpbPvkMtb6DtFL4hinHbtaV5Pyz0koK9TtxQWVJpyGv8mtG9%2BkE7i6TRwq1HtL9MqmsZn9eJ59rjZ9wnV%2FLQp9V93IdntSZR6qCSIRcfFOUwnHQPu8vRXjQDF0TmILhTHtRCXvJj6Nj5U2A3%2BeCD7lICWn1WHF%2BAwPxr7gebgaAxbyz3Uvpt8auDSOhb9lphd8Org1K3nuadhWJnRPm3%2Fa3cu3hPf2offNZMd1NGywZxgE6jaW%2B1nsqd0IwpzV6kiHictmCLprAJGTl2Zl1tzfR2yl62a8uU5uqM%2Fvxp%2Fi1MCq13Z32RIkI0r46KNnU8mvl0UGKB0oYVsIYWpXDHJu6OwzOilKpojCC19%2FMBjqxAaZVCxlixycq0GTqMOiifq0w7eA3iBU4MmlzowiM2ZCd6PGs97u62rjwTX6wdVjOpONgrfQt79tuTCEAhimUV5PP35pQAdwxumEQDVU5COT5UEeutqwwcchGQkllqdudmdTCDpMI5gJAu5V4za1eCS%2Fnb7QWk77pxs7aiJF3BkdadbJ20LqvdBdcH155JZ6O0IHlxh%2FJKhaqCla2HRdLxAqwHdZqKjJFtv634fIBmIXxtQ%3D%3D&X-Amz-Signature=def5f054ad0a284958b8f83c0d4af6c0016f7898dab86fd0071bea0cdc72ae79&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 10

Figure 11
![Total pore pressure contours (Pa)[28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_011.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLACURJPQ%2F20260220%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260220T061906Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMX%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIC2MP3CUMB0E7pCy2drvQhvbO4S%2Fi0ISuvQRa7g6PL7oAiEA3zjebGZBwyFr7eeKbfzLpFASP81JpPUY%2FSvseKJaVZIqxgUIjv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJH%2BpGFDU7yH4gA7GCqaBWqcm0q6xQoCaAO3lmWLZx0yqvLuQlHtWpAPMYaDhez0XDRF58bxcGFE0tPZ6y5EjYput0QgO%2BJs9n0VQx907DMMZNrUJmWQ36%2BUhnlAUjz9xoAUgmu4jRk7Py7mGdMSHnFci9Da89pzdLEkDDrn1n5DvPBp7d1a3E2HPXDy5ocb7u41ajWq6jRFPpws0j5QfKPD%2Fg1qFflXroW7eq2itSygCNtJI0NkFeaBxIxBLoGze7YY9rfHVj2sVcNX573UVEbotFpr%2FuQSNCt%2BZjOi%2B6bteuSAuncmdKjUVNSukzgwAByrtXB9mDQ0ZPf5S26J18axe2kvgzHdDJKHRhqGCZFOCvB64do6MgszmRI1ym07WAveSwbR0R0YILRtJFuopWeKCHHgH7HhRlVOVmOO4XhRvxonSHWYAZXRtM2ARW%2FhZmfqigZrbr9%2FJ8BOVAKyt5KO03VH4yGKvCXBuRUhQ4xYL6N8L7KbpTd2%2BSsJvqOU6YNrIW59nJLUg2jz5Fzo9Fdk3V8XYdCMhX6iau%2BchDVijgpbPvkMtb6DtFL4hinHbtaV5Pyz0koK9TtxQWVJpyGv8mtG9%2BkE7i6TRwq1HtL9MqmsZn9eJ59rjZ9wnV%2FLQp9V93IdntSZR6qCSIRcfFOUwnHQPu8vRXjQDF0TmILhTHtRCXvJj6Nj5U2A3%2BeCD7lICWn1WHF%2BAwPxr7gebgaAxbyz3Uvpt8auDSOhb9lphd8Org1K3nuadhWJnRPm3%2Fa3cu3hPf2offNZMd1NGywZxgE6jaW%2B1nsqd0IwpzV6kiHictmCLprAJGTl2Zl1tzfR2yl62a8uU5uqM%2Fvxp%2Fi1MCq13Z32RIkI0r46KNnU8mvl0UGKB0oYVsIYWpXDHJu6OwzOilKpojCC19%2FMBjqxAaZVCxlixycq0GTqMOiifq0w7eA3iBU4MmlzowiM2ZCd6PGs97u62rjwTX6wdVjOpONgrfQt79tuTCEAhimUV5PP35pQAdwxumEQDVU5COT5UEeutqwwcchGQkllqdudmdTCDpMI5gJAu5V4za1eCS%2Fnb7QWk77pxs7aiJF3BkdadbJ20LqvdBdcH155JZ6O0IHlxh%2FJKhaqCla2HRdLxAqwHdZqKjJFtv634fIBmIXxtQ%3D%3D&X-Amz-Signature=66abf3ee4220f8d4a2939df1fc9ef75109fa944abde86e5018244861c2e97310&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 12

Soil parameters used for HS model
| Parameters | Unit | Dense sand | Loose sand | Rockfill |
|---|---|---|---|---|
| kN/m2 | 6.032 × 104 | 1.638 × 104 | 2.232 × 104 | |
| kN/m2 | 4.826 × 104 | 1.310 × 104 | 1.786 × 104 | |
| kN/m2 | 1.810 × 104 | 4.914 × 104 | 6.696 × 104 | |
| Pref | kN/m2 | 100 | 100 | 100 |
| M | - | 0.5 | 0.5 | 0.5 |
| - | 0.3982 | 0.4524 | 0.2929 | |
| Rf | - | 0.9 | 0.9 | 0.9 |
Additional input parameters of HSS model_
| Parameters | Unit | Dense sand | Loose sand | Rockӿll |
|---|---|---|---|---|
| γ0.7 | - | 4.918 × 10–4 | 3.629 × 10–4 | 4.246 × 10–4 |
| kN/m2 | 1.051 × 105 | 9.108 × 104 | 1.038 × 105 |
Lateral and vertical displacement time histories at the top and at the toe of the rock dike_
| Model | Lateral and vertical displacements at the rock dike top | Lateral and vertical displacements at the rock dike toe |
|---|---|---|
| MC | ||
| HS | ||
| HSS |
Soil parameters used for the MC model_
| Parameters | Unit | Dense sand | Loose sand | Rockfill |
|---|---|---|---|---|
| φ | ° | 37 | 33.2 | 45 |
| ψ | ° | 21 | 7 | 0 |
| C | kN/m2 | 0.5 | 0.5 | 15 |
| ν | - | 0.3 | 0.3 | 0.2 |
| E | kN/m2 | 6.032 × 104 | 1.638 × 104 | 2.232 × 104 |
Pile and deck properties_
| Parameters | Unit | Pile | Deck |
|---|---|---|---|
| EA | kN/m | 162.75 × 104 | 17.85 × 106 |
| EI | kN.m2/m | 70.49 × 103 | 96.724 × 103 |
| w | kN/m/m | 0.633 | 6.9436 |
| ν | - | 0.2 | 0.2 |