diff --git a/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs.prj b/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs.prj
index 4b8c74da71d42ace153f44335390eddd2508f2a6..b39940e46066d4e324ba8e7001ae2f857117789a 100644
--- a/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs.prj
+++ b/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs.prj
@@ -356,7 +356,7 @@
         <vtkdiff>
             <regex>square_1e1_2_matIDs_t_.*.vtu</regex>
             <field>temperature</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
+            <absolute_tolerance>2e-13</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -369,7 +369,7 @@
         <vtkdiff>
             <regex>square_1e1_2_matIDs_t_.*.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>5e-13</absolute_tolerance>
+            <absolute_tolerance>3e-8</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -381,7 +381,7 @@
         <vtkdiff>
             <regex>square_1e1_2_matIDs_t_.*.vtu</regex>
             <field>NodalForces</field>
-            <absolute_tolerance>3e-12</absolute_tolerance>
+            <absolute_tolerance>2e-5</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <!--internal state variables-->
@@ -412,14 +412,14 @@
         <vtkdiff>
             <regex>square_1e1_2_matIDs_t_.*.vtu</regex>
             <field>PreConsolidationPressure</field>
-            <absolute_tolerance>1e-14</absolute_tolerance>
+            <absolute_tolerance>2e-8</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <!--integration point variables-->
         <vtkdiff>
             <regex>square_1e1_2_matIDs_t_.*.vtu</regex>
             <field>sigma_ip</field>
-            <absolute_tolerance>5e-13</absolute_tolerance>
+            <absolute_tolerance>5e-8</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -455,7 +455,7 @@
         <vtkdiff>
             <regex>square_1e1_2_matIDs_t_.*.vtu</regex>
             <field>material_state_variable_PreConsolidationPressure_ip</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
+            <absolute_tolerance>2e-8</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
     </test_definition>
diff --git a/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs_restart.xml b/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs_restart.xml
index 239d6fb592f05371098c697be83e022b29ad8f4e..e455d0f2778c82ce5d516c411556afd05f2fa02a 100644
--- a/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs_restart.xml
+++ b/Tests/Data/ThermoHydroMechanics/MultiMaterial/DP_MCC/TM/square_1e1_2_matIDs_restart.xml
@@ -38,7 +38,7 @@
             <vtkdiff>
                 <regex>square_1e1_2_matIDs_restart_t_.*.vtu</regex>
                 <field>temperature</field>
-                <absolute_tolerance>1e-15</absolute_tolerance>
+                <absolute_tolerance>2e-13</absolute_tolerance>
                 <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
             <vtkdiff>
@@ -51,7 +51,7 @@
             <vtkdiff>
                 <regex>square_1e1_2_matIDs_restart_t_.*.vtu</regex>
                 <field>sigma</field>
-                <absolute_tolerance>5e-13</absolute_tolerance>
+                <absolute_tolerance>2e-8</absolute_tolerance>
                 <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
             <vtkdiff>
@@ -63,7 +63,7 @@
             <vtkdiff>
                 <regex>square_1e1_2_matIDs_restart_t_.*.vtu</regex>
                 <field>NodalForces</field>
-                <absolute_tolerance>3e-12</absolute_tolerance>
+                <absolute_tolerance>2e-5</absolute_tolerance>
                 <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
             <!--internal state variables-->
@@ -94,14 +94,14 @@
             <vtkdiff>
                 <regex>square_1e1_2_matIDs_restart_t_.*.vtu</regex>
                 <field>PreConsolidationPressure</field>
-                <absolute_tolerance>1e-14</absolute_tolerance>
+                <absolute_tolerance>1e-8</absolute_tolerance>
                 <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
             <!--integration point variables-->
             <vtkdiff>
                 <regex>square_1e1_2_matIDs_restart_t_.*.vtu</regex>
                 <field>sigma_ip</field>
-                <absolute_tolerance>5e-13</absolute_tolerance>
+                <absolute_tolerance>3e-8</absolute_tolerance>
                 <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
             <vtkdiff>
@@ -137,7 +137,7 @@
             <vtkdiff>
                 <regex>square_1e1_2_matIDs_restart_t_.*.vtu</regex>
                 <field>material_state_variable_PreConsolidationPressure_ip</field>
-                <absolute_tolerance>1e-14</absolute_tolerance>
+                <absolute_tolerance>1e-8</absolute_tolerance>
                 <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
         </test_definition>
diff --git a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj
index 2dbb23feedd5322a710e895ae53e17abbe609e9f..a124c3079e70cbf024e41d8056fbaa8e37713575 100644
--- a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj
+++ b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part1.prj
@@ -161,14 +161,6 @@
     </time_loop>
     <parameters>
         <!--Modified Cam clay parameters-->
-        <parameter>
-            <name>sigma0</name>
-            <type>Function</type>
-            <expression>-5e3</expression>
-            <expression>-5e3</expression>
-            <expression>-5e3</expression>
-            <expression>0</expression>
-        </parameter>
         <parameter>
             <name>YoungModulus</name>
             <type>Constant</type>
@@ -205,6 +197,14 @@
             <value>1.76</value>
         </parameter>
         <!-- Initial and boundary values -->
+        <parameter>
+            <name>sigma0</name>
+            <type>Function</type>
+            <expression>-5e3</expression>
+            <expression>-5e3</expression>
+            <expression>-5e3</expression>
+            <expression>0</expression>
+        </parameter>
         <parameter>
             <name>displacement0</name>
             <type>Constant</type>
@@ -333,7 +333,7 @@
         <vtkdiff>
             <regex>mfront_restart_part1_t_.*.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>1e-12</absolute_tolerance>
+            <absolute_tolerance>3e-10</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -362,10 +362,10 @@
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
-                <regex>mfront_restart_part1_t_.*.vtu</regex>
-                <field>PreConsolidationPressure</field>
-                <absolute_tolerance>1e-14</absolute_tolerance>
-                <relative_tolerance>0</relative_tolerance>
+            <regex>mfront_restart_part1_t_.*.vtu</regex>
+            <field>PreConsolidationPressure</field>
+            <absolute_tolerance>6e-11</absolute_tolerance>
+            <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
         <!--integration point variables-->
         <vtkdiff>
diff --git a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml
index ca0f8697beb430e1bca0c1d43943a90902818248..7756d863ab5c4b4d417c451bb95575d4e3a7b558 100644
--- a/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml
+++ b/Tests/Data/ThermoHydroMechanics/RestartMCC/mfront_restart_part2.xml
@@ -67,7 +67,7 @@
         <vtkdiff>
             <regex>mfront_restart_part2_t_.*.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>1e-12</absolute_tolerance>
+            <absolute_tolerance>3e-10</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -96,10 +96,10 @@
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
-                <regex>mfront_restart_part2_t_.*.vtu</regex>
-                <field>PreConsolidationPressure</field>
-                <absolute_tolerance>1e-14</absolute_tolerance>
-                <relative_tolerance>0</relative_tolerance>
+            <regex>mfront_restart_part2_t_.*.vtu</regex>
+            <field>PreConsolidationPressure</field>
+            <absolute_tolerance>3e-10</absolute_tolerance>
+            <relative_tolerance>0</relative_tolerance>
             </vtkdiff>
         <!--integration point variables-->
         <vtkdiff>